CN116913439A - UDPD finite element coupling method and system for quasi-brittle material damage - Google Patents

UDPD finite element coupling method and system for quasi-brittle material damage Download PDF

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CN116913439A
CN116913439A CN202311161752.1A CN202311161752A CN116913439A CN 116913439 A CN116913439 A CN 116913439A CN 202311161752 A CN202311161752 A CN 202311161752A CN 116913439 A CN116913439 A CN 116913439A
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吕海宁
李双
张贝
孙鹏飞
秦睿
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Sanya Yazhouwan Deep Sea Science And Technology Research Institute Shanghai Jiaotong University
Shanghai Jiaotong University
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Abstract

The invention belongs to the technical field of quasi-brittle material failure prediction and mechanical numerical simulation, and discloses a UDPD finite element coupling method, a system and equipment for quasi-brittle material damage, wherein a novel fourth-order polynomial attenuation function is introduced into the coupling method; introducing a damage model of a key, dividing the UDPD key force in the coupling model into linear deformation and nonlinear deformation, and describing the mechanical behavior of the quasi-brittle material; the damage model of the bond is in a form of a unitary quadratic equation, and the breakage of the bond occurs cumulatively by damage; the fracture criteria of the coupling model is a function of the tensile and compressive strengths of the quasi-brittle material; using the shared node method, the coupling of UDPD and FEM for the destruction of quasi-brittle material will be described. The coupling model does not need an additional fracture criterion, and can simulate and predict the automatic crack germination and expansion of the quasi-brittle material; the coupling of UDPD and FEM overcomes the limit of fixed Poisson's ratio of traditional bond-based PD, and expands the application range of the Poisson's ratio of the material.

Description

UDPD finite element coupling method and system for quasi-brittle material damage
Technical Field
The invention belongs to the technical field of quasi-brittle material failure prediction and mechanical numerical simulation, and particularly relates to a UDPD finite element coupling method and system for quasi-brittle material damage.
Background
Currently, the destruction of quasi-brittle materials such as rock, marine concrete, metal gray cast iron, ceramics and the like is always a focus and difficulty of attention in the mechanical field and the marine engineering field. There are some patents: 1. conventional continuous media mechanics methods such as FEM and extended FEM are employed to simulate predicted damage to a quasi-brittle material. 2. Simulation of a quasi-brittle material is performed using a discontinuous media mechanical method such as a discrete element method. 3. Some patents use conventional bond-based PD to simulate the failure of a quasi-brittle material. 4. Some patents directly reduce the characteristics of a quasi-brittle material to a brittle material to perform simulation calculations.
Problems or deficiencies of the prior art 1. Methods based on traditional continuous media mechanics such as FEM and extended FEM can produce singularities and grid dependencies when dealing with failure problems, and crack initiation and propagation both require the introduction of additional fracture criteria. 2. Based on a discontinuous medium mechanical method, such as a discrete element method, a quasi-brittle material is cut into discrete blocks to serve as a research object, a crack can only be expanded along a contact surface between unit blocks, and the method is equivalent to artificially determining an expansion path of the crack and has path dependence. 3. When the traditional bond-based PD method is used for simulating the damage of the quasi-brittle material, the calculation cost is higher due to the non-local effect of PD, the existence of the boundary effect of the bond-based PD has a larger influence on the calculation precision, and the bond-based PD has a fixed Poisson ratio effect (the Poisson ratio of a plane stress material is fixed at 1/3, and the plane strain and the three-dimensional Poisson ratio are fixed at 1/4). 4. The method is characterized in that the quasi-brittle material is simplified into a brittle material, the stress process of the obtained quasi-brittle material is completely linear elastic, the post-peak strain softening stage of the quasi-brittle material in the loading process is omitted, and the real deformation and the destruction behavior of the quasi-brittle material are not met. 5. The existing coupling model ignores the long-range force attenuation effect of single-bond dual-parameter near-field dynamics (UDPD) subdomain.
Through the above analysis, the problems and defects existing in the prior art are as follows: the prior art ignores the post-peak strain softening stage of the quasi-brittle material in the loading process, and does not accord with the actual deformation and the destructive behavior of the quasi-brittle material; the existing coupling model ignores the long-range force attenuation effects of the UDPD sub-domain.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a UDPD finite element coupling method and system for the damage of a quasi-brittle material.
The invention is realized by a UDPD finite element coupling method for the damage of a quasi-brittle material, wherein a new fourth-order polynomial attenuation function is introduced into the coupling method; introducing a damage model of a key, dividing the UDPD key force in the coupling model into linear deformation and nonlinear deformation, and describing the mechanical behavior of the quasi-brittle material; the damage model of the bond is in a form of a unitary quadratic equation, and the breakage of the bond occurs cumulatively by damage; the fracture criteria of the coupling model is a function of the tensile and compressive strengths of the quasi-brittle material; using the shared node method, the coupling of UDPD and FEM for the destruction of quasi-brittle material will be described.
Further, the UDPD finite element coupling method for the damage of the quasi-brittle material comprises the following steps:
Firstly, constructing a numerical model according to the existing quasi-brittleness information;
the second step, the object is scattered completely, the whole area is divided into two parts, the periphery of the object is divided into FEM nodes, the interior of the object is divided into UDPD nodes, and the width of the FEM nodes is equal to the neighborhood radius of the mass points of the UDPD object; the junction of FEM and UDPD material points is a shared node;
thirdly, introducing an attenuation function of a fourth-order polynomial into the UDPD motion equation, and establishing the UDPD motion equation considering the PD long-range force attenuation effect;
fourth, based on a motion equation, introducing a damage model of a unitary quadratic function into the connecting key to describe the damage accumulation state of the connecting key under the action of external force;
fifthly, dividing the PD key force into linear deformation and nonlinear deformation stages based on the introduction of the damage model;
sixthly, establishing a UDPD motion equation considering long-range force attenuation and connection bond damage, and simultaneously taking PD fracture criteria into the motion equation;
seventh, realizing UDPD-FEM modeling of the quasi-brittle material and construction of a UDPD motion equation of the quasi-brittle material;
eighth step, boundary conditions and displacement constraints are applied to the outermost periphery FEM area of the test piece, and external force born by the UDPD area comes from the transmission of the node force of the FEM area;
And ninth, adopting a self-adaptive dynamic relaxation algorithm to iteratively solve the UDPD-FEM model of the quasi-brittle material to obtain the acceleration, the speed and the displacement of each object point, and realizing the damage prediction of the UDPD-FEM coupling model of the quasi-brittle material.
Further, the nondestructive error analysis of the UDPD finite element coupling method for the damage of the quasi-brittle material comprises the following steps:
and step one, constructing a UDPD-FEM coupling numerical model of the quasi-brittle material under the condition of two-dimensional plane stress. Rectangular thin plate test pieces with the length of 1m, the width of 0.5m and the thickness of 0.01m are respectively provided with the material parameters of 200GPa of Young modulus, 7850kg/m of mass density and 0.2 of Poisson's ratio;
step two, dispersing the square thin plate into uniformly distributed PD object particles and FEM nodes, wherein the FEM area is distributed around the test piece, and wrapping the UDPD area inside, and the thickness of the FEM area is the same as the neighbor radius of the UDPD; selecting a substance point spacing with the UDPD neighborhood radius of 3 times, wherein the substance point spacing is 0.01m, namely delta is 0.03mm, and dividing a test piece into 10000 substance points altogether, so as to construct a neighborhood matrix of all the substance points;
applying uniform uniaxial tensile load of 200MPa along the x axis of the test piece on the numerical model by adopting a stress boundary condition;
Step four, adopting a self-adaptive dynamic relaxation algorithm to carry out static force solution, inputting a virtual mass density matrix and a virtual damping coefficient, and carrying out iterative solution on the acceleration, the speed and the displacement of a material point at each time step;
step five, the displacement increment of all the object points at any time step is less than 10 -10m For convergence conditions, the coupling model is used for calculating all object point displacements of the object in the elastic deformation stage, and meanwhile, the traditional key-based PD model is used for calculating all object point displacements. The relative errors of the calculation results and the analytic solutions of the two models along the x direction are shown in the figure.
Further, the damage simulation prediction of the UDPD finite element coupling method for the damage of the quasi-brittle material comprises the following steps:
step one, a quasi-brittle concrete material UDPD-FEM coupling numerical model under a two-dimensional plane stress condition is constructed, and the length and the width of the model are respectively as follows: 0.1m and 0.03m, cracks with bilateral prefabrication length of 0.005m and width of 0.002m respectively, double crack spacing of 0.005m and 0.01m respectively, material parameters of 24GPa and mass density of 2400kg/m respectively 3 Poisson's ratio 0.2, uniaxial tensile strength 2.86MPa;
step two, the square thin plate is discretized into uniformly distributed UDPD material particles and FEM nodes, wherein the FEM area is distributed around a test piece, the UDPD area is wrapped inside, the thickness of the FEM area is the same as the radius of a UDPD neighborhood, the material point spacing with 3 times of the radius of the UDPD neighborhood is selected, the material point spacing is 0.5mm, namely delta is 1.5mm, the test piece is divided into 28800 material particles altogether, and a neighborhood matrix of all the material particles is constructed;
Step three, uniformly applying a tensile displacement control load to two ends of the test piece, wherein each load is controlled by each tensile displacementThe increment of the load of the step is 10 -8m Solving by adopting a dynamic relaxation method, wherein the time step is 1;
step four, adopting a self-adaptive dynamic relaxation algorithm to carry out static force solution, inputting a virtual mass density matrix and a virtual damping coefficient, and carrying out iterative solution on the acceleration, the speed and the displacement of a material point at each time step;
fifthly, judging damage accumulation and breaking condition of each material point bond according to the deformation length of the bond, when the material point elongation s exceeds the elastic elongation s et The bond enters a nonlinear strengthening stage when the elongation s of the object point exceeds the critical elongation s nt The bond enters the damage accumulation stage when the elongation s of the object point exceeds the elongation s at break t The corresponding bond is broken.
Further, the motion equation of single bond double parameter near field dynamics of the UDPD finite element coupling method for the damage of the quasi-brittle material:
wherein, u represents the acceleration,and->Representative particle->And->Is (are) displacement (are)>Is the relative position vector of two mass points, +.>Is the relative displacement vector of two mass points, +.>Representing mass density->Physical strength of->Representing the point-to-point force of the object point. Single bond double parameter near field dynamics available coefficient of force for point >Tangential coefficient->Elongation of sum bondThe representation is:
；
wherein the method comprises the steps ofAnd->The relative displacement vector of the key is the component along the key initial direction and perpendicular to that direction, respectively; />And->Indicating the elongation of the bond in the normal and tangential directions, respectively; wherein the normal and tangential stiffness coefficient expressions of UDPD are:
a fourth order polynomial function is introduced:
the constitutive force function of single bond dual parameter near field dynamics is expressed as:
wherein the method comprises the steps ofIs a micro-modulus function taking into account the attenuation effect, +.>Is the neighborhood radius of the object point;
normal coefficient of attenuation effectTangential coefficient->The micro modulus function is expressed as:
after the damage model K was introduced, the point-to-point force function of UDPD was expressed as:
here, theAnd->Respectively representing the elastic elongation of the key in stretching and compression, respectively corresponding to the elastic deformation of the material;and->The critical elongations of the keys during stretching and compression are respectively represented, and the maximum key forces are respectively corresponding to the critical elongations; />And->Respectively represents elongation at break under the action of stretching and compression, and the corresponding bond fails; deformation of the key under tensile load (+)>) The breaking of the bond comprises a phase of elastic deformation of the wire (+)>) Nonlinear reinforcement phase (+)>) And softening stage (+)>）。
Further, the damage function of the UDPD finite element coupling method for the damage of the quasi-brittle material is expressed as:
The single bond two parameter near field dynamics point force function is expressed as:
the whole solving area is uniformly scattered by adopting an improved near field dynamics and finite element sharing node type coupling method and is divided into a UDPD area and a FEM area, and the distance between UDPD substance points is kept consistent with the distance between FEM nodes; a layer of FEM nodes with the thickness equal to the UDPD neighborhood radius is arranged at the boundary of the coupling model so as to ensure that all UDPD material points have complete neighborhood;
the critical elongation of the bond of the quasi-brittle material under the action of pulling and pressing is expressed as follows:
wherein the method comprises the steps ofAnd->Represents uniaxial tensile strength and uniaxial compressive strength of the quasi-brittle material;
elastic elongation of quasi-brittle material under action of tension and compression，/>) And elongation at break (+)>，/>) Expression:
wherein the method comprises the steps ofAnd->Represents UDPD microcosmic parameters in the coupling model, +.>Derived from the geometrical relationship of bond stretch and bond force, < >>Critical fracture energy for matched brittle material, < >>And (5) taking a value according to the absorption capacity of the uniaxial compressive energy.
It is a further object of the present invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the UDPD finite element coupling method for the destruction of a quasi-brittle material.
It is another object of the present invention to provide a computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the UDPD finite element coupling method for the damage of a quasi-brittle material.
Another object of the present invention is to provide an information data processing terminal for implementing the UDPD finite element coupling method for quasi-brittle material destruction.
Another object of the present invention is to provide a UDPD finite element coupling system for quasi-brittle material fracture, which implements the UDPD finite element coupling method for quasi-brittle material fracture, the UDPD finite element coupling system for quasi-brittle material fracture comprising:
the model construction module is used for constructing a numerical model according to the existing quasi-brittleness information;
the regional division module is used for dispersing all objects, dividing the whole region into two parts, dividing the periphery of the object into FEM nodes, dividing the inside of the object into UDPD nodes, and enabling the width of the FEM nodes to be equal to the neighborhood radius of the mass points of the UDPD objects; the junction of FEM and UDPD material points is a shared node;
the equation building module is used for introducing a fourth-order polynomial attenuation function into the UDPD motion equation to build the UDPD motion equation considering the PD long-range force attenuation effect;
The model introduction module is used for introducing a damage model of a unitary quadratic function into the connecting key based on a motion equation to describe the damage accumulation state of the connecting key under the action of external force;
the key force dividing module is used for dividing the key force of the PD into linear deformation and nonlinear deformation stages based on the introduction of the damage model;
the equation updating module is used for simultaneously taking PD fracture criteria into a motion equation based on the established UDPD motion equation considering long-range force attenuation and connection bond damage;
the new process construction module is used for realizing UDPD-FEM modeling of the quasi-brittle material and construction of a UDPD motion equation of the quasi-brittle material;
the condition applying module is used for applying boundary conditions and displacement constraints on the outermost periphery FEM area of the test piece, and the external force born by the UDPD area is transmitted from the node force of the FEM area;
and the damage prediction module is used for iteratively solving the UDPD-FEM model of the quasi-brittle material by adopting a self-adaptive dynamic relaxation algorithm to obtain the acceleration, the speed and the displacement of each object point and realize the damage prediction of the UDPD-FEM coupling model of the quasi-brittle material.
In combination with the technical scheme and the technical problems to be solved, the technical scheme to be protected has the following advantages and positive effects:
First, the technical problem that exists and the difficulty of solving this problem to above-mentioned prior art, some technical effects that bring after solving the problem possess creativity. The specific description is as follows:
the invention adopts a key-based near-field dynamics and a finite element coupling method (UDPD-FEM) to simulate and predict the damage process of a quasi-brittle material, improves the calculation efficiency of the UDPD method, eliminates the boundary effect problem of the UDPD, overcomes the problem of fixed Poisson's ratio of the key-based PD (Poisson's ratio range (0, 1/3)), considers the size effect of long-range force, avoids the problem of singularity generated when the finite element method processes the discontinuity, divides the stress process of the quasi-brittle material into linear and nonlinear stages and considers the strain softening behavior of the stress stage of the quasi-brittle material, introduces a new fourth polynomial attenuation function into the coupling method, considers the attenuation of the UDPD long-range force, divides the UDPD bond force in the coupling model into linear deformation and nonlinear deformation to describe the mechanical behavior of the quasi-brittle material, considers the problem of singularity caused by the damage accumulation of the key, adopts a crack path dependence problem of human intervention, divides the stress process of the quasi-brittle material into linear and nonlinear stage, and considers the strain softening behavior of the stress stage of the quasi-brittle material, and adopts a friction coefficient of the UDPD to extend the coupling equation of the UDPD to the coupling method to describe the mechanical behavior of the quasi-brittle material, and the expansion of the stress stage of the quasi-brittle material, thereby solving the problem of the stress problem.
Second, the method for predicting the damage BPS-FEM of the quasi-brittle material is as follows: the coupling of FEM improves the calculation efficiency of the method of singly adopting the internal UDPD; the FEM nodes are arranged around the test piece to serve as virtual UDPD points, so that the problem of boundary effect of UDPD is solved; the introduction of the fourth-order polynomial attenuation function describes the long-range force size effect and reduces the wave dispersion problem of the UDPD; the damage model expressed by the unitary quadratic function is introduced, so that the solution is easier, and the breakage of the bond is understood as the result of damage accumulation; the introduction of the damage model divides the constitutive force function of the key into a linear stage and a nonlinear stage, so that the stress behavior of the quasi-brittle material is accurately described; the coupling model does not need an additional fracture criterion, and can simulate and predict the automatic crack germination and expansion of the quasi-brittle material; the coupling of UDPD and FEM overcomes the limit of fixed Poisson's ratio of traditional bond-based PD, and expands the application range of the Poisson's ratio of the material.
Drawings
FIG. 1 is a flow chart of a UDPD finite element coupling method for the destruction of a quasi-brittle material provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a UDPD-FEM coupling model of a one-dimensional rod provided by an embodiment of the invention;
FIG. 3 is a graph showing the relationship between the damage function K and the bond elongation according to the embodiment of the present invention;
FIG. 4 is a schematic diagram of relative error contrast (Poisson's ratio 0.2) between mass point displacement and analytical solution for a coupled model and a conventional PD model according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of the damage prediction and test result comparison (Poisson's ratio 0.2) of a quasi-brittle rectangular concrete test piece provided by an embodiment of the present invention;
fig. 6 is a flowchart of a coupling model calculation provided in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, the UDPD finite element coupling method for the damage of the quasi-brittle material provided by the embodiment of the present invention includes the following steps:
s101: constructing a numerical model according to the existing quasi-brittleness information;
s102: the method comprises the steps of dispersing all objects, dividing the whole area into two parts, dividing the periphery of the object into FEM nodes, dividing the inside of the object into UDPD nodes, and enabling the width of the FEM nodes to be equal to the neighborhood radius of particles of the UDPD objects; the junction of FEM and UDPD material points is a shared node;
s103: introducing a fourth-order polynomial attenuation function into the UDPD motion equation, and establishing the UDPD motion equation taking the PD long-range force attenuation effect into consideration;
S104: based on a motion equation, introducing a damage model of a unitary quadratic function into the connecting key to describe the damage accumulation state of the connecting key under the action of external force;
s105: dividing the bond force of the PD into linear deformation and nonlinear deformation stages based on the introduction of the damage model;
s106: based on establishing a UDPD motion equation taking into account long-range force attenuation and bond damage, simultaneously taking PD fracture criteria into the motion equation;
s107: realizing UDPD-FEM modeling of the quasi-brittle material and construction of a UDPD motion equation of the quasi-brittle material;
s108: applying boundary conditions and displacement constraints on the outermost periphery FEM area of the test piece, wherein the external force born by the UDPD area is transmitted by the node force of the FEM area;
s109: and adopting a self-adaptive dynamic relaxation algorithm to iteratively solve the UDPD-FEM model of the quasi-brittle material to obtain the acceleration, the speed and the displacement of each object point, and realizing the damage prediction of the UDPD-FEM coupling model of the quasi-brittle material.
Calculation example 1: nondestructive error analysis
And step one, constructing a UDPD-FEM coupling numerical model of the quasi-brittle material under the condition of two-dimensional plane stress. Rectangular thin plate test pieces with the length of 1m, the width of 0.5m and the thickness of 0.01m are respectively provided, wherein the material parameters are respectively 200GPa of Young modulus, 7850kg/m of mass density and 0.2 of Poisson's ratio.
And secondly, dispersing the square thin plate into uniformly distributed PD object particles and FEM nodes, wherein the FEM area is distributed around the test piece, and wrapping the UDPD area inside, wherein the thickness of the FEM area is the same as the radius of the UDPD neighborhood. Selecting a substance point spacing with the UDPD neighborhood radius of 3 times, wherein the substance point spacing is 0.01m, namely delta is 0.03mm, dividing a test piece into 10000 substance points, and constructing a neighborhood matrix of all the substance points.
And thirdly, applying uniform uniaxial tensile load of 200MPa along the x axis of the test piece on the numerical model by adopting stress boundary conditions.
And fourthly, carrying out static force solving by adopting a self-adaptive dynamic relaxation algorithm, inputting a virtual mass density matrix and a virtual damping coefficient, and carrying out iterative solving on the acceleration, the speed and the displacement of the material point at each time step.
Step five, the displacement increment of all the object points at any time step is less than 10 -10m For convergence conditions, the coupling model of the invention is used for calculating all object point displacements of the object in the elastic deformation stage, and meanwhile, the traditional key-based PD model is used for calculating all object point displacements. The relative errors of the calculation results and the analytic solutions of the two models along the x direction are shown in the figure.
EXAMPLE 2 destructive simulation prediction
And step one, constructing a UDPD-FEM coupling numerical model of the quasi-brittle concrete material under the condition of two-dimensional plane stress. The length and width of the model are respectively as follows: 0.1m and 0.03m, and the double-sided prefabricated length is 0.005m and the width is 0.002m respectively. The double crack spacing was 0.005m and 0.01m, respectively. The parameters of the material are respectively Young modulus 24GPa and mass density 2400kg/m 3 Poisson's ratio is 0.2 and uniaxial tensile strength is 2.86MPa.
And secondly, dispersing the square thin plate into uniformly distributed UDPD material particles and FEM nodes, wherein the FEM area is distributed around the test piece, wrapping the UDPD area inside, and the thickness of the FEM area is the same as the radius of the UDPD neighborhood. Selecting a substance point spacing with the UDPD neighborhood radius of 3 times, wherein the substance point spacing is 0.5mm, namely delta is 1.5mm, dividing a test piece into 28800 substance points, and constructing a neighborhood matrix of all the substance points.
Step three, uniformly applying a tensile displacement control load to two ends of the test piece, wherein the load increment of each step is 10 -8m And solving by adopting a dynamic relaxation method, wherein the time step is 1.
And fourthly, carrying out static force solving by adopting a self-adaptive dynamic relaxation algorithm, inputting a virtual mass density matrix and a virtual damping coefficient, and carrying out iterative solving on the acceleration, the speed and the displacement of the material point at each time step.
And fifthly, judging damage accumulation and fracture conditions of each material point bond according to the deformation length of the bond. When the elongation s of the object point exceeds the elastic elongation s et (the present embodiment is set to s et =0.5f t /E=5.95×10 −5 ) The bond enters a nonlinear strengthening stage when the elongation s of the object point exceeds the critical elongation s nt (the present embodiment is set to s nt =f t /E=1.19×10 −4 ) The bond enters the damage accumulation stage when the elongation s of the object point exceeds the elongation s at break t (the present embodiment is set to s t =5f t /E=5.95×10 −4 ) The corresponding bond is broken.
Equation of motion for single bond dual parameter near field dynamics:
wherein, u represents the acceleration,and->Representative particle->And->Is (are) displacement (are)>Is the relative position vector of two mass points, +.>Is the relative displacement vector of two mass points, +.>Representing mass density->Physical strength of->Representing the point-to-point force of the object point. Single bond double parameter near field dynamics available coefficient of force for point>Tangential coefficient->Elongation of sum bondThe representation is:
；
wherein the method comprises the steps ofAnd->The relative displacement vector of the key is the component along the key initial direction and perpendicular to that direction, respectively; />And->Indicating the elongation of the bond in the normal and tangential directions, respectively. Wherein the normal and tangential stiffness coefficient expressions of UDPD are:
1. to account for long range force size effects, consider a fourth order polynomial decay function. From a physical perspective, the attenuation function is a kernel function for describing the spatial distribution of the remote force intensity in the material, and the problems of wave dispersion and boundary effect of near-field dynamics can be reduced by selecting a proper influence function for numerical analysis and calculation. A fourth order polynomial function is introduced:
The constitutive force function of single bond dual parameter near field dynamics can be expressed as:
wherein the method comprises the steps ofIs a micro-modulus function taking into account the attenuation effect, +.>Is the neighborhood radius of the object point.
The normal coefficient of the attenuation effect is consideredTangential coefficient->The micro modulus function can be expressed as:
2. in order to be able to describe the breaking behaviour of a quasi-brittle material, in conventional UDPD, a damage model of the bond is introduced. The breaking of the bond is regarded as the result of the accumulation of the bond damage under the action of external load, and the introduction of the damage model divides the constitutive force function of the bond into a linear stage and a nonlinear stage, so that an improved UDPD model is provided. After the damage model K was introduced, the point-to-point force function of UDPD was expressed as:
here, theAnd->Respectively representing the elastic elongation of the key in stretching and compression, respectively corresponding to the elastic deformation of the material;and->The critical elongations of the keys during stretching and compression are respectively represented, and the maximum key forces are respectively corresponding to the critical elongations; />And->Elongation at break under tensile and compressive effects, respectively, is indicated for failure of the corresponding bond. Deformation of the key under tensile load (+)>) The breaking of the bond comprises a phase of elastic deformation of the wire (+)>) Nonlinear reinforcement phase (+)>) And softening stage (+) >）。
3. In order to accurately express the damage accumulation behavior of the bond, a damage model of the bond is expressed in a form of a unitary quadratic function. And compared with an exponential damage function, the method is easier to solve. The damage function is expressed as, as shown in figure 3,
the single bond two parameter near field dynamics point force function is expressed as:
4. in order to increase the computational efficiency and solve the problem of boundary effects, an improved near field dynamics and finite element sharing node type coupling method is adopted. Compared with an overlapping area coupling method, the coupling method does not need to set an overlapping area and a transfer function, and the numerical implementation is simpler. The whole solving area is uniformly scattered and divided into a UDPD area and an FEM area, and the distance between the UDPD substance points is consistent with the distance between the FEM nodes. And a layer of FEM nodes with the thickness equal to the UDPD neighborhood radius is arranged at the boundary of the coupling model so as to ensure that all UDPD material points have complete neighborhood, thereby achieving the purpose of eliminating the UDPD boundary effect. Since the magnitude of the FEM node forces is only related to the nodes it contacts, the arrangement of FEM nodes improves the computational efficiency of the coupling model compared to the computation of UDPD point non-local forces. It is noted that the distribution range of FEM nodes and UDPD material points in the coupling strategy can be flexibly arranged according to actual needs. For example, UDPD can be sub- The region is arranged in a region where crack initiation and propagation is possible, and the remaining region may be set as a FEM sub-region. In the coupling strategy, the internal force of a material point is calculated by adopting a respective solving method in different areas, the internal force of a FEM node is calculated by adopting a FEM method, and the internal force of a UDPD material point is calculated by adopting a UDPD method. To clearly illustrate the interaction between material points, consider a one-dimensional bar as an example, as shown in FIG. 2, assuming a material point spacing ofNeighborhood radius +.>. Blue dots represent PD material points and red square points represent FEM nodes. As shown in FIG. 2, since UDPD force is a non-local force, its neighborhood radius is +.>Each UDPD species dot interacts with the other four dots through a UDPD bond. For example, material point 3 is connected to points 1, 2, 4, 5 by a UDPD bond, while FEM node forces are localized forces, each of which interacts only with its neighbors. For example, node 6 only interacts with adjacent nodes 5 and 7, and node 5 only interacts with nodes 4 and 6. Object point 4 and node 5 are UDPD object point and FEM node, respectively, and are also considered coupling points or shared nodes, since they are located at the interface of the UDPD and FEM regions. The shared node 4 is also a UDPD object point, so the internal force is calculated by using the UDPD method. The shared node 5 is also a FEM node, so the FEM method is used to calculate the internal force. The interactions acting on the UDPD particles are in the form of force densities, while the interactions acting on the FEM nodes are in the form of forces. The policy can easily determine the transfer force value between the FEM node and the UDPD object point. There is no overlapping area between the two models, and information is transferred between the two grids in a physical information sharing mode of sharing nodes.
5. In order to accurately describe the fracture behaviour of a quasi-brittle material, fracture criteria related to the tensile strength of the material itself are proposed. The critical elongation of the bond of the quasi-brittle material under the action of pulling and pressing is expressed as follows:
wherein the method comprises the steps ofAnd->Representing the uniaxial tensile strength and uniaxial compressive strength of the quasi-brittle material.
Elastic elongation of quasi-brittle material under action of tension and compression，/>) And elongation at break (+)>，/>) Expression: />
Wherein the method comprises the steps ofAnd->Represents UDPD microcosmic parameters in the coupling model, +.>Can be derived from the geometric relationship of bond stretch to bond force. />Critical fracture energy for matched brittle material, < >>And (5) taking a value according to the absorption capacity of the uniaxial compressive energy.
The UDPD finite element coupling system for the damage of the quasi-brittle material provided by the embodiment of the invention comprises the following components:
the model construction module is used for constructing a numerical model according to the existing quasi-brittleness information;
the regional division module is used for dispersing all objects, dividing the whole region into two parts, dividing the periphery of the object into FEM nodes, dividing the inside of the object into UDPD nodes, and enabling the width of the FEM nodes to be equal to the neighborhood radius of the mass points of the UDPD objects; the junction of FEM and UDPD material points is a shared node;
the equation building module is used for introducing a fourth-order polynomial attenuation function into the UDPD motion equation to build the UDPD motion equation considering the PD long-range force attenuation effect;
The model introduction module is used for introducing a damage model of a unitary quadratic function into the connecting key based on a motion equation to describe the damage accumulation state of the connecting key under the action of external force;
the key force dividing module is used for dividing the key force of the PD into linear deformation and nonlinear deformation stages based on the introduction of the damage model;
the equation updating module is used for simultaneously taking PD fracture criteria into a motion equation based on the established UDPD motion equation considering long-range force attenuation and connection bond damage;
the new process construction module is used for realizing UDPD-FEM modeling of the quasi-brittle material and construction of a UDPD motion equation of the quasi-brittle material;
the condition applying module is used for applying boundary conditions and displacement constraints on the outermost periphery FEM area of the test piece, and the external force born by the UDPD area is transmitted from the node force of the FEM area;
and the damage prediction module is used for iteratively solving the UDPD-FEM model of the quasi-brittle material by adopting a self-adaptive dynamic relaxation algorithm to obtain the acceleration, the speed and the displacement of each object point and realize the damage prediction of the UDPD-FEM coupling model of the quasi-brittle material.
The specific embodiment of the invention is as follows:
1) And (3) constructing a numerical model: and constructing a numerical model of the quasi-brittle material according to the existing quasi-brittle material information.
2) Discretizing an object: the object is fully discrete, the periphery of the object is divided into Finite Element (FEM) nodes, the interior is divided into near field dynamics (UDPD) nodes, and the width of the FEM nodes is equal to the neighborhood radius of the UDPD substance points. And a shared node is arranged at the junction of the FEM and the UDPD material points.
3) The decay function of the fourth order polynomial is introduced: in the UDPD motion equation, a new fourth-order polynomial attenuation function is introduced in consideration of the attenuation effect of PD long-range force.
4) Introducing a damage model: and introducing a damage model of a unitary quadratic function into the connecting key to describe the damage accumulation state of the connecting key under the action of external force.
5) PD bond force is processed in stages: the bond force of the PD is divided into linear deformation and nonlinear deformation stages, and is processed based on an introduced damage model.
6) Constructing a UDPD motion equation: the PD fracture criteria are incorporated into the equation of motion based on the principle of considering long-range force attenuation and bond damage.
7) Implement UDP-FEM modeling: and realizing UDPD-FEM modeling of the quasi-brittle material and construction of a UDPD motion equation of the quasi-brittle material.
8) Applying boundary conditions: boundary conditions and displacement constraints are applied to the outermost periphery FEM area of the test piece, and external forces born by the UDPD area come from transmission of node forces of the FEM area.
9) And (3) iteration solution: and (3) carrying out iterative solution on the UDPD-FEM model of the quasi-brittle material by adopting a self-adaptive dynamic relaxation algorithm to obtain the acceleration, the speed and the displacement of each object point, thereby realizing the damage prediction of the UDPD-FEM coupling model of the quasi-brittle material.
Example 1: analysis of concrete structural failure
In this example we will apply the above mentioned UDPD finite element coupling method to analyze the failure process of a concrete structure under external forces.
1) And constructing a numerical model according to the quasi-brittleness information of the concrete, such as compressive strength, tensile strength, density and the like.
2) Discretizing the concrete structure, dividing the periphery of the structure into FEM nodes, and dividing the inside of the structure into UDPD nodes. And a shared node is arranged at the junction of the FEM and the UDPD object point.
3) The damping function of the fourth-order polynomial is introduced into the UDPD motion equation, and the PD long-range force damping effect is considered.
4) And introducing a damage model of a unitary quadratic function into the connecting key to describe the damage accumulation state of the connecting key under the action of external force.
5) The key force of the PD is divided into linear deformation and nonlinear deformation phases.
6) A UDPD equation of motion is established that accounts for long range force attenuation and bond damage, and the PD fracture criteria are incorporated into the equation of motion.
7) And completing the UDPD-FEM modeling of the concrete structure and the construction of a UDPD motion equation of the quasi-brittle material.
8) Boundary conditions and displacement constraints are applied to the outermost periphery FEM area of the concrete structure, and external forces born by the UDPD area come from transmission of node forces of the FEM area.
9) And adopting a self-adaptive dynamic relaxation algorithm to iteratively solve a UDPD-FEM model of the concrete structure, so as to obtain the acceleration, the speed and the displacement of each object point and realize the damage prediction of the concrete structure.
Example 2: analysis of glass structural failure
In this example we will apply the above mentioned UDPD finite element coupling method to analyze the failure process of a glass structure under external forces.
1) A numerical model is constructed based on the quasi-brittle information of the glass, such as compressive strength, tensile strength, density, etc.
2) The glass structure is discretized, the periphery of the structure is divided into FEM nodes, and the inside is divided into UDPD nodes. And a shared node is arranged at the junction of the FEM and the UDPD object point.
3) The damping function of the fourth-order polynomial is introduced into the UDPD motion equation, and the PD long-range force damping effect is considered.
4) And introducing a damage model of a unitary quadratic function into the connecting key to describe the damage accumulation state of the connecting key under the action of external force.
5) The key force of the PD is divided into linear deformation and nonlinear deformation phases.
6) A UDPD equation of motion is established that accounts for long range force attenuation and bond damage, and the PD fracture criteria are incorporated into the equation of motion.
7) And completing the UDPD-FEM modeling of the glass structure and the construction of a UDPD motion equation of the quasi-brittle material.
8) Boundary conditions and displacement constraints are applied to the outermost periphery FEM area of the glass structure, and external forces born by the UDPD area come from transmission of node forces of the FEM area.
9) And adopting a self-adaptive dynamic relaxation algorithm to iteratively solve a UDPD-FEM model of the glass structure to obtain the acceleration, the speed and the displacement of each object point, and realizing the damage prediction of the glass structure.
These two examples show how the UDPD finite element coupling method can be applied to analyze the failure process of quasi-brittle materials (concrete and glass) under external forces, respectively. The broad applicability of this coupling method in practical engineering applications can be better understood by performing a failure analysis of these two different types of quasi-brittle materials.
It should be noted that the embodiments of the present invention can be realized in hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or special purpose design hardware. Those of ordinary skill in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such as provided on a carrier medium such as a magnetic disk, CD or DVD-ROM, a programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present invention and its modules may be implemented by hardware circuitry, such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., as well as software executed by various types of processors, or by a combination of the above hardware circuitry and software, such as firmware.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.

Claims (10)

1. A UDPD finite element coupling method for quasi-brittle material destruction, characterized in that a new fourth-order polynomial attenuation function is introduced into the coupling method; introducing a damage model of a key, dividing the UDPD key force in the coupling model into linear deformation and nonlinear deformation, and describing the mechanical behavior of the quasi-brittle material; the damage model of the bond is in a form of a unitary quadratic equation, and the breakage of the bond occurs cumulatively by damage; the fracture criteria of the coupling model is a function of the tensile and compressive strengths of the quasi-brittle material; using the shared node method, the coupling of UDPD and FEM for the destruction of quasi-brittle material will be described.
2. The UDPD finite element coupling method for the destruction of a quasi-brittle material according to claim 1, comprising the specific steps of:
firstly, constructing a numerical model according to the existing quasi-brittleness information;
The second step, the object is scattered completely, the whole area is divided into two parts, the periphery of the object is divided into FEM nodes, the interior of the object is divided into UDPD nodes, and the width of the FEM nodes is equal to the neighborhood radius of the mass points of the UDPD object; the junction of FEM and UDPD material points is a shared node;
thirdly, introducing an attenuation function of a fourth-order polynomial into the UDPD motion equation, and establishing the UDPD motion equation considering the PD long-range force attenuation effect;
fourth, based on a motion equation, introducing a damage model of a unitary quadratic function into the connecting key to describe the damage accumulation state of the connecting key under the action of external force;
fifthly, dividing the PD key force into linear deformation and nonlinear deformation stages based on the introduction of the damage model;
sixthly, establishing a UDPD motion equation considering long-range force attenuation and connection bond damage, and simultaneously taking PD fracture criteria into the motion equation;
seventh, realizing UDPD-FEM modeling of the quasi-brittle material and construction of a UDPD motion equation of the quasi-brittle material;
eighth step, boundary conditions and displacement constraints are applied to the outermost periphery FEM area of the test piece, and external force born by the UDPD area comes from the transmission of the node force of the FEM area;
and ninth, adopting a self-adaptive dynamic relaxation algorithm to iteratively solve the UDPD-FEM model of the quasi-brittle material to obtain the acceleration, the speed and the displacement of each object point, and realizing the damage prediction of the UDPD-FEM coupling model of the quasi-brittle material.
3. The UDPD finite element coupling method for quasi-brittle material failure according to claim 1, wherein the non-destructive error analysis of the UDPD finite element coupling method for quasi-brittle material failure comprises the steps of:
firstly, constructing a quasi-brittle material UDPD-FEM coupling numerical model under a two-dimensional plane stress condition, wherein the length is 1m, the width is 0.5m, the thickness is 0.01m, the material parameters are respectively 200GPa of Young modulus, 7850kg/m of mass density and 0.2 of Poisson's ratio;
step two, dispersing the square thin plate into uniformly distributed PD object particles and FEM nodes, wherein the FEM area is distributed around the test piece, and wrapping the UDPD area inside, and the thickness of the FEM area is the same as the neighbor radius of the UDPD; selecting a substance point spacing with the UDPD neighborhood radius of 3 times, wherein the substance point spacing is 0.01m, namely delta is 0.03mm, and dividing a test piece into 10000 substance points altogether, so as to construct a neighborhood matrix of all the substance points;
applying uniform uniaxial tensile load of 200MPa along the x axis of the test piece on the numerical model by adopting a stress boundary condition;
step four, adopting a self-adaptive dynamic relaxation algorithm to carry out static force solution, inputting a virtual mass density matrix and a virtual damping coefficient, and carrying out iterative solution on the acceleration, the speed and the displacement of a material point at each time step;
Step five, the displacement increment of all the object points at any time step is less than 10 -10m For convergence conditions, the coupling model is used for calculating all object point displacements of the object in the elastic deformation stage, and meanwhile, the traditional key-based PD model is used for calculating all object point displacements.
4. The UDPD finite element coupling method for the damage to a quasi-brittle material according to claim 1, wherein the damage simulation prediction of the UDPD finite element coupling method for the damage to a quasi-brittle material comprises the steps of:
step one, a quasi-brittle concrete material UDPD-FEM coupling numerical model under a two-dimensional plane stress condition is constructed, and the length and the width of the model are respectively as follows: 0.1m and 0.03m, cracks with bilateral prefabrication length of 0.005m and width of 0.002m respectively, double crack spacing of 0.005m and 0.01m respectively, material parameters of 24GPa and mass density of 2400kg/m respectively 3 Poisson's ratio 0.2, uniaxial tensile strength 2.86MPa;
step two, the square thin plate is discretized into uniformly distributed UDPD material particles and FEM nodes, wherein the FEM area is distributed around a test piece, the UDPD area is wrapped inside, the thickness of the FEM area is the same as the radius of a UDPD neighborhood, the material point spacing with 3 times of the radius of the UDPD neighborhood is selected, the material point spacing is 0.5mm, namely delta is 1.5mm, the test piece is divided into 28800 material particles altogether, and a neighborhood matrix of all the material particles is constructed;
Step three, uniformly applying a tensile displacement control load to two ends of the test piece, wherein the load increment of each step is 10 -8m Solving by adopting a dynamic relaxation method, wherein the time step is 1;
step four, adopting a self-adaptive dynamic relaxation algorithm to carry out static force solution, inputting a virtual mass density matrix and a virtual damping coefficient, and carrying out iterative solution on the acceleration, the speed and the displacement of a material point at each time step;
fifthly, judging damage accumulation and breaking condition of each material point bond according to the deformation length of the bond, when the material point elongation s exceeds the elastic elongation s et The bond enters a nonlinear strengthening stage when the elongation s of the object point exceeds the critical elongation s nt The bond enters the damage accumulation stage when the elongation s of the object point exceeds the elongation s at break t The corresponding bond is broken.
5. The UDPD finite element coupling method for quasi-brittle material failure according to claim 1, wherein the motion equation of single bond dual parameter near field dynamics of the UDPD finite element coupling method for quasi-brittle material failure:
；
wherein, u represents the acceleration,and->Representative particle->And->Is (are) displacement (are)>Is the relative position vector of two mass points, +.>Is the relative displacement vector of two mass points, +. >Representing mass density->Physical strength of->Representing the point-to-point force of the object point; single bond double parameter near field dynamics available coefficient of force for point>Tangential coefficient->And elongation of bond->The representation is:
；
wherein the method comprises the steps ofAnd->The relative displacement vector of the key is the component along the key initial direction and perpendicular to that direction, respectively;and->Indicating the elongation of the bond in the normal and tangential directions, respectively; wherein the normal and tangential stiffness coefficient expressions of UDPD are:
；
a fourth order polynomial function is introduced:
；
the constitutive force function of single bond dual parameter near field dynamics is expressed as:
；
wherein the method comprises the steps ofIs a micro-modulus function taking into account the attenuation effect, +.>Is the neighborhood radius of the object point;
normal coefficient of attenuation effectTangential coefficient->The micro modulus function is expressed as:
；
after the damage model K was introduced, the point-to-point force function of UDPD was expressed as:
；
here, theAnd->Respectively represent the elastic elongation of the bond in stretching and compression, respectively correspond to the materialsElastic deformation of (a); />Andthe critical elongations of the keys during stretching and compression are respectively represented, and the maximum key forces are respectively corresponding to the critical elongations; />And->Respectively represents elongation at break under the action of stretching and compression, and the corresponding bond fails; deformation of the key under tensile load (+) >) The breaking of the bond comprises a phase of elastic deformation of the wire (+)>) Nonlinear reinforcement phase (+)>) And softening stage (+)>）。
6. The UDPD finite element coupling method for quasi-brittle material failure according to claim 1, wherein the damage function of the UDPD finite element coupling method for quasi-brittle material failure is expressed as:
；
the single bond two parameter near field dynamics point force function is expressed as:
；
the whole solving area is uniformly scattered by adopting an improved near field dynamics and finite element sharing node type coupling method and is divided into a UDPD area and a FEM area, and the distance between UDPD substance points is kept consistent with the distance between FEM nodes; a layer of FEM nodes with the thickness equal to the UDPD neighborhood radius is arranged at the boundary of the coupling model so as to ensure that all UDPD material points have complete neighborhood;
the critical elongation of the bond of the quasi-brittle material under the action of pulling and pressing is expressed as follows:
；
wherein the method comprises the steps ofAnd->Represents uniaxial tensile strength and uniaxial compressive strength of the quasi-brittle material;
elastic elongation of quasi-brittle material under action of tension and compression，/>) And elongation at break (+)>，/>) Expression:
；
wherein the method comprises the steps ofAnd->Represents UDPD microcosmic parameters in the coupling model, +.>Derived from the geometrical relationship of bond stretch and bond force, < > >Critical fracture energy for matched brittle material, < >>And (5) taking a value according to the absorption capacity of the uniaxial compressive energy.
7. A computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the UDPD finite element coupling method for quasi-brittle material destruction according to any of claims 1-6.
8. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the UDPD finite element coupling method for quasi-brittle material destruction according to any of claims 1-6.
9. An information data processing terminal, characterized in that the information data processing terminal is configured to implement the UDPD finite element coupling method for the damage of a quasi-brittle material according to any one of claims 1 to 6.
10. A UDPD finite element coupling system for a quasi-brittle material failure implementing the UDPD finite element coupling method for a quasi-brittle material failure of any of claims 1-6, characterized in that the UDPD finite element coupling system for a quasi-brittle material failure comprises:
The model construction module is used for constructing a numerical model according to the existing quasi-brittleness information;
the regional division module is used for dispersing all objects, dividing the whole region into two parts, dividing the periphery of the object into FEM nodes, dividing the inside of the object into UDPD nodes, and enabling the width of the FEM nodes to be equal to the neighborhood radius of the mass points of the UDPD objects; the junction of FEM and UDPD material points is a shared node;
the equation building module is used for introducing a fourth-order polynomial attenuation function into the UDPD motion equation to build the UDPD motion equation considering the PD long-range force attenuation effect;
the model introduction module is used for introducing a damage model of a unitary quadratic function into the connecting key based on a motion equation to describe the damage accumulation state of the connecting key under the action of external force;
the key force dividing module is used for dividing the key force of the PD into linear deformation and nonlinear deformation stages based on the introduction of the damage model;
the equation updating module is used for simultaneously taking PD fracture criteria into a motion equation based on the established UDPD motion equation considering long-range force attenuation and connection bond damage;
the new process construction module is used for realizing UDPD-FEM modeling of the quasi-brittle material and construction of a UDPD motion equation of the quasi-brittle material;
The condition applying module is used for applying boundary conditions and displacement constraints on the outermost periphery FEM area of the test piece, and the external force born by the UDPD area is transmitted from the node force of the FEM area;
and the damage prediction module is used for iteratively solving the UDPD-FEM model of the quasi-brittle material by adopting a self-adaptive dynamic relaxation algorithm to obtain the acceleration, the speed and the displacement of each object point and realize the damage prediction of the UDPD-FEM coupling model of the quasi-brittle material.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110414167A (en) * 2019-08-02 2019-11-05 贵州大学 Near field dynamics this structure force function modeling method of quasi-brittle material
US20200089826A1 (en) * 2018-09-14 2020-03-19 Northwestern University Integrated process-structure-property modeling frameworks and methods for design optimization and/or performance prediction of material systems and applications of same
CN113792440A (en) * 2021-09-27 2021-12-14 上海交通大学三亚崖州湾深海科技研究院 Method for calculating structural force response of floating structure under unsteady state load action
CN114136779A (en) * 2021-11-26 2022-03-04 河北工业大学 Quasi-brittle material I-II type fracture toughness test solving method

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20200089826A1 (en) * 2018-09-14 2020-03-19 Northwestern University Integrated process-structure-property modeling frameworks and methods for design optimization and/or performance prediction of material systems and applications of same
CN110414167A (en) * 2019-08-02 2019-11-05 贵州大学 Near field dynamics this structure force function modeling method of quasi-brittle material
CN113792440A (en) * 2021-09-27 2021-12-14 上海交通大学三亚崖州湾深海科技研究院 Method for calculating structural force response of floating structure under unsteady state load action
CN114136779A (en) * 2021-11-26 2022-03-04 河北工业大学 Quasi-brittle material I-II type fracture toughness test solving method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
SHUANG LI: "An improved unibond dual-parameter peridynamic model for fracture analysis of quasi-brittle materials", 《INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES》, vol. 2021, no. 204, pages 1 - 14 *
SHUANG LI: "Prediction of bearing capacities and fracture processes in open-hole plates using a hybrid model of peridynamics and FEM", 《OCEAN ENGINEERING》, vol. 278, no. 114322, pages 1 - 19 *

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