CN110750933B - Accurate interface tracking processing method for coupling Lagrange particles and Euler method - Google Patents
Accurate interface tracking processing method for coupling Lagrange particles and Euler method Download PDFInfo
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Abstract
The invention relates to an accurate interface tracking processing method for coupling Lagrange particles and a Euler method, and belongs to the field of computational explosion mechanics. The method comprises the steps of 1, aiming at a simulation model to be analyzed, and carrying out initialization setting on the created simulation model; 2. and calculating the artificial viscosity value, the stress tensor and the grid speed updating amount of the grid in each set time step. 3. Determining a topological relation between the grid and the particle to realize the mapping of the grid physical quantity to the particle; 4. determining the position of particle movement; 5. determining a topological relation between the moved particles and the grid so as to realize the mapping of the particle physical quantity to the grid; 6. calculating a state equation and a control equation corresponding to the simulation model; 7. and updating the grid and particle physical quantities of the simulation model at the boundary of the computational domain. The invention well processes the large deformation and dynamic damage process of the material and effectively realizes the accurate numerical simulation calculation of the explosion and impact problems.
Description
Technical Field
The invention relates to an accurate interface tracking processing method for coupling Lagrange particles and a Euler method, and belongs to the field of computational explosion mechanics.
Background
Computer numerical simulation has gradually become an important means to solve complex problems in engineering applications and scientific computing. The computer numerical simulation test technology has the advantages of safety, confidentiality, flexible design, good repeatability, controllable environment and process, high cost effectiveness ratio and the like, has important functions and significance for understanding the nature of problems and establishing theoretical models, and is an effective means for improving the research and development of weapons and ammunition and the prevention and rescue level of explosion disasters in the future. In addition, the numerical simulation is not restricted by external environment and conditions, the change rule of each physical quantity under different conditions can be researched, and the limitation of experiment and theoretical research can be broken through. With the continuous improvement of computer hardware performance and the development of parallel technology, the scale and efficiency of solving problems by using a numerical simulation method are greatly improved, and the method is more and more widely applied to the research of explosion problems.
The explosion and impact problems are transient dynamics problems related to extreme conditions such as high strain rate, high temperature, high pressure, phase change, mutual coupling and even mixing among various media such as gas, liquid and solid, severe deformation and even breakage of materials and the like. Under these extreme conditions, numerical simulation of explosion and shock problems becomes very difficult, requiring the handling of large deformations of the material, interfaces of various substances and various strong discontinuities, much more complex than the usual fluid, aerodynamic and structural dynamics problems. The Euler method is a preferred method for solving the problems, and the core idea is that a fixed space coordinate system is adopted, materials flow in and out through a grid boundary, and the large deformation of the materials does not directly influence numerical calculation, so that the large deformation problem can be naturally processed, but the problem of interface processing among multiple materials is accompanied, and the precision of the method on tracking the material interface is not higher than that of the Lagrange method.
Later, a coupling algorithm combining the advantages of the Euler method and the Lagrange method, namely an ale (arbitrary Lagrangian eulerian) method, has appeared, the idea of which is mainly based on the Lagrange method, a large deformation problem of a Euler grid processing grid is locally introduced, but the Euler grid processing grid can only process a local area, and a lot of difficulties are still faced to solve transient problems with large deformation, such as explosive shock waves and deep penetration. In recent years, various high-precision algorithms have appeared, which can better deal with the material interface problem and effectively improve the material interface resolution, representative examples of which are tvd (total Variation digital), ENO (essential Non-oscillotory), weno (weighted ENO), and the like, but the solution of the algorithms is more complicated and the calculation time is increased rapidly; meanwhile, various non-grid methods mainly including an SPH smooth particle fluid dynamics method, a unitless Galerkin method, a Material Point Method (MPM), and the like, are also gradually becoming hot points for research in the fields of computational fluid dynamics and computational explosion dynamics, and the non-grid method has advantages in tracking material flow, but for large-scale scientific problems, an increase in computational scale causes a rapid increase in computational load, and under certain hardware conditions, a program is deadlocked and has a long computational duration.
Disclosure of Invention
The invention aims to solve the problem that the Euler method is difficult to clearly track the motion history of a multi-material interface, and provides an accurate interface tracking processing method for coupling Lagrange particles with the Euler method.
The method has the advantages that the Euler method is easy to handle the problem of large deformation and the Lagrange method is easy to track the deformation process of the material, overcomes the numerical fluctuation of the particle method caused by the limited number of particles, and realizes the accurate numerical simulation calculation of the explosion and impact problems.
The purpose of the invention is realized by the following technical scheme.
A method of precision interface tracking processing coupling Lagrange particles and Euler methods, comprising the steps of:
step 1: aiming at a simulation model to be analyzed, initializing the created simulation model, wherein the initialization comprises the steps of determining the size of a calculation domain, position information and geometric dimension information of various materials in the calculation domain, grid step length and coordinates, grid medium identification, particle arrangement, material properties and parameters, setting of simulation conditions, initial calculation control parameters and the like;
step 2: and calculating the artificial viscosity value, the stress tensor and the grid speed updating amount of the grid in each set time step. Wherein the artificial viscosity value is determined by the velocity gradient change of the adjacent grids, the density of the material and the artificial viscosity coefficient; circularly obtaining the strain rate, rotation rate and stress of each grid, and determining the stress tensor of the current grid based on a stress rate formula; further, considering the gradient effect of the stress tensor, determining the speed updating amount of the material in the grid;
and step 3: the topological relationship between the mesh and the particles is determined to achieve mapping of the mesh physical quantity to the particles.
Wherein the grid physical quantity is updated after a set time step is carried out after the step 2. Based on the topological relation between the grids and the particle influence domains, the volume share of the particle influence domains in each grid is obtained through solving, all the particle influence domain volumes in the grids are added and summed to obtain the sum of the influence domain volumes of the grids, and the physical quantities of the grids are mapped to the particles according to the volume share ratio, wherein the physical quantities comprise mass, momentum, volume, energy and the like.
And 4, step 4: the location of the particle movement is determined.
And 2, updating the physical quantity of the particles, and further obtaining the velocity of the particles through a volume weighting formula. After the velocity is obtained, the position coordinate of the particle at the next moment can be obtained by multiplying the velocity by the time step length.
And 5: determining a topological relationship between the moved particles and the grid to achieve mapping of the particle physical quantities to the grid.
Based on the topological relation between the moved particle influence domains and the grids, the volume share of the moved particle influence domains in each grid is obtained through solving, the volume ratio of the volume share in the particle influence domains is calculated, and the physical quantities of the particles are mapped to the grids according to the ratio, wherein the physical quantities comprise mass, momentum, volume, energy and the like.
Step 6: and calculating a state equation and a control equation corresponding to the simulation model.
After step 5, each physical quantity in the grid changes, and the state of each material needs to be updated and calculated, that is, the state equation and the control equation are solved. Wherein the calculation of the state equations includes determining the pressure of each material within each grid, with different materials corresponding to different state equations. The calculation of the control equation comprises solving conservation equations of mass, momentum and energy, and updating the mass, momentum and energy of each material medium in the grid.
And 7: and updating the grid and particle physical quantities of the simulation model at the boundary of the computational domain.
After the step 6, whether each material medium in the calculation domain flows to the boundary or not needs to be judged and corresponding processing is carried out, and if the material medium does not flow to the boundary, the material medium does not need to be processed; when the material medium flows to the boundary, it is necessary to perform boundary condition calculation, that is, to update the physical quantities of the boundary mesh and the particles in accordance with the set boundary conditions when the material medium flows to the boundary.
And 8: and outputting a corresponding simulation result based on the set termination condition, wherein the simulation result comprises the merged output of all the simulation data and the output of the restart file.
The eight steps are adopted to realize accurate numerical simulation calculation of explosion and impact problems.
Advantageous effects
According to the method, the particles with a certain influence domain are introduced into the background grid of the Euler method to track the substances in the grid, the hexahedron influence domain is used for carrying out interpolation mapping on the particles and the grid physical quantity, numerical value fluctuation of the particle method due to limited particle quantity is overcome, the accurate interface tracking processing method for coupling the Lagrange particles and the Euler method has more excellent calculation performance, and the fixed grid is added, so that embedding cannot occur between different substances due to the single value of mapping. The accurate interface tracking processing method for coupling the Lagrange particles and the Euler method has the advantages that the Euler method is easy to process the large deformation problem and the Lagrange method is easy to track the deformation process of the material, solves the problem that the Euler method is difficult to clearly track the movement process of the multi-material interface, and effectively realizes accurate numerical simulation calculation of the explosion and impact problems.
Drawings
FIG. 1 is a flowchart showing the steps of a method for accurate interface tracking of a coupled Lagrange particle and Euler method according to the present invention;
FIG. 2 is a schematic diagram of a two-dimensional mapping of grid physical quantities to particles according to the present invention;
FIG. 3 is a schematic diagram of the present invention showing the influence domain of particles falling completely on the current grid;
FIG. 4 is a diagram illustrating the influence domain of a particle divided by two adjacent grids according to the present invention;
FIG. 5 is a diagram illustrating an influence domain of particles divided by four grids according to the present invention;
FIG. 6 is a schematic diagram of an influence domain of a particle divided by eight grids according to the present invention;
FIG. 7 is a schematic diagram of a two-dimensional mapping of particle physical quantities to a grid according to the present invention;
FIG. 8 is a comparison of the results of numerical simulations of the process of the present invention for penetration of a steel sheet with real experiments;
FIG. 9 is a comparison of the numerical results of the residual velocity of a projectile penetrating a steel sheet in accordance with the present invention with real experimental data;
figure 10 is a comparison of shaped charge form figure results according to the present invention with experimental results.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the method for processing an accurate interface tracking by coupling Lagrange particles with a Euler method according to the present invention includes the following steps:
(1) creating a simulation model aiming at the problem to be analyzed, and carrying out initialization setting on the created simulation model; determining the size of a calculation domain, position information and geometric dimension information of various materials in the calculation domain, grid step length and coordinates, grid medium identification, arrangement of particles, material properties and parameters, setting of simulation conditions, initial calculation control parameters and the like;
specifically, as a preferred example of the present invention, the step 1 includes:
step 101, creating a simulation model aiming at a problem to be analyzed, and setting the size of an area needing calculation, namely calculation area intervals in three directions; in the calculation domain, constructing a geometric model of each material of a problem to be simulated;
step 102, setting grid step lengths in three directions to realize grid division, obtaining information of the divided grids and storing the information into grid data, wherein the grid information comprises grid serial numbers, grid coordinates and material medium identifications represented by the grids;
and 103, combining the material medium marks represented by the grids, selecting the grids needing to accurately track the deformation process of the material, and distributing Lagrange particles in each direction according to actual requirements. Determining the step length of the influence domain of Lagrange particles based on the principle that Lagrange particle influence areas are closely connected and completely cover all media in a calculation domain, and calculating the coordinate information of each Lagrange particle;
step 104, setting the properties and model parameters of the materials, and determining the data of density, yield strength, internal energy of melt ratio, Young modulus, Poisson ratio, type and parameters of the material model and the like of each material related to the simulation model;
step 105, setting boundary conditions, and determining the boundary conditions of the simulation model, wherein the boundary conditions comprise a solid wall boundary condition, a continuous boundary condition, a symmetric boundary condition and the like;
106, setting initial calculation control parameters; the calculation control parameters comprise information such as total calculation steps, initial time step length, step interval of stored results and the like.
(2) Calculating the artificial viscosity value, the stress tensor and the grid speed updating amount of the grid in each set time step; (ii) a Specifically, as a preferred example of the present invention, the step 2 includes:
step 22, calculating a stress tensor of the grid, circularly obtaining a strain rate, a rotation rate and a stress of each grid, calculating the stress tensor of the current grid based on a stress rate formula, obtaining a temporary updated stress through the stress of the grid and the stress tensor, judging whether the stress is greater than the corresponding material yield strength, obtaining the stress after yielding by using a radial return method if yielding occurs, and not processing if yielding does not occur;
and step 23, updating the grid speed. The gradient effect of the stress tensor is considered, the speed and the specific internal energy of the material in the grid are obtained, and the momentum and the energy of the material in the grid are further calculated; specifically, the velocity and specific energy content of the material can be calculated from the following equations
Wherein u is the grid velocity, t is the time parameter, e is the internal energy of the grid ratio, I is the volume stress tensor, S is the bias stress tensor,
for the strain rate tensor, P is the hydrostatic pressure.
(3) Determining the topological relation between the grids and the particles in each set time step to realize the mapping of the grid physical quantity to the particles; fig. 2 shows a schematic diagram of the mapping of grid physical quantities to particles in a two-dimensional case. In the three-dimensional numerical calculation, 27 positional relationships are counted in the case where there are 4 topological relationships affected by grids and particles, as shown in fig. 3 to 6. FIG. 3 shows a case where the influence domain of the particles falls completely in the current mesh, and only one topological relationship exists; FIG. 4 shows a case where the influence domain of a particle is divided by two adjacent grids, and 6 topological relations are included; FIG. 5 shows a case where the influence domain of a particle is divided by four grids, and 12 topological relations are included; FIG. 6 shows a case where the influence domain of a particle is divided by eight grids, and 8 topological relations are included. Based on the topological relation between the grids and the particle influence domains, the volume share of the particle influence domains in each grid is obtained through solving, all the particle influence domain volumes in the grids are added and summed to obtain the sum of the influence domain volumes of the grids, and the physical quantities of the grids are mapped to the particles according to the volume share ratio, wherein the physical quantities comprise mass, momentum, volume, energy and the like.
(4) Determining the position of particle movement after a set time step; similar to the mapping of grid physical quantities to particles, the velocity of particles can be obtained by a volume weighting formula. After the velocity is obtained, the position coordinate of the particle at the next moment can be obtained by multiplying the velocity by the time step length.
(5) Determining the topological relation between the moved mass points and the grid in each set time step to realize the mapping of the mass point physical quantity to the grid; FIG. 7 is a schematic diagram showing the mapping of particle physical quantities to a grid in a two-dimensional case. Similarly, in the three-dimensional numerical calculation, there are 27 kinds of positional relationships in total in the case of 4 topological relationships between the moved particle influence domain and the mesh, and the schematic diagrams thereof can be shown in fig. 3 to 6. Based on the topological relation between the moved particle influence domains and the grids, the volume share of the moved particle influence domains in each grid is obtained through solving, the volume ratio of the volume share in the particle influence domains is calculated, and the physical quantities of the particles are mapped to the grids according to the ratio, wherein the physical quantities comprise mass, momentum, volume, energy and the like.
(6) Calculating a state equation and a control equation corresponding to the simulation model in each set time step; specifically, as a preferred example of the present invention, the step 6 includes:
and step 61, calculating a state equation, and solving the pressure of each substance in each grid, wherein different substances correspond to different state equations. Both the explosion and impact problems are high pressure, high strain rate conditions, in which case the solid material will enter the fluid state instantaneously, its ability to resist deformation can be neglected, only the relation between hydrostatic pressure and volumetric strain, specific internal energy needs to be considered, and the solid material can be treated as a non-viscous compressible fluid. Thermodynamic parameters related to the fluid mechanics equation set are density rho, pressure P, temperature T, internal energy e, thermodynamic entropy s and enthalpy h. According to the thermodynamic theory, only two of the above parameters are mutually independent parameters, and the rest parameters can be derived from other two parameters. The equation of state considered is in the form of pressure as a function of density and internal energy:
P＝P(ρ,e) (1)
the pressure determined by equation (1) includes an elastoplastic component, and therefore when determining the hydrostatic pressure, the plastic pressure component must be subtracted, here using the following method:
wherein, the plane is a pressure correction coefficient, Y0Is the yield strength of the material.
The numerical simulation of concrete failure under blast and impact loads involves media such as explosives, metals, air, and concrete. For the state equations of the media, variable index multi-party gas state equation, JWL state equation, Grunersen state equation, ideal gas state equation, HJC state equation and the like can be respectively adopted, and the pure grid pressure for a single substance can be directly calculated by the state equations. For the calculation of the mixed grid pressure, the volume fraction weighting method is adopted to calculate the pressure of the mixed grid, and the pressure P of each substance is calculated by the formula (1)αThe pressure of the hybrid grid is calculated by:
wherein σαIs the volume fraction of each substance;
and step 62, calculating a control equation, solving a mass, momentum and energy conservation equation, and updating the mass, momentum and energy of each material medium in the grid.
(7) Updating the grid physical quantity of the simulation model at the boundary of the calculation domain within each set time step; specifically, as a preferred example of the present invention, the step 7 includes performing boundary condition calculation to update the physical quantities of the boundary mesh and the particles by processing the material medium flowing to the boundary according to the set boundary conditions. The method specifically comprises the following steps: judging the material flow in the boundary grid, and if the material flow in the grid does not reach the boundary in the time step, normally updating the physical quantities of the grid and the particles; if the material flow in the grid reaches the boundary, processing the grid and the particle physical quantity according to the set boundary condition;
(8) and outputting a corresponding simulation result based on the set termination condition.
Specifically, as a preferred example of the present invention, the step 8 includes: if the currently calculated step number meets the output set condition, merging and outputting all the simulation data and recording the serial number mark of the output file; writing variables and variable names contained in grids and particles into a file; after finishing the data output required by post-processing display, writing the increment information, the material and the calculation control information required by restart into the same file and recording the name of the output file.
Specifically, fig. 8 shows the comparison of the results of numerical simulation of the process of piercing a steel sheet with an elastomer with the real experiment, where (a) is the real experiment data and (b) is the numerical simulation result, and the numerical simulation result is well matched with the real experiment data from the comparison at each time. The simulation was performed on the projectiles at different initial speeds to obtain corresponding residual speed data, and fig. 9 shows the comparison of the numerical results of the residual speeds of the projectiles penetrating through the steel sheet with the real experimental data. The accurate interface tracking processing method coupled with the Larange particle and the Euler method can better track the deformation condition of the target plate in the penetration process of the projectile body, and the residual speed is well matched with real experimental data. Figure 10 shows the comparison of shaped charge shaping values with experimental results, from which it can be seen that the use of a precise interface tracking process coupled with the Larange particle and Euler methods according to the present invention effectively simulates the shaped charge shaping process.
Through the embodiment, the accurate interface tracking processing method for coupling Lagrange particles and the Euler method combines the advantages of the Euler method and the Lagrange method, can well process the large deformation and dynamic damage process of materials, and can be better applied to numerical simulation research of various explosion impact problems.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution of the present invention and its inventive concept within the technical scope of the present invention.
Claims (4)
1. A method of accurate interface tracking processing coupling Lagrange particles and Euler methods, comprising the steps of:
step 1, aiming at a simulation model to be analyzed, initializing the created simulation model, wherein the initialization comprises the steps of determining the size of a calculation domain, and setting position information and geometric dimension information, grid step length and coordinates, grid medium identification, particle arrangement, material attributes and parameters, simulation condition setting and initial calculation control parameters of various materials in the calculation domain;
step 2, calculating the artificial viscosity value, the stress tensor and the grid speed updating amount of the grid in each set time step, wherein the artificial viscosity value is determined by the speed gradient variation of adjacent grids, the density of the material and the artificial viscosity coefficient; circularly obtaining the strain rate, rotation rate and stress of each grid, and determining the stress tensor of the current grid based on a stress rate formula; further, considering the gradient effect of the stress tensor, determining the speed updating amount of the material in the grid;
step 3, determining a topological relation between the grids and the particles to realize mapping of grid physical quantities to the particles, wherein the grid physical quantities are updated after a set time step is carried out after the step 2, solving to obtain volume shares of the particle influence domains in each grid based on the topological relation between the grids and the particle influence domains, adding and summing all the particle influence domain volumes in the grids to obtain the sum of the influence domain volumes of the grids, and mapping the physical quantities of the grids to the particles by volume share ratio, wherein the physical quantities comprise mass, momentum, volume and energy physical quantities;
step 4, determining the moving position of the particles; step 2, updating of physical quantity of the particles is realized, and the velocity of the particles can be obtained through a volume weighting formula; after the speed is obtained, multiplying by the time step length to obtain the position coordinate of the particle at the next moment;
step 5, determining a topological relation between the moved particles and the grids to realize the mapping of the particle physical quantity to the grids, solving to obtain volume shares of the moved particle influence domains in each grid based on the topological relation between the moved particle influence domains and the grids, calculating the volume proportion of the volume shares in the particle influence domains, and mapping the particle physical quantity to the grids by the proportion, wherein the physical quantities comprise mass, momentum, volume and energy physical quantity;
step 6, calculating a state equation and a control equation corresponding to the simulation model; after the step 5, all physical quantities in the grid are changed, and the states of all materials need to be updated and calculated, namely the solution of a state equation and a control equation is carried out; wherein the calculation of the state equation comprises determining the pressure of each substance in each grid, and different substances correspond to different state equations; calculating a control equation, namely solving a mass, momentum and energy conservation equation, and updating the mass, momentum and energy of each material medium in the grid;
step 7, updating grid and particle physical quantities of the simulation model at the boundary of the computational domain; after the step 6, whether each material medium in the calculation domain flows to the boundary or not needs to be judged and corresponding processing is carried out, and if the material medium does not flow to the boundary, the material medium does not need to be processed; if the material medium flows to the boundary, the physical quantities of the boundary grid and the mass points are updated according to the set boundary conditions by calculating the boundary conditions;
and 8, outputting a corresponding simulation result based on the set termination condition, wherein the simulation result comprises the merged output of all the simulation data and the output of the restart file.
2. The method of claim 1, wherein step 1 comprises the steps of:
step 101, creating a simulation model aiming at a problem to be analyzed, and setting the size of an area needing calculation, namely calculation area intervals in three directions; in the calculation domain, constructing a geometric model of each material of a problem to be simulated;
step 102, setting grid step lengths in three directions to realize grid division, obtaining information of the divided grids and storing the information into grid data, wherein the grid information comprises grid serial numbers, grid coordinates and material medium identifications represented by the grids;
103, selecting a grid which needs to accurately track the deformation process of the material by combining material medium marks represented by the grid, distributing Lagrange particles in each direction according to actual requirements, determining the influence domain step length of the Lagrange particles on the basis of the principle that Lagrange particle influence areas are closely connected and completely cover all media in a calculation domain, and calculating coordinate information of each Lagrange particle;
step 104, setting the properties and model parameters of the materials, and determining the density, yield strength, internal energy of melt ratio, Young modulus, Poisson ratio and the type and parameter data of the material model of each material related to the simulation model;
step 105, setting boundary conditions, and determining the boundary conditions of the simulation model, wherein the boundary conditions comprise a solid wall boundary condition, a continuous boundary condition and a symmetrical boundary condition;
106, setting initial calculation control parameters; the calculation control parameters comprise the total calculation step number, the initial time step length and the step number interval information of the stored result.
3. The method of claim 1, wherein step 2 comprises the steps of:
step 21, calculating the current grid speed uiAnd next mesh velocity ui+1Defining a velocity gradient Δ u ═ ui+1-uiThen the artificial tack can be represented by q ═ ρ (| Δ u | - Δ u) [ a |n(|Δu|-Δu)+bnc]Calculated, where ρ is in the gridDensity of material, anAnd bnSecond and first order artificial viscosity coefficients, c being a constant associated with the material;
step 22, calculating a stress tensor of the grid, circularly obtaining a strain rate, a rotation rate and a stress of each grid, calculating the stress tensor of the current grid based on a stress rate formula, obtaining a temporary updated stress through the stress of the grid and the stress tensor, judging whether the stress is greater than the corresponding material yield strength, obtaining the stress after yielding by using a radial return method if yielding occurs, and not processing if yielding does not occur;
step 23, updating the speed of the grid, considering the gradient effect of the stress tensor to obtain the speed and specific internal energy of the material in the grid, and further calculating to obtain the momentum and energy of the material in the grid; the velocity and specific energy content of the material were calculated from the following formulas
Wherein u is the grid velocity, t is the time parameter, e is the internal energy of the grid ratio, I is the volume stress tensor, S is the bias stress tensor,
for the strain rate tensor, P is the hydrostatic pressure.
4. The method of claim 1, wherein said step 6 comprises the steps of:
step 61, calculating a state equation, solving the pressure of each substance in each grid, wherein different substances correspond to different state equations, and explosion and impact problems are both the conditions of high pressure and high strain rate, under the conditions, a solid material can instantly enter a fluid state, the deformation resistance of the solid material can be neglected, only the relation between hydrostatic pressure and volume strain and specific internal energy needs to be considered, the solid material can be treated as a non-viscous compressible fluid, and thermodynamic parameters related to a fluid mechanics equation set are density rho, pressure P, temperature T, internal energy e, thermodynamic entropy s and enthalpy h; according to the thermodynamic theory, only two parameters are mutually independent parameters, other parameters can be derived from other two parameters, and the considered state equation is in the form of a function of pressure, density and internal energy:
P＝P(ρ,e) (1)
the pressure determined by equation (1) includes an elastoplastic component, and therefore when determining the hydrostatic pressure, the plastic pressure component must be subtracted, here using the following method:
wherein, the plane is a pressure correction coefficient, Y0Is the yield strength of the material;
the numerical simulation of concrete destruction under explosion and impact load involves explosive, metal, air and concrete media, variable index multi-party gas state equation, WL state equation, Grunersense state equation, ideal gas state equation and HJC state equation are respectively adopted for the state equations of the media, pure grid pressure for a single substance can be directly calculated by the state equations, the pressure of a mixed grid is calculated by adopting a volume fraction weighting method for calculating the pressure of the mixed grid, and the pressure P of each substance is calculated by the formula (1)αThe pressure of the hybrid grid is calculated by:
wherein σαIs the volume fraction of each substance;
and step 62, calculating a control equation, solving a mass, momentum and energy conservation equation, and updating the mass, momentum and energy of each material medium in the grid.
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| CN107133397B (en) * | 2017-04-27 | 2018-10-19 | 山东大学 | A method of two-way wind-structure interaction is carried out to biovalve based on ALE methods |
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