CN114254423B - Structural effect calculation method for porous concrete SHPB test with randomly distributed spherical holes - Google Patents
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Abstract
When a numerical model of porous concrete SHPB (short-term evolution) samples with randomly distributed spherical holes is established by using a finite element method, a fitting curve of parameters of equivalent materials of a mesomonas model along with hole rates is calculated, porous concrete SHPB samples with randomly distributed spherical holes are divided by a cube grid, then the porous concrete SHPB test with randomly distributed spherical holes and a corresponding finite element analysis model are combined, an actually measured incident wave on an incident rod is taken as an input stress wave of the finite element model, and a stress-strain curve of the porous concrete SHPB test with randomly distributed spherical holes under different incident waves is reconstructed. The method considers the influence of random distribution of the ball holes in the porous concrete, avoids the problems of too thin grid, long calculation time and easy occurrence of 'hourglass' site in dynamic numerical simulation calculation caused by directly dividing grids aiming at the SHPB sample matrix, and the model is more in accordance with the characteristic of random distribution of the ball holes of the actual sample.
Description
Technical Field
The invention relates to the technical fields of civil engineering materials and computer application, in particular to a method for calculating the structural effect of a porous concrete SHPB test with randomly distributed spherical pores.
Background
In order to solve the problems that sand and stone building raw materials required by the construction of the concrete of the offshore island engineering are long in transportation distance, and limited in site stacking and storage space and the like, the invention patent ZL201318000238.0 relates to the seawater aggregate self-compacting concrete, which takes the production of concrete raw materials by using island-rich seawater resources on site as a starting point, and prepares a novel self-compacting concrete material based on an inner shell structure by specially-made high-performance water-absorbing resin, composite additive and the like, thereby realizing the on-site material taking and rapid preparation of island engineering concrete coarse aggregate, greatly reducing the transportation quantity of concrete raw materials and reducing the construction cost of the offshore island engineering.
The seawater aggregate concrete is prepared by adding modified high-performance spherical water absorbent resin (Super-Absorbent Polymer, SAP) into seawater, and condensing into a large amount of artificial quasi-solid filling materials to replace coarse aggregates in the concrete. The SAP can quickly absorb water with multiple mass to expand, a small amount of super absorbent resin and seawater are used for preparing a large amount of expanded aggregate to replace crushed stone aggregate in conventional concrete, the water-absorbent expanded SAP gradually loses water in the concrete curing process, and finally porous concrete with randomly distributed spherical holes is formed.
The unique spherical hole structure of the inner shell of the seawater aggregate concrete has the outstanding characteristics of low relative density, small wave impedance and the like of porous materials, can be used in the island protection engineering field (invention patent ZL 201811451500.1), and needs to study the dynamic mechanical characteristics of the seawater aggregate concrete. At present, the dynamic mechanical properties of concrete materials are usually tested by using a split Hopkinson pressure bar (Split Hopkinson Pressure Bar, SHPB) experimental technology, and the core is to determine the strain rate effect of the concrete materials, in particular the strain rate effect of compressive strength. Studies have shown that the strain rate effect exhibited by the mechanical properties of concrete in SHPB test is mainly caused by the combined action of the strain rate effect (true strain rate effect) of the material itself and the structural effect, which mainly includes the lateral inertia constraint effect and the end face friction effect. In order to guide island engineering design, ensure structural safety and accurately analyze the influence on the protective performance of the protective engineering, structural effects (lateral inertia constraint effects and end face friction effects) in the sea water aggregate concrete SHPB experiment with different hole rates need to be removed, and then the real strain rate effect can be obtained. The structural effect in the SHPB experiment is difficult to determine by an experimental means, because the inertia of the sample exists objectively under the impact load, and therefore, the result of the SHPB experiment necessarily contains both the strain rate effect caused by the structural effect and the strain rate effect of the sample material itself. No test method has been proposed to separate these two effects.
The patent ZL201610964811.2 relates to a computer dynamic simulation method for determining the real strain rate effect of seawater aggregate concrete, which utilizes a separated Hopkinson compression bar test and a corresponding finite element analysis model of the seawater aggregate concrete, and takes an actually measured compression bar test incident wave as an input stress wave of the finite element model; the expansion Drucker-Prager model is selected as a material model of the seawater aggregate concrete matrix, the strain rate effect of the material is not set, and the strength increase of the seawater aggregate concrete under the high strain rate caused by the structural effect alone is simulated; and determining the actual strain rate effect of the seawater aggregate concrete according to the strain rate effect obtained by the SHPB test and the calculated strain rate effect caused by the structural effect (lateral inertia constraint and end face friction). Patent ZL201610964811.2 avoids the decoupling of the true strain rate effect of seawater aggregate concrete with randomly distributed spherical pore structure from the strain rate effect caused by structural effect in a complex design experiment.
However, the patent ZL201610964811.2 relates to a computer dynamic simulation method for determining the real strain rate effect of seawater aggregate concrete, which mainly has the following defects:
1. the established numerical model is a uniform ball hole distribution model, ball holes in actual seawater aggregate concrete are randomly distributed, the research method is inconsistent with the heterogeneity of the seawater aggregate concrete in a microscopic level, namely, the ball holes which are closely gathered in the actual seawater aggregate concrete can be locally present, so that the hole wall is too thin, the additional bending moment is obviously increased to cause local premature failure, thereby causing the reduction of the integral strength of a sample, and meanwhile, the microscopic heterogeneity of the actual seawater concrete can also influence the inertial confinement effect in an SHPB (short time period) test, thereby influencing the calculation accuracy of the structural effect and the actual strain rate effect;
2. the matrix meshing quality around the walls of the ball holes is a main reason for influencing the accuracy and effectiveness of dynamic calculation results, so that the meshing quality must be strictly ensured in order to ensure the performance of dynamic numerical simulation calculation and the occurrence of no "hourglass", and for seawater aggregate concrete with high hole rate, very fine meshing is required to ensure the performance of calculation and the occurrence of no "hourglass", the occupied calculation resources are large, the calculation time is very long, and for seawater aggregate concrete SHPB samples with high hole rate, the rapid rise of the accumulation of the hourglass is difficult to avoid even if the very fine meshing is used, so that the accuracy of solving the real strain rate effect of the seawater aggregate concrete of the high hole rate samples is reduced.
Disclosure of Invention
1. Technical problem to be solved
The invention aims to solve the problems that in the prior art, the strain rate effect solving result caused by the structural effect of a seawater aggregate concrete SHPB test does not accord with the actual micro-non-uniformity, and meanwhile, the strain rate effect caused by the structural effect of a high-void-rate seawater aggregate concrete SHPB sample and the numerical calculation effectiveness, calculation precision and calculation efficiency of the actual strain rate effect are low, and provides a structural effect calculating method for a porous concrete SHPB test with randomly distributed spherical holes.
2. Technical proposal
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the method for calculating the structural effect of the porous concrete SHPB test with randomly distributed spherical holes comprises the following steps:
s1: generating a micro-unit cell model, namely generating a micro-unit cell model with initial uniform distribution of ball holes, simulating randomness by a Monte Carlo method, generating center coordinates of pseudo-random number simulated ball holes, modifying the initial uniformly distributed center coordinates one by one, judging the effectiveness of the generated random ball holes by intrusion discrimination among the ball holes, and generating the random micro-unit cell model when the random evolution of the last ball hole is finished;
s2: calculating the hole rate of the mesomonas model according to the shape of the part of the ball hole cut by the boundary of the mesomonas model, wherein the part of the ball hole cut by one plane is contained in the unit cell, the part of the ball hole cut by two perpendicular planes is contained in the unit cell, and the part of the ball hole cut by three perpendicular planes is contained in the unit cell, and calculating the volume of the ball hole in the mesomonas model, so that the hole rate of the mesomonas model is obtained;
s3: uniaxial compression numerical test of a mesomonas model, in order to obtain equivalent material model parameters of mesomonas of an established spherical pore random distribution porous concrete SHPB sample numerical model, carrying out numerical simulation test on uniaxial compression mechanical behaviors of the mesomonas model with the same size and different pore rates to obtain a nominal stress-strain curve of the mesomonas model, obtaining a fitting curve of uniaxial compression mechanical property indexes (compressive strength, initial elastic modulus and the like) of the mesomonas model along with the pore rates on the basis, adopting an expansion Drucker-Prager model to obtain a spherical pore random distribution porous concrete matrix, selecting a linear yield surface and an associated flow rule, and describing equivalent stress of a hardening rule
Taking the uniaxial compressive strength f cs Equivalent plastic strain
The friction angle beta is determined by a conventional triaxial test of a matrix (namely, a sample with a void fraction of 0), intensity data under at least three different surrounding pressures are plotted on a p-t plane, linear fitting is carried out, the inclination angle of a fitting straight line is the friction angle of an extended linear dragger-Prager model, a simplified stress-strain curve is adopted to describe the uniaxial compressive mechanical behavior of the matrix of the porous concrete with randomly distributed spherical pores, and the simplified stress-strain curve is loaded from the beginning to the compressive strength f cs The previous stress strain is in a linear relation, and the compressive strength f is achieved cs The strain softening stage and the residual strength stage are followed in sequence; freely dividing grids to enable unit cell load acting surfaceThe load direction displacement coupling of all the nodes is simulated, and the actual loading surface is kept in a plane state; according to the stress-strain curve obtained by the uniaxial compression numerical test of the mesomonas model, the compressive strength f 'of the equivalent simplified stress-strain curve of the mesomonas model is obtained' cs And an elastic modulus E';
s4: the method comprises the steps of (1) carrying out a triaxial compression numerical test on a mesoscopic unit model, selecting a proper finite element grid to divide material units of a spherical hole random distribution porous concrete matrix to represent the inner boundary of the spherical hole of the unit cell, describing single-axis compression mechanical behaviors of the matrix by adopting an expanded drager-Prager model and adopting a simplified stress-strain curve, freely dividing grids, carrying out displacement coupling on load directions of all nodes on a unit cell load acting surface, and simulating an actual loading surface to keep a plane state; simulating compression mechanical behavior of the mesomonas model under three different confining pressures, wherein the test piece is subjected to uniform confining pressure sigma 2 ＝σ 3 Then is subjected to additional compressive stress sigma in the axial direction 1 The method comprises the steps of carrying out a first treatment on the surface of the After raising the confining pressure to a predetermined value, applying an additional pressure sigma 1 Recording the additional pressure sigma during pressurization 1 -σ 3 Axial strain ε 1 Lateral strain ε 3 Is changed by the body strain epsilon v ＝ε 1 +2ε 3 The additional pressure sigma can also be derived 3 Satellite strain epsilon v Is a law of variation of (a); drawing the intensity data under three surrounding pressures on a p-t plane, and performing linear fitting, wherein the inclination angle of a fitting straight line is the equivalent friction angle beta' of the extended line type Drucker-Prager model of the mesomonas model;
s5: statistical homogenization, considering randomness and size effect of the mesomonas model, and simultaneously analyzing the compressive strength f of random factors such as void rate, random distribution of spherical pores, unit cell size and the like on equivalent simplified stress-strain curve of the mesomonas model c ′ s And the elastic modulus E ', the influence of the equivalent friction angle beta' of the extended linear drager-Prager model; setting the size of the mesomonas model to be 7mm, and repeating the steps S1 to S4 to obtain the compressive strength f of the equivalent simplified stress-strain curve of the mesomonas model under different hole rates c ′ s And elastic modulus E', expanded linear Drucker-PFitting equivalent parameters of the mesomonas model one by using an equivalent friction angle beta' of the rager model to obtain a relational expression of each equivalent parameter and the void fraction p;
s6: the method comprises the steps of establishing an SHPB test device and a random sample numerical model, simplifying the cross sections of an incident rod, a transmission rod and a sample of the SHPB test device from a circular shape to a square shape, adopting an incident wave measured in the test as an input stress wave of the numerical model, carrying out finite element mesh division, equally dividing the sample with randomly distributed ball holes into cube units with the side length of 7mm, and dividing the grids with the size the same as that of the selected cube units with the side length of 7 mm; the incident rod and the transmission rod adopt linear elastic material models, and the porous concrete samples with randomly distributed spherical holes adopt an expanded Drucker-Prager model;
s7: solving a dynamic display finite element method, reconstructing an SHPB test stress-strain curve, setting end face friction coefficients of a sample and an input transmission rod according to set material model parameters, calculating and solving by adopting a dynamic explicit finite element method, and obtaining a structural effect considering a lateral inertia constraint effect and an end face friction effect by 'reconstructing' the porous concrete SHPB test stress-strain curve with randomly distributed ball outlet holes without considering the dynamic compressive strength of the real strain rate effect of the concrete material;
s8: further, the true strain rate effect of the porous concrete with randomly distributed spherical pores can be calculated, and the dynamic strength growth factor DIF-f obtained by test c (ratio of compressive Strength at high Strain Rate loading to compressive Strength at quasi-static loading) dynamic Strength growth factor DIF-f when the true strain Rate Effect of a ball-hole randomly distributed porous concrete Material is not considered cd,lat-μ To be caused only by the lateral inertia constraint effect and the end face friction effect, the dynamic strength increase factor DIF-f generated by the real strain rate effect of the material c,r ＝DIF-f c -DIF-f cd,lat-μ +1。
Preferably, the calculation method can be applied to porous concrete pavement engineering with randomly distributed spherical pores.
Preferably, the calculation method is applicable to island protection engineering.
Preferably, the calculation method is applicable to open sea island reef breakwater engineering.
Preferably, the calculation method is applicable to lawn road engineering.
Preferably, in S3, the material units of the porous concrete matrix with randomly distributed spherical pores are selected to represent the inner boundaries of the spherical pores of the unit cell by using a suitable finite element mesh.
Preferably, the value of the divergence angle ψ in S3 is equal to the value of the friction angle β, and the out-of-plane parameter k=1.
Preferably, the parameter in S5 is a random variable related to the hole rate of the mesomonas model, the random distribution of the holes, the size of the holes, and the like, so that the randomness caused by the random distribution of the holes can be ignored for simplifying the calculation, and only the randomness of the hole rate of the mesomonas model is considered.
Preferably, the equivalent simplified stress-strain curve compressive strength f 'of each grid cell material model in the S6' cs The modulus of elasticity E 'and the equivalent friction angle beta' are determined from the calculated void fraction of the cell and the fitted curve obtained previously.
3. Advantageous effects
Compared with the prior art, the invention has the advantages that:
according to the invention, the influence of random distribution of ball holes in the seawater aggregate concrete is considered by adopting the finite element model, and the method of statistical homogenization of mechanical parameters of the mesomonas model is adopted, so that the problems of too thin grid, long calculation time and easy occurrence of 'hourglass' site in dynamic numerical simulation calculation caused by dividing grids directly aiming at a matrix are avoided for the seawater aggregate concrete sample with high hole rate, and the model is more in accordance with the characteristic of random distribution of the ball holes of an actual sample.
Drawings
Fig. 1 is a flowchart of a method for calculating a true strain rate effect of porous concrete with randomly distributed spherical pores based on statistical homogenization according to an embodiment of the invention.
FIG. 2 is a flowchart of a mesomonas model generation procedure according to an embodiment of the present invention
FIG. 3 is a schematic diagram of a boundary cut pattern of a spherical hole in a mesomonas model according to an embodiment of the present invention.
FIG. 4 is a schematic diagram of a model of a mesomonas cell provided by an embodiment of the present invention.
Fig. 5 is a simplified graph of uniaxial compressive stress-strain for a porous concrete matrix with randomly distributed spherical pores according to an embodiment of the present invention.
FIG. 6 is a graph showing compressive strength f 'of an equivalent simplified stress-strain curve of a porous concrete microstructure model with randomly distributed spherical pores according to an embodiment of the present invention' cs And (5) calculating a result and fitting a curve along with the hole rate p.
Fig. 7 is a calculation result and a fitting curve of an elastic modulus E' of a spherical pore random distribution porous concrete mesomonas model equivalent simplified stress-strain curve according to a porosity p provided by the embodiment of the invention.
FIG. 8 is a calculation result and a fitting curve of an equivalent friction angle beta' of a spherical pore random distribution porous concrete mesomonas model expansion Drucker-Prager model along with a pore rate p.
Fig. 9 is a schematic diagram of an SHPB test device according to an embodiment of the present invention.
Fig. 10 is a simplified numerical model schematic diagram of an SHPB test device according to an embodiment of the present invention.
FIG. 11 is a schematic diagram of measured incident stress waves provided by an embodiment of the present invention.
Fig. 12 is a schematic diagram of a measured quasi-static stress-strain curve, a dynamic stress-strain curve and a "reconstructed" stress-strain curve of porous concrete with a porosity of 40% and randomly distributed sphere holes according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
Example 1:
as shown in fig. 1, the method for calculating the structural effect of the porous concrete SHPB test with randomly distributed spherical pores comprises the following steps:
(1) Mesomonas model generation
As shown in fig. 2, the flow of the mesomonas model generation includes the following steps:
1) Determination of the model size (side Length) l of the mesomonas e The number of ball holes in a unit cell is N, and the diameter of the ball holes is d.
2) Uniformly distributing N ball holes in a unit cell to generate uniformly distributed ball hole models, wherein the spherical center coordinate of each ball hole is
3) Coordinates of the sphere center of the ith (i=1, 2,3 … N) sphere hole are sequentially calculated
Randomly evolve into coordinates
Is in the unit cell region [ a, b ]]Interval (where b-a=l e ) A uniformly distributed random number is generated.
4) Judging whether the ith ball hole invades the rest N-1 ball holes or not according to the invasion judgment criterion of the following formula (1), and if not, generating the random evolution sphere center coordinates of the (i+1) th ball hole
Repeating the steps 3) and 4), if the ball is invaded, returning to the step 3), and regenerating the random sphere center evolution coordinates of the ith sphere hole.
(x i ,y i ,z i )、(x j ,y j ,z j ) The center coordinates of the ith and jth ball holes are respectively, r is the radius of the ball hole, and s is the minimum thickness between the ball holes.
5) And when the random evolution of the Nth ball hole is finished, generating a random unit cell model, and ending the program.
(2) Mesomonas model void fraction calculation
The part of the spherical hole divided by the boundary is mainly 4 types, and the radius of the spherical hole is r:
1) When the sphere hole is fully contained within the cell, the volume of the divided portion:
2) The part of the hole cut by a plane (also called the segment) is contained in a cell, the segment has a height h as shown in fig. 3a, and the volume of the cut part is:
3) The part of the ball hole cut by two perpendicular planes is contained in a cell, as shown in FIG. 3b, the two heights of the part are h 1 、h 2 The volume was calculated by triple integration:
4) The ball hole is contained in a cell by a section of three mutually perpendicular planes, the three heights of which are respectively h as shown in FIG. 3c 1 、h 2 、h 3 The volume was calculated:
the void fraction p of the model containing N ball-hole mesonas is:
l e for unit cell size, V i The volume occupied by the ith ball hole in the mesomonas model is calculated.
The dimension l is given in fig. 4 e In a 10mm minicell model, a 6-sphere random model and an 8-sphere random model, sphere diameters were 5mm, and sphere volume fractions were 25.82% and 29.50%, respectively.
(3) Uniaxial compression numerical test of mesomonas model
And carrying out a uniaxial compression numerical test on the mesomonas model to obtain a nominal stress-strain curve of the mesomonas model, and obtaining a fitting curve of uniaxial compression mechanical characteristic indexes (compressive strength, initial elastic modulus and the like) of the mesomonas model along with the void ratio of the mesomonas model on the basis of the nominal stress-strain curve. Uniaxial compression numerical tests were performed using ANSYS14.0 finite element computing software, with sol 186 selected as the material element of the seawater aggregate concrete matrix to represent the complex inner boundary of a cell. The seawater aggregate concrete matrix adopts an extended Drucker-Prager model, adopts a linear yield surface and an associated flow rule, and describes the equivalent stress of a hardening rule
Taking the uniaxial compressive strength f cs Equivalent plastic strain->
The friction angle beta is determined by a conventional triaxial test of a water aggregate concrete matrix (namely, a sample with a void fraction of 0), intensity data under at least three different surrounding pressures are plotted on a p-t plane, linear fitting is carried out, the inclination angle of a fitting straight line is the friction angle beta of an expanded driver-Prager model, and beta=46 degrees is obtained according to test fitting results. The value of the divergence angle psi is equal to the value of the friction angle beta, and the offset plane parameter K=1. The uniaxial compressive mechanical behavior of a seawater concrete matrix is described using a simplified stress-strain curve as shown in FIG. 5, which is loaded from the beginning to the compressive strength f cs The previous stress strain is in a linear relation, and the compressive strength f is achieved cs Followed by a strain softening stage and a residual strength stage. Setting the density of the seawater aggregate concrete matrix to 2172kg/m according to the test result 3 Simplified stress-strain curve compressive strength f cs =70 Mpa, elastic modulus e=2Poisson's ratio v=0.21, 4.2 GPa.
And freely dividing grids, carrying out displacement coupling on the load directions of all nodes on the unit load acting surface, and simulating the actual loading surface to keep a plane state. The load direction pressure sigma of the coupling node under the load action is set cp Displacement u ep Nominal equivalent stress sigma as unit cell, respectively e Displacement u e Definition of nominal Strain ε e ＝u e /l e . According to the stress-strain curve obtained by the uniaxial compression numerical test of the mesomonas model, the compressive strength f 'of the equivalent simplified stress-strain curve of the mesomonas model is obtained' cs And an elastic modulus E'.
(4) Triaxial compression numerical test of random unit cell model
Uniaxial compression numerical tests were performed using ANSYS14.0 finite element computing software, with sol 186 selected as the material element of the seawater aggregate concrete matrix to represent the complex inner boundary of a cell. The seawater aggregate concrete matrix adopts an extended Drucker-Prager model, adopts a linear yield surface and an associated flow rule, and describes the equivalent stress of a hardening rule
Taking the uniaxial compressive strength f cs Equivalent plastic strain->
The friction angle beta is determined by a conventional triaxial test of a water aggregate concrete matrix (namely, a sample with a void fraction of 0), intensity data under at least three different surrounding pressures are plotted on a p-t plane, linear fitting is carried out, the inclination angle of a fitting straight line is the friction angle beta of an expanded driver-Prager model, and beta=46 degrees is obtained according to test fitting results. The value of the divergence angle psi is equal to the value of the friction angle beta, and the offset plane parameter K=1. The uniaxial compressive mechanical behavior of a seawater concrete matrix is described using a simplified stress-strain curve as shown in FIG. 5, which is loaded from the beginning to the compressive strength f cs The previous stress strain is in a linear relation, and the compressive strength f is achieved cs Followed by a strain softening stage and a residual strength stage. According toTest results set seawater aggregate concrete matrix Density 2172kg/m 3 Simplified stress-strain curve compressive strength f cs 70Mpa, elastic modulus e=24.2 GPa, poisson's ratio v=0.21. And freely dividing grids, carrying out displacement coupling on the load directions of all nodes on the unit load acting surface, and simulating the actual loading surface to keep a plane state.
Simulating compression mechanical behavior of the mesomonas model under three different confining pressures, wherein the test piece is subjected to uniform confining pressure sigma 2 ＝σ 3 Then is subjected to additional compressive stress sigma in the axial direction 1 . After raising the confining pressure to a predetermined value, applying an additional pressure sigma 1 Recording the additional pressure sigma during pressurization 1 -σ 3 Axial strain ε 1 Lateral strain ε 3 Is changed by the body strain epsilon v ＝ε 1 +2ε 3 The additional pressure sigma can also be derived 3 Satellite strain epsilon v Is a law of variation of (c). The intensity data under three surrounding pressures are plotted on a p-t plane, and a linear fitting is performed, wherein the inclination angle of a fitting straight line is the equivalent friction angle beta' of the extended Drucker-Prager model of the mesomonas model.
(5) Statistical homogenization
Setting the size of the mesomonas model to be 7mm, and repeating the steps (1) to (4) to obtain the compressive strength f 'of the equivalent simplified stress-strain curve of the mesomonas model under different hole rates' cs And the elastic modulus E ', and the equivalent friction angle beta' of the extended Drucker-Prager model, fitting the equivalent parameters of the mesomonas model one by one, and obtaining the relation between each equivalent parameter and the void ratio p.
1) Compressive strength f 'of equivalent simplified stress-strain curve' cs
The equivalent simplified stress-strain curve compressive strength f 'obtained by uniaxial compression numerical test of the mesomonas model with the size of 7mm under different void ratios' cs As shown in fig. 6. Compressive strength f 'of equivalent simplified stress-strain curve' cs The fit relation with the void fraction p is:
f′ cs ＝70-57.5p (7)
2) Equivalent simplified stress-strain curve elastic modulus E'
The equivalent simplified stress-strain curve elastic modulus E' obtained by uniaxial compression numerical test of the model of micro-unit cell with the size of 7mm under different void ratios is shown in FIG. 7. The fitting relation of the elastic modulus E' of the equivalent simplified stress-strain curve along with the void fraction p is as follows:
E′＝24.2[1-2.53(1-e -1.06p )] (8)
3) Expansion of Drucker-Prager model equivalent friction angle beta'
The equivalent friction angle beta' of the extended Drucker-Prager model obtained by the uniaxial compression numerical test of the mesomonas model with the size of 7mm under different hole rates is shown in figure 8. The fitting relation of the equivalent friction angle beta' of the expansion Drucker-Prager model obtained by the uniaxial compression numerical test along with the void fraction p is as follows:
β′＝41.88+4.13e -p/0.07 (9)
(6) SHPB test device and random sample numerical model establishment
1) Simplified numerical model of SHPB (short-term test) test device
The cross-section of the incident beam, the transmission beam, and the sample of the test device shown in fig. 9 was simplified from circular to square (fig. 10). The incident wave measured in the test is used as an input stress wave of a numerical model (fig. 11 is an incident stress wave of a 40% porosity sample under SHPB test, three different strain rates are actually measured), and the cross sections of the incident rod and the transmission rod in the simplified numerical model are equal-section rods, the lengths of the incident rod and the transmission rod are 800mm, the side lengths of the sections are 74mm, the thickness of the sample is 35mm, and the side lengths of the sections are 70mm.
2) Random sample numerical model
A random sample numerical model was generated in which spherical holes (diameter d=5 mm) were randomly distributed in SHPB samples (thickness h=35 mm, cross-sectional side length l=70 mm), comprising the steps of:
a. and (5) preliminarily determining the number N of ball holes in the sample according to the sample hole rate p.
b. Uniformly distributing N ball holes in the sample to generate uniformly distributed ball hole models, wherein the spherical center coordinates of each ball hole are as follows
/>
c. Coordinates of the sphere center of the ith (i=1, 2,3 … N) sphere hole are sequentially calculated
Randomly evolve into coordinates
Is a uniformly distributed random number generated inside the sample.
d. Judging whether the ith ball hole invades the rest N-1 ball holes and the side wall of the sample or not by the intrusion judging criterion of the following (10) (the coordinate interval of two side lengths of the cross section is set as [0,l ]]) If no invasion exists, generating the random evolution sphere center coordinates of the (i+1) th sphere hole
Repeating the steps 3) and 4), if the ball is invaded, returning to the step 3), and regenerating the random sphere center evolution coordinates of the ith sphere hole.
e. And when the random evolution of the Nth ball hole is finished, generating a random unit cell model, and ending the program.
3) Meshing grid
And carrying out finite element mesh division by adopting ANSYS, and simulating an incident rod and a transmission rod by adopting an eight-node three-dimensional stress reduction integral unit. For the samples with randomly distributed ball holes, the samples are equally divided into cube units with the side length of 7mm, three-dimensional stress reduction integral units are selected for simulation, grids are divided, and the sizes of the three-dimensional stress reduction integral units are the same as those of the selected cube units with the side length of 7 mm.
4) Gridded material model parameter assignment
The incident rod and the transmission rod are made of linear elastic material, and the density is 7850kg/m 3 The elastic modulus is 210GPa, the Poisson's ratio is 0.3, and the compressive strength is 400MPa. The seawater aggregate concrete sample adopts an extended Drucker-Prager model, adopts a linear yield surface and an associated flow rule, and describes the equivalent stress of a hardening rule
Taking the uniaxial compressive strength f cs Equivalent plastic strain
The equivalent friction angle beta' of each calculation grid unit is determined according to the calculation hole rate of the unit through a fitting curve of formula (9), the value of the expansion angle phi is equal to the value of the friction angle beta, and the out-of-plane parameter K=1. The seawater aggregate concrete sample describes the uniaxial compressive mechanical behavior of each grid cell of the seawater concrete sample by adopting an equivalent simplified stress-strain curve similar to that shown in fig. 5, and the compressive strength f of the equivalent simplified stress-strain curve c ′ s The equivalent simplified stress-strain curve elastic modulus E' is determined from the calculated void fraction of the cell by fitting the curve of formula (7), and the poisson ratio takes v=0.21 from the calculated void fraction of the cell by fitting the curve of formula (8).
(7) Solving the dynamic display finite element method and reconstructing an SHPB test stress-strain curve
According to the set material model parameters, the end face friction coefficients of the sample and the input and transmission rods are 0.1, a dynamic explicit finite element method is adopted to calculate and solve, a porous concrete SHPB test stress-strain curve with randomly distributed ball outlet holes is reconstructed, and the structural effect of considering the lateral inertia constraint effect and the end face friction effect is obtained without considering the dynamic compressive strength of the true strain rate effect of the concrete material. FIG. 12 is a graph of the measured quasi-static stress-strain curve, the measured stress-strain curve under dynamic loading, and the "reconstructed" stress-strain curve taking into account the lateral inertial confinement effect and the end face friction effect for a porous concrete with a theoretical void fraction of 40% and randomly distributed spherical voids.
(8) Calculating true strain rate effect of porous concrete with randomly distributed spherical pores
For the dynamic intensity growth factor DIF-f obtained by experimental test c Dynamic strength increase factor DIF-f when the true strain rate effect of the concrete material itself is not considered cd,lat-μ To be caused only by the lateral inertia constraint effect and the end face friction effect, the dynamic strength increase factor DIF-f generated by the real strain rate effect of the material c,r ＝DIF-f c -DIF-f cd,lat-μ +1. From FIG. 12, it can be derived that the dynamic strength increase factor DIF-f of the compressive strength strain rate effect of porous concrete with 40% void fraction and ball hole random distribution is measured at three strain rate levels of 70/s, 100/s and 140/s c 1.97, 2.31 and 2.58, respectively, the dynamic strength increase factor DIF-f caused by the lateral inertial confinement effect and the end face friction effect alone cd,lat-μ 1.039, 1.102 and 1.155, respectively, thus yielding a dynamic strength increase factor DIF-f reflecting the true strain rate effect c,r 1.931, 2.208 and 2.425, respectively. Using equations
Fitting the true strain rate effect to obtain a fitting type
Wherein->
For the strain rate at high strain rate loading, +.>
Is the strain rate at quasi-static loading (here, 2 x 10 -4 /s)。
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (8)
1. The method for calculating the structural effect of the porous concrete SHPB test with randomly distributed spherical holes is characterized by comprising the following steps of:
s1: generating a micro-unit cell model, namely generating a micro-unit cell model with initial uniform distribution of ball holes, simulating randomness by a Monte Carlo method, generating center coordinates of pseudo-random number simulated ball holes, modifying the initial uniformly distributed center coordinates one by one, judging the effectiveness of the generated random ball holes by intrusion discrimination among the ball holes, and generating the random micro-unit cell model when the random evolution of the last ball hole is finished;
s2: calculating the hole rate of the mesomonas model according to the shape of the part of the ball hole cut by the boundary of the mesomonas model, wherein the part of the ball hole cut by one plane is contained in the unit cell, the part of the ball hole cut by two perpendicular planes is contained in the unit cell, and the part of the ball hole cut by three perpendicular planes is contained in the unit cell, and calculating the volume of the ball hole in the mesomonas model, so that the hole rate of the mesomonas model is obtained;
s3: uniaxial compression numerical test of a mesomonas model, in order to obtain equivalent material model parameters of mesomonas of an established spherical pore random distribution porous concrete SHPB sample numerical model, carrying out numerical simulation test on uniaxial compression mechanical behaviors of the mesomonas model with the same size and different pore rates to obtain a nominal stress-strain curve of the mesomonas model, obtaining a fitting curve of uniaxial compression mechanical property indexes of the mesomonas model along with the pore rates on the basis of the nominal stress-strain curve, adopting an expansion Drucker-Prager model for a spherical pore random distribution porous concrete matrix, selecting a linear yield surface and an associated flow rule, and describing equivalent stress of a hardening rule
Taking the uniaxial compressive strength f cs Equivalent plastic strain->
The friction angle beta is determined by a conventional triaxial test of a seawater aggregate concrete matrix, intensity data under at least three different surrounding pressures are plotted on a p-t plane, linear fitting is carried out, the inclination angle of the fitting straight line is the friction angle of an extended linear driver-Prager model, a simplified stress-strain curve is adopted to describe the uniaxial compressive mechanical behavior of the matrix, and the stress-strain curve is simplified from the beginning of loading to the compressive strength f cs The previous stress strain is in a linear relation, and the compressive strength f is achieved cs The strain softening stage and the residual strength stage are followed in sequence; freely dividing grids, carrying out displacement coupling on load directions of all nodes on a unit load acting surface, and simulating an actual loading surface to keep a plane state; according to the stress-strain curve obtained by the uniaxial compression numerical test of the mesomonas model, the compressive strength f 'of the equivalent simplified stress-strain curve of the mesomonas model is obtained' cs And an elastic modulus E';
s4: the microscopic unit cell model triaxial compression numerical test adopts a finite element grid to divide the material units of a spherical hole random distribution porous concrete matrix to represent the spherical hole inner boundary of a unit cell, the matrix adopts an expanded Drucker-Prager model, a simplified stress-strain curve is adopted to describe the uniaxial compression mechanical behavior of the matrix, the grid is freely divided, the load directions of all nodes on a unit cell load acting surface are coupled in a displacement manner, and an actual loading surface is simulated to keep a plane state; simulating compression mechanical behavior of the mesomonas model under three different confining pressures, wherein the test piece is subjected to uniform confining pressure sigma 2 ＝σ 3 Then is subjected to confining pressure sigma in the axial direction 1 The method comprises the steps of carrying out a first treatment on the surface of the Will sigma 2 Sum sigma 3 After the confining pressure rises to a preset value, confining pressure sigma is applied 1 Recording confining pressure sigma in pressurizing process 1 -σ 3 Axial strain ε 1 Lateral strain ε 3 Is changed by the body strain epsilon v ＝ε 1 +2ε 3 Also can obtain the confining pressure sigma 3 Satellite strain epsilon v Is a law of variation of (a); drawing the intensity data under three surrounding pressures on a p-t plane, and performing linear fitting, wherein the inclination angle of a fitting straight line is the equivalent friction angle beta' of the extended line type Drucker-Prager model of the mesomonas model;
s5: statisticsHomogenizing, considering randomness and size effect of the mesomonas model, analyzing the void ratio, the random distribution of the spherical holes and the compressive strength f of the unit cell size random factors on the equivalent simplified stress-strain curve of the mesomonas model simultaneously c ′ s And the elastic modulus E ', the influence of the equivalent friction angle beta' of the extended linear drager-Prager model; setting the size of the mesomonas model to be 7mm, and repeating the steps S1 to S4 to obtain the compressive strength f 'of the equivalent simplified stress-strain curve of the mesomonas model under different hole rates' cs And elastic modulus E ', expanding equivalent friction angle beta' of the linear Drucker-Prager model, fitting equivalent parameters of the mesomonas model one by one, and obtaining a relational expression of each equivalent parameter and the void ratio p;
s6: the method comprises the steps of establishing an SHPB test device and a random sample numerical model, simplifying the cross sections of an incident rod, a transmission rod and a sample of the SHPB test device from a circular shape to a square shape, adopting an incident wave measured in the test as an input stress wave of the numerical model, carrying out finite element mesh division, equally dividing the sample with randomly distributed ball holes into cube units with the side length of 7mm, and dividing the grids with the size the same as that of the selected cube units with the side length of 7 mm; the incident rod and the transmission rod are made of linear elastic materials, and the seawater aggregate concrete sample is made of an expanded Drucker-Prager model;
s7: solving by a dynamic explicit finite element method, reconstructing an SHPB test stress-strain curve, setting end face friction coefficients of a sample and an input transmission rod according to set material model parameters, calculating and solving by adopting a dynamic explicit finite element method, and obtaining a structural effect of taking side inertia constraint effect and end face friction effect into consideration by 'reconstructing' the porous concrete SHPB test stress-strain curve with randomly distributed ball outlet holes, thereby obtaining dynamic compressive strength of true strain rate effect of a concrete material without taking into consideration;
s8: calculating the true strain rate effect of the porous concrete with randomly distributed spherical pores, and obtaining a dynamic strength growth factor DIF-f through experimental test c Dynamic strength growth factor DIF-f when the true strain rate effect of the sphere hole random distribution porous concrete material is not considered cd,lat-μ To be only structurally effectiveIt should be caused that the dynamic strength increase factor DIF-f is generated by the true strain rate effect of the material c,r ＝DIF-f c -DIF-f cd,lat-μ +1。
2. The method for calculating the structural effect of the porous concrete SHPB test with randomly distributed spherical pores according to claim 1, wherein the calculation method can be applied to porous concrete pavement engineering with randomly distributed spherical pores.
3. The method for calculating the structural effect of the porous concrete SHPB test with randomly distributed spherical holes according to claim 1, wherein the calculation method can be applied to island protection engineering.
4. The method for calculating the structural effect of the porous concrete SHPB test with randomly distributed spherical holes according to claim 1, wherein the calculation method can be applied to open sea island reef breakwater engineering.
5. The method for calculating the structural effect of the porous concrete SHPB test with randomly distributed spherical pores according to claim 1, wherein the calculation method can be applied to lawn road engineering.
6. The method for calculating the structural effect of the SHPB test of porous concrete with randomly distributed spherical pores according to claim 1, wherein the step S3 is to divide the material units of the porous concrete matrix with randomly distributed spherical pores by finite element grids to represent the inner boundaries of the spherical pores of the unit cell.
7. The method for calculating the structural effect of the porous concrete SHPB with randomly distributed spherical pores according to claim 1, wherein the parameters in S5 are random variables related to the pore rate of the mesomonas model, the random distribution of the spherical pores, and the unit cell size, and only the randomness of the pore rate of the mesomonas model is considered for simplifying the calculation of randomness caused by the random distribution of the spherical pores.
8. The method for calculating the structural effect of the porous concrete SHPB with randomly distributed spherical pores according to claim 1, wherein the equivalent simplified stress-strain curve compressive strength f of each mesh unit material model in S6 is characterized by c ′ s The modulus of elasticity E 'and the equivalent friction angle beta' are determined from the calculated void fraction of the cell and the fitted curve obtained previously.
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