Near-field dynamics simulation method based on split Hopkinson bar impact test

Abstract

The invention discloses a near-field dynamics simulation method based on a split Hopkinson bar impact test, and the method comprises the following steps: building an SHPB test system bar system and test piece entity model, endowing each region with material parameters, and using a material point set to disperse a structure; calculating the interaction of material points in the rod piece and the test piece by using a key type or axial symmetry near-field dynamic model; respectively adopting a key force density function, a contact algorithm of a rigid body and a deformable body and a short-distance repulsive force model to simulate interaction between SHPB rod pieces, between the rod pieces and a test piece and between damaged substance points; an initial speed is given to an impact rod, an initial condition and a boundary condition are set, the position and the speed of a material point are updated in real time by adopting a Verlet algorithm, structural damage and cracking are described by using a broken key criterion, and analysis of the spallation thickness, the spallation section flying speed and the strain time travel curve of the typical spallation problem of the SHPB impact test piece is carried out. According to the invention, the simulation of the SHPB rod piece wave propagation process and the impact stratification damage of a typical SHPB impact test piece can be stably and accurately realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of material and structural failure simulation, and particularly relates to a peridynamic simulation method based on a split Hopkinson bar impact test. Background Art

[0002] Spall fracture is a common dynamic fracture mode in structures subjected to high-speed impact, also known as Hopkinson fracture. Specifically, the compressive stress wave reflected from the free surface generates a tensile stress wave, and the combined action of the tensile wave and the compressive wave causes the stress state of the material to exceed the tensile strength, and spall fracture may occur.

[0003] In the early 20th century, Hopkinson discovered the spall phenomenon and designed a prototype of the pressure bar device in 1914. After continuous improvement by researchers, the split Hopkinson pressure bar (SHPB) technology was finally established. At present, the SHPB test has become a basic technology for studying the dynamic fracture behavior, dynamic mechanical properties, and dynamic constitutive relationship of materials at high strain rates in impact dynamics. However, experimental research has limitations such as a relatively high risk factor, scattered data, and difficulty in observation, while numerical simulation methods can make up for some deficiencies in experiments.

[0004] Currently, relatively few numerical simulation studies on the split Hopkinson bar impact test technology have been published. The root cause lies in the theoretical limitations of classical continuum mechanics, the computational scale limitations of methods such as molecular dynamics, and the fact that dynamic load conditions exacerbate the complexity of the problem. In addition, based on the basic assumptions of one-dimensional stress waves and uniform stress distribution, some studies have ignored the influence of transverse inertia effects on the wave propagation process in the Hopkinson bar impact test technology. Therefore, it is of great significance to develop a systematic theoretical method and numerical calculation tool for the split Hopkinson bar impact test technology.

[0005] The simulation of solid structure failure has long been a concern in both academic and engineering fields. Spall fracture of structures is a typical phenomenon of solid failure. The conventional modeling and analysis methods for such discontinuous problems are based on the traditional continuum mechanics theory of partial differential equations and its finite element method. However, due to the lack of length scale parameters for describing fractures, this method requires preset crack paths and crack propagation criteria, thus facing problems such as singularities at discontinuities, mesh dependence, inaccurate fracture description, and computational accuracy bottlenecks. Subsequently, the extended finite element method and various meshless methods have been developed. Although the extended finite element method has difficulties in tracking crack surfaces when dealing with complex three-dimensional fractures, and meshless methods have advantages in the simulation and analysis of large deformations of structures, there are still problems such as low computational accuracy and efficiency, and singularities at discontinuities. Peridynamics uses non-local spatial integral equations to describe the mechanical behavior of materials, introduces length scale parameters for describing structural fractures, and avoids singularities in solving discontinuous problems by traditional numerical calculation methods, showing inherent advantages in analyzing fracture failure problems such as crack propagation and spallation.

[0006] However, there are still some areas that need to be developed and improved in the three mainstream models of existing peridynamics (bond-based, classical state-based, and non-classical state-based peridynamics) and their meshless particle methods. The bond-based and classical state-based peridynamics have insufficient descriptions of complex mechanical behaviors such as plasticity and strain rate effects, and are not closely related to the traditional stress-strain tensor. The non-classical state-based peridynamics can effectively overcome the above limitations. However, the developed non-classical state-based peridynamics models show numerical instability of displacement oscillation during static and dynamic deformation calculations, and the models need to be further improved and the computational efficiency needs to be increased.

[0007] Recently, the non-spherical influence function method has been proposed and used to solve the numerical instability of the non-classical state-based peridynamics method. This method improves the computational accuracy of the model without additional computational costs, but this method has not been applied to structural dynamic deformation, especially damage cracking analysis, and the model algorithm also needs to be further improved. In addition, considering the deficiency of the bond-based model in simulating complex dynamic mechanical behaviors such as strain rate effects, it is necessary to improve the bond-based model by combining with a bilinear damage model. Therefore, it is very necessary to develop the above bond-based and non-classical state-based peridynamics models and numerical algorithms, and apply them to the analysis of problems such as wave propagation in rods and spall fracture of typical SHPB impact specimens in split Hopkinson bar impact tests, and give theoretical modeling and numerical implementation details to give full play to the advantages of peridynamics in analyzing discontinuous problems and effectively guide engineering practice. Summary of the Invention

[0008] In order to solve the bottleneck problems faced by traditional continuum mechanics in dealing with discontinuous problems, the imperfections of existing peridynamics theoretical models and numerical solution systems, and the lack of simulation prediction and analysis means for split Hopkinson bar impact test technology, the present invention aims to provide a peridynamics simulation method based on split Hopkinson bar impact test. This method gives full play to the advantages of improved bond types and unconventional state-type axisymmetric peridynamics in accurate stability and fracture failure analysis, providing a scientific method for accurately simulating the wave propagation and spallation problems of split Hopkinson bar impact test technology.

[0009] In order to solve the technical problems, the technical solution of the present invention is as follows:

[0010] A peridynamics simulation method based on split Hopkinson bar impact test, the method comprising:

[0011] S1: Establish a geometric model of the split Hopkinson pressure bar (SHPB) test system and simplify it, divide the position areas of the bar system and the specimen, and respectively determine the corresponding material properties and configurations;

[0012] S2: Generate a set of discrete material points with uniform orthogonal distribution on the simplified model in step S1, and based on the bond-type peridynamics model or axisymmetric peridynamics model, establish the interaction relationship between the material points in the bar and the specimen. Combine experimental data to introduce a dynamic enhancement factor to dynamically strengthen the constitutive parameters of the material, and obtain a well-defined set of material points and interaction force model;

[0013] S3: For the contact interaction behaviors between the various parts of the test system, respectively adopt the following strategies to establish a contact force model, including: using a bond force density function model between the bars, using a rigid body and deformable body contact model between the bar and the specimen, and using a short-range repulsive force model between the material points in the damage evolution region, so as to completely describe the interaction mechanical behaviors of the contact regions in the system, and output the contact force model and the interaction force between the contact regions;

[0014] S4: Determine the uniform initial velocity of the impact bar, and the other parts of the system are initially in a stationary state. Simulate the process of the bullet device impacting and loading in the real test, and output the velocity and displacement state evolution information of each bar during the impact process through dynamic simulation, and establish the dynamic response basis under the initial loading conditions, that is, obtain the preliminary simulation results of the impact process;

[0015] S5: Select the corresponding material points in the geometric models of the bar and the specimen to calculate and output the strain, select velocity test points on the incident bar and the specimen, output and record the velocity data of the entire impact process, and determine the flying-out velocity of the specimen spallation section and the velocity of the incident bar;

[0016] S6: Initialize the strain, stress, resultant force, and damage variable, set the initial conditions, and apply body force, stress, and displacement boundary conditions;

[0017] S7: Perform explicit dynamic calculations to update the positions, velocities, and accelerations of the material points in real time; use the critical elongation rate bond-breaking criterion to describe damage cracking; output the displacement results and damage results at different times, record the incident bar velocity and the spall segment flying velocity, as well as the strain time history data of the test points on the specimen, calculate the relationship between the spall segment flying velocity and the incident bar velocity, the spall occurrence position and the spall thickness, and plot the strain time history curve of the test points to analyze the stress wave propagation behavior in the bar and the evolution mechanism of the spall failure process of the typical SHPB impact specimen in the split Hopkinson bar impact test.

[0018] Furthermore, in the step S2, generating a discrete set of material points includes:

[0019] Perform a uniform orthogonal meshless particle division on the geometric model of the entire SHPB system. The size of the material points meets the calculation accuracy requirements. There are a total of N material points. The geometric model uses square material points with a size of d. For the SHPB bar, d = L / 6000 to L / 1000, and for the specimen, d = l / 1500 to l / 200, where L and l are the maximum side lengths of the bar system and the specimen solid model;

[0020] Determine the radius of the near-field range as δ = m×d according to the material point size d and the characteristic scale of the loaded material structure, where m is the ratio of the near-field range to the material point size; determine the near-field range associated with the point according to the initial position coordinates of the material point and the radius of the near-field range Expressed as:

[0021]

[0022] where, x (i) and x (j) are the coordinates of the material points in the initial configuration.

[0023] Furthermore, in the step S2, using the bond-type peridynamic model to establish the interaction relationship between the material points in the bar and the specimen, including:

[0024] The peridynamic equation of motion is:

[0025]

[0026] where, u (i) and u (j) are displacement vectors, ρ is the material point density, f (ij) is the non-local interaction force density vector between any two material points, with the unit of N / (m 3 ·m3 ), where \(b\) is the body force density, and the initial relative position vector and the current relative position vector are defined as \(\xi\) (ij) = \(x\) (j) - \(x\) (i) and \(\eta\) (ij) = \(u\) (j) - \(u\) (i) ;

[0027] Introduce the bilinear damage constitutive model into the improved micro - elastic - brittle model, and the bond force density vector of the bond - type peridynamics is obtained as:

[0028]

[0029] where the relative elongation of the bond is \(s = (|\xi\) (ij) +\(\eta\) (ij) |-|\xi\) (ij) |) / |\xi\) (ij) |, \(\mu\) is a scalar function describing the history - dependence of the fracture behavior, expressed as \(c(\xi\) (ij) , \(\delta)\) is the micro - modulus function, \(g(\xi\) (ij) , \(\delta)\) and \(c(0,\delta)\) are the kernel function of the cubic polynomial and the micro - modulus constant respectively, and \(d\) is a parameter used to describe the bilinear damage of the bond. They are respectively expressed as:

[0030]

[0031]

[0032] where \(E\) is the elastic modulus, \(v\) is the Poisson's ratio, the critical elongation \(\sigma\) T is the tensile strength of the specimen, and \(G\) F is the fracture energy release rate of the material.

[0033] Furthermore, in the step S2, or an axisymmetric peridynamics model is used to establish the interaction relationship between the rod and the material points in the specimen, including:

[0034] Based on the peridynamic differential operator method PDDO and the axisymmetric model of elasticity in space, establish an axisymmetric unconventional - state - type peridynamics model, and at the same time introduce the non - spherical influence function method to solve the numerical instability problem in the model. Define the following bond - associated nonlocal strain tensor:

[0035]

[0036] where \(u\) m = \(u\) m (x\) (i) ), \(u'\) m = \(u'\) m(x (i) + ξ (ij) )(m = z, r) are the displacement components of the material point, and r represents the radial distance of the material point from the axis of symmetry. and are peridynamic functions, which can be constructed by polynomials and include the non-spherical influence function ω(|ξ (ip) |, θ) term. The subscript on the left side of the equation indicates that the bond-associated integral on the right side of the equation is used. The bond-associated integral and the point-associated integral share the same peridynamic range. The influence of both the bond length and the change in the angle between bonds is considered simultaneously. ξ (ip) = x (p) - x (i) is the initial relative position vector between the material points of other bonds during the bond-associated integral. It also includes the target bond ξ . θ is the angle between ξ (ij) and ξ (ij) and ξ (ip) . The specific form of the non-spherical influence function is:

[0037]

[0038] where n1, n2, and n3 are constant coefficients. The magnitude of n1 represents the degree of influence of the bond length change, and n1 can be taken as 5 - 15. n2n3 controls the contribution degree of other bonds ξ (ip) in the (ij) to the target bond ξ

[0039] . n2n3 can be taken as 10 - 30, and n3 is an odd number.

[0040]

[0041] When damage occurs to the material point, the following damage reduction model is adopted for the influence function in the bond-associated nonlocal strain tensor: ij where s is the elongation rate of the bond, (i) is the critical elongation rate, D(x (i) , t) is the damage degree of the material point x critical . D

[0042] For the constitutive model part, the stress-strain relationship is updated using Hooke's law in generalized form, expressed as:

[0043] σ mn = λθδ mn + 2με mn

[0044] where the subscripts m and n represent z and r, and the volumetric strain should be The Lamé constants are and When damage occurs to a material point, each stress component is multiplied by a reduction factor 1 - D(x (i) , t);

[0045] The energy equivalence method is adopted to derive and establish a new bond - associated force vector t or force - vector state T[x (i) , t], expressed as:

[0046]

[0047] where t is the time variable, is the bond - associated Cauchy stress tensor. Under the small - deformation condition, the Cauchy stress tensor σ(x (i) ) is equal to the first Piola - Kirchhoff stress tensor P. The square brackets <·> indicate that the force - vector state acts on a certain bond to obtain a force vector, is for the material point x (i) the sum of the volumes of all material points x (j) within the near - field range of;

[0048] Furthermore, a new integral - type strong - form axisymmetric unconventional - state - type peridynamic motion equation is constructed as:

[0049]

[0050] where ρ is the material mass density and b is the body - force density vector acting on the material point.

[0051] Furthermore, in the step S2, the constitutive parameters of the material are dynamically strengthened, including:

[0052] The strain - rate conditions of different impact - velocity groups are obtained from the strain data collected through experiments. Then, combined with the existing experimental studies, the dynamic - enhancement factor DIF is used to strengthen the material - mechanical parameters of the geometric model, including the tensile strength σ T and the fracture - energy release rate G F , and the strengthening method is to directly multiply the above - mentioned mechanical parameters by the dynamic - enhancement factor DIF.

[0053] Furthermore, in the step S3, a rigid - body and deformable - body contact model is adopted between the rod and the specimen, and a short - range repulsive force model is adopted between the material points in the damage - evolution region, including:

[0054] During the impact - contact process, from time step t to the next time step t + Δt, it involves the material point x (k)The position update process and the update process of the interaction force between the rigid body and the deformable body are respectively expressed as:

[0055]

[0056] Among them, and v (k) represent the displacement and velocity of the material point x (k) , F (k) is the force exerted by the material point x (k) on the rigid impact body, and F is the resultant force received by the rigid impact body. When contact occurs On the contrary

[0057] In order to describe the interaction force between severely damaged material points or between severely damaged material points and the intact part of the specimen, the short-range repulsive force is expressed as:

[0058]

[0059] Among them, is the repulsive force constant, d = min{|x (i) -x (j) |, 1.414|Δx|} is the maximum action distance of the repulsive force.

[0060] Furthermore, in the step S5, in order to obtain strain data, it is necessary to select corresponding material points in the geometric models of the rod and the specimen according to the pasting positions of the strain gauges in the test device for strain calculation and output. The strain calculation formula of the material point x (k) is expressed as:

[0061]

[0062] Among them, x (k+d) and x (k-d) are adjacent material points with a distance of d from the material point x (k) ;

[0063] In order to obtain velocity data, it is necessary to select five to six material points at the non-impact ends of the incident rod and the specimen, output and record the velocity data of the entire impact process, and then calculate the weighted average of the velocities of these material points to represent the velocities of the incident rod and the spallation section of the specimen.

[0064] Furthermore, in the step S6, the initial conditions and boundary conditions are set as follows:

[0065] In the initial conditions, the initial velocities of the material points in the incident rod, the transmitted rod, and the specimen model are set to zero, and the initial displacement of the entire model is set to zero;

[0066] In the boundary conditions, displacement and force boundaries can be applied to one or more layers of material points at the boundary positions as needed. In the unconventional state-type axisymmetric peridynamic elastic model, a radial displacement constraint condition is applied to the material points on the axis of symmetry to restrict their radial displacement, i.e., the axisymmetric boundary.

[0067] Furthermore, in the step S7, explicit dynamics Velocity-Verlet calculation is performed, including:

[0068] Given the displacements and velocities at the initial moment, and applying time-dependent body forces as well as stress and displacement boundary conditions, an iterative loop calculation of time stepping is realized through the difference algorithm of the explicit Verlet velocity format to obtain the velocities and displacements at time t+Δt, which are:

[0069]

[0070]

[0071] where t is the current deformation moment, Δt is the time step, the subscripts n and n+1 correspond to the moments t and t+Δt respectively, and n is the number of calculation steps; are the velocities of the material points at t+Δt and t respectively, u (n+1) ,u (n) are the displacements of the material points at t+Δt and t respectively; for transient problems, the velocity field needs to be smoothed using the weighted average method, and the formula is:

[0072] <sin<2000320>

[0073] where ω(|ξ (ij) |) is the influence function, which is only related to the length of the bond. In addition, the velocity of the material point x (i) itself needs to be taken into account.

[0074] A peridynamic simulation system based on the split Hopkinson bar impact test, the system is applied to any one of the above methods, and the system includes:

[0075] Geometric modeling module: Establish a geometric model of the split Hopkinson pressure bar SHPB test system and perform simplification processing, divide the position areas of the bar system and the specimen, and determine the corresponding material properties and configurations respectively;

[0076] Discrete material point distribution module: Generate a set of uniformly orthogonally distributed discrete material points on the model simplified by the geometric modeling module, and based on the bond-type peridynamic model or the axisymmetric peridynamic model, establish the interaction relationship between the material points in the bar and the specimen, and introduce a dynamic enhancement factor to dynamically strengthen the constitutive parameters of the material in combination with experimental data to obtain a well-defined set of material points and the interaction force model;

[0077] Contact force model construction module: For the contact interaction behaviors between various parts in the test system, the following strategies are respectively adopted to establish a contact force model, including: adopting a bond force density function model between rods, a rigid body and deformable body contact model between rods and specimens, and a short-range repulsive force model between material points in the damage evolution region, so as to completely describe the interactive mechanical behaviors of each contact region in the system, and output the contact force model and the mutual forces between contact regions;

[0078] Impact loading simulation module: Determine the uniform initial velocity of the impact rod, and other parts in the system are initially in a static state. Simulate the process of the bullet device impacting and loading in the real test. Through dynamic simulation, output the evolution information of the velocity and displacement states of each rod during the impact process, and establish the basis of the dynamic response under the initial loading conditions, that is, obtain the preliminary simulation results of the impact process;

[0079] Strain and velocity output module: Select corresponding material points in the geometric models of the rods and specimens to calculate and output the strain. Select velocity test points on the incident rod and the specimen, output and record the velocity data throughout the impact process, and determine the flying-out velocity of the spallation section of the specimen and the velocity of the incident rod;

[0080] Initial condition setting module: Initially assign values to strain, stress, resultant force, and damage variables, set the initial conditions, and apply body force, stress, and displacement boundary conditions;

[0081] Explicit dynamics calculation module: Conduct explicit dynamics calculations, and update the positions, velocities, and accelerations of material points in real time; use the critical elongation rate bond-breaking criterion to describe damage cracking; output the displacement results and damage results at different times, and record the velocity of the incident rod, the flying-out velocity of the spallation section, and the strain time-history data of the test points on the specimen, calculate the relationship between the flying-out velocity of the spallation section and the velocity of the incident rod, the spallation occurrence position and the spallation thickness, and draw the strain time-history curve of the test points, and conduct an analysis of the propagation behavior of stress waves in the rod and the evolution mechanism of the spallation failure process of typical SHPB impact specimens in the split Hopkinson bar impact test.

[0082] A computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements a non-local dynamics simulation method based on the split Hopkinson bar impact test described in any one of the above.

[0083] A computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements a non-local dynamics simulation method based on the split Hopkinson bar impact test described in any one of the above.

[0084] A peridynamic simulation method based on the split Hopkinson bar impact test, and the specific inputs and outputs of each step are as follows:

[0085] S1: Geometric modeling and material property definition

[0086] Input: Specimen geometric features: including the geometric dimensions of the specimen and each rod. Material properties: the material properties of the specimen and the rods (such as elastic modulus, Poisson's ratio, tensile strength, etc.). Test conditions: including the applied loading conditions, environmental temperature, etc. Boundary conditions and initial conditions: such as boundary constraints, initial velocity, initial displacement, etc.

[0087] Output: Simplified geometric model: a simplified geometric model of the test system, which divides the position areas of the rod system and the specimen. Material property assignment: the material properties (such as elastic, plastic, fracture parameters, etc.) of each area have been defined.

[0088] S2: Discrete material point and interaction force modeling

[0089] Input: Simplified geometric model: the geometric model from step S1. Material constitutive model: the material properties determined according to step S1. Experimental data: such as stress-strain rate experimental data, used to determine the dynamic increase factor (DIF). Peridynamic model: such as the bond-based peridynamic model or the axisymmetric peridynamic model.

[0090] Output: Discrete material point set: a set of uniformly orthogonally distributed material points, representing the discretization of the entire test system. Interaction force model: a model of the interaction forces between material points, based on peridynamic theory, considering the dynamic behavior and damage evolution of the material.

[0091] S3: Contact mechanics and interaction force modeling

[0092] Input: Discrete material point set: the material point set and the interaction force model from step S2. Contact mechanics model: including the bond force density function model, the rigid body and deformable body contact model, the short-range repulsive force model, etc.

[0093] Output: Contact force model: a model describing the interaction forces between rods, between the rod and the specimen, and between damaged material points. Interaction forces in the contact area: the interaction forces between different material points within the contact area.

[0094] S4: Initial velocity and impact process simulation

[0095] Input: Initial velocity of the impact rod: simulating the impact process in the actual test. Initial stationary state: the initial state of other parts of the system (such as the incident rod, the specimen) is stationary. The established contact mechanics model: the contact force model output from step S3.

[0096] Output: Simulation results of the impact process: including time-evolution information such as the motion state, velocity, displacement, etc. between the impact rod and the incident rod. Basis for dynamic response: Preliminary results of the impact process for subsequent simulation analysis.

[0097] S5: Strain and velocity data acquisition

[0098] Input: Geometric model and set of material points: The distribution of material points and the model from steps S2 and S3. Positions of velocity and strain test points: Selected strain and velocity test points.

[0099] Output: Strain time-history data: Data of the strain varying with time recorded at the specified strain test points. Velocity time-history data: Data of the velocity varying with time recorded at the selected velocity test points. Flying-out velocity of the spall segment and incident rod velocity: The relationship between the flying-out velocity of the spall segment and the incident rod velocity obtained through data analysis.

[0100] S6: Setting of initial conditions and boundary conditions

[0101] Input: Initial conditions: Including the initial displacement and velocity of the material points. Boundary conditions: Such as boundary conditions of body force, stress, displacement, etc.

[0102] Output: Set initial and boundary conditions: All initial conditions and boundary conditions are ready for explicit dynamics calculation.

[0103] S7: Explicit dynamics calculation and result output

[0104] Input: Initial conditions and boundary conditions: From step S6. States of material points and contact mechanics model: From steps S2 and S3. Damage criterion: Critical elongation rate bond-breaking criterion.

[0105] Output: Update of material point states: Dynamical information such as the real-time updated positions, velocities, accelerations, etc. of the material points. Damage results: Damage evolution data at different times, including crack propagation, fracture regions, etc. Spall analysis results: Including the flying-out velocity of the spall segment, spall position, spall thickness. Strain time-history curve: Data curve of the strain varying with time at the test points. Analysis of the spall failure process of the impact specimen: Based on the output dynamic response, analyze the failure mechanism and wave propagation behavior of the impact specimen.

[0106] Compared with the prior art, the advantages of the present invention are:

[0107] (1) The explicit dynamic meshless particle method of the improved bond-type peridynamics introducing a bilinear damage constitutive model given by the present invention can avoid some unrealistic damages existing in the simulation of spallation by the original model when simulating the spallation problem; the explicit dynamic meshless particle method of the unconventional state-type axisymmetric peridynamics containing a non-spherical influence function given can improve the stability and calculation accuracy of the model without introducing additional computational effort; generally speaking, the above two methods expand and improve the peridynamics model and the numerical solution system, laying a foundation for the engineering application of peridynamics.

[0108] (2) The present invention adopts a bond-breaking criterion between meshless particles, which can naturally describe the whole process of structural damage accumulation, crack propagation until fracture. The method is complete and reliable, and has excellent effects on the analysis of the spallation problem of a split Hopkinson bar impact.

[0109] (3) The present invention can efficiently, accurately and stably solve problems of structural static and dynamic deformations, elastic wave propagation and cracking failure. It has high calculation accuracy and stability and wide applicability, and can provide a reliable solution for systematically establishing a numerical simulation method for the split Hopkinson bar impact test technology. Description of the Drawings

[0110] Figure 1 is the flowchart of the method of the embodiment of the present invention;

[0111] Figure 2 is the schematic diagram of the principle of the embodiment of the present invention;

[0112] Figure 3 is the schematic diagram of the bilinear damage constitutive model reflecting strain rate dependence of the embodiment of the present invention;

[0113] Figure 4 is the schematic diagram of the bond-associated integral and the bond direction influence function of the embodiment of the present invention;

[0114] Figure 5 is the schematic diagram of the solid model of the specimen-free SHPB non-destructive impact test containing geometric information provided by the embodiment of the present invention;

[0115] Figure 6 (a) to 6(d) are the schematic diagrams of the axial strain and radial strain history curves of the wave propagation process of the calculation results provided by the embodiment of the present invention;

[0116] Figure 7 (a) to 7(c) are the schematic diagrams of the damage distribution during the SHPB impact spallation process of the calculation results provided by the embodiment of the present invention;

[0117] Figure 8 (a) to 8(c) are the schematic diagrams of the strain-time curves of the test points during the SHPB impact spallation process of the calculation results provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0118] The specific implementation of the present invention is described below in conjunction with embodiments:

[0119] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the efficacy and purpose that can be achieved by the present invention.

[0120] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" quoted in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0121] Example 1:

[0122] like Figure 1 As shown, the peridynamic simulation method of the split Hopkinson bar impact test technology provided by the embodiment of the present invention has a modeling and solution process as shown in FIG. Figure 2 , which has high reliability in analyzing the wave propagation process of the rod in the split-Hopkinson bar impact test and the spallation failure of the typical SHPB impact specimen. This embodiment takes the SHPB impact spallation failure test of cement mortar specimens with length and diameter of 220mm and 37mm as an example. The water, cement and sand mix ratio of the cement mortar specimen is 0.4:1:2. The method of the present invention is used to perform near-field dynamic modeling and analysis of the SHPB non-destructive impact test without specimens and the SHPB impact spallation test with specimens; the Young's modulus of the rod in the SHPB is E=193GPa, the Poisson's ratio is υ=0.3, and the mass density is ρ=8027kg / m 3 The length of the rod is Figure 5 As shown, the diameter of the cement mortar specimen is 37 mm, the Young's modulus is E = 1.76391 GPa, the Poisson's ratio is υ = 0.3, and the mass density is ρ = 1909.96 kg / m 3 , the energy release rate of cement mortar specimen is G F =55N / m, tensile strength is σ T= 4.993 MPa; In the SHPB non-destructive impact test without specimens, a uniform initial velocity v = 7 m / s was assigned to each material point of the impact bar. In the SHPB impact spallation test with specimens, there were three impact test groups, that is, three uniform initial velocities v = 5 m / s, v = 6 m / s, and v = 7 m / s were assigned to each material point of the impact bar respectively. The other surfaces of the bar were all free and unconstrained. The specific implementation includes the following steps:

[0123] S101: Establish the geometric model of the Split Hopkinson Pressure Bar (SHPB) test system. The SHPB bar system is simplified into a one-dimensional model or an axisymmetric model. According to the problem characteristics, the geometric modeling of the specimen can adopt a two-dimensional model, an axisymmetric model, or a three-dimensional model. Determine the position areas of the bar system and the specimen and assign corresponding material properties. In the SHPB non-destructive impact test without specimens in this embodiment, two solid models were established, that is, the bar models respectively adopted a one-dimensional model and an axisymmetric model, and the same material parameters were assigned to the materials. It should be noted that the Poisson's ratio of the bar in the one-dimensional model was set to 0, and the solid model is as Figure 5 shown; In the SHPB impact spallation test with specimens in this embodiment, the bar model adopted a one-dimensional model, and the cement mortar specimen adopted a plane stress two-dimensional model, and the corresponding material parameters were assigned to the materials. It should be noted that the transmission bar was not considered in this test model.

[0124] S102: Generate a uniformly orthogonal discrete set of material points. The interaction forces between the material points in the SHPB bar are described by the bond-type peridynamic one-dimensional elastic model or the unconventional state-type peridynamic axisymmetric elastic model. The interaction forces between the material points in the specimen are described by the bond-type peridynamic two-dimensional elastic-brittle model or the unconventional state-type peridynamic axisymmetric elastic-brittle model; Combining the stress-strain rate data collected in the experiment, the material mechanical parameters of the specimen in the above model are strengthened by using the Dynamic Increase Factor (DIF);

[0125] Specifically as follows: For the geometric model of the entire SHPB system, a uniformly orthogonal meshless particle division is performed. The size of the material points meets the calculation accuracy requirements. There are a total of N material points. The model uses square material points, and the size of the material points is d. The value of d for the one-dimensional model of the SHPB bar is d = L / 6000 = 0.0005 m, the value of d for the axisymmetric model of the SHPB bar is d = L / 3750 = 0.0008 m, and the value of d for the two-dimensional model of the specimen is d = l / 1100 = 0.0002 m. L and l are the maximum side lengths of the bar system and the specimen solid models. In this embodiment, the one-dimensional model of the SHPB non-destructive impact test without specimens was discretized to obtain a total of N = 13,201 material points, the axisymmetric model was discretized to obtain a total of N = 198,024 material points, and the model of the SHPB impact spallation test with specimens was discretized to obtain a total of N = 211,986 material points.

[0126] Next, according to the material point size d and the characteristic scale of the loaded material structure, the radius of the near-field range is determined as δ = m×d, where m is the ratio of the near-field range to the material point size. Except for the axisymmetric model, m takes the value of 3 for other models in this embodiment. To analyze the influence of the near-field range on the axisymmetric model, m takes the values of 2 and 3 respectively in the axisymmetric model of the SHPB non-destructive impact test without specimens; according to the initial position coordinates of the material points and the radius of the near-field range, the near-field range associated with the points is determined It is expressed as:

[0127]

[0128] where x (i) and x (j) are the coordinates of the material points in the initial configuration.

[0129] The method of the pairwise force between material points using the bond-type peridynamics model is as follows:

[0130] The motion equation of peridynamics is:

[0131]

[0132] where u (i) and u (j) are displacement vectors, ρ is the material point density, f (ij) is the nonlocal pairwise force density vector between any two material points, with the unit of N / (m 3 ·m 3 ), b is the body force density, and the initial relative position vector and the current relative position vector are defined as ξ (ij) = x (j) - x (i) and η (ij) = u (j) - u (i) .

[0133] Introducing the bilinear damage constitutive model into the improved microelastic-brittle (PMB) model, the nonlocal pairwise force density vector of the bond-type peridynamics is obtained as:

[0134]

[0135] where the relative elongation of the bond is s = (|ξ (ij) + η (ij) |-|ξ (ij) |) / |ξ (ij) |, μ is a scalar function describing the history dependence of the fracture behavior, expressed as c(ξ (ij) ,δ) is the micro-modulus function, g(ξ (ij), δ) and c(0, δ) are the kernel function and the differential modulus constant of the cubic polynomial respectively, and d is a parameter used to describe the bilinear damage of the bond. They are respectively expressed as:

[0136]

[0137] Among them, E is the elastic modulus, v is the Poisson's ratio, and the critical elongation σ T is the tensile strength of the specimen, G F is the fracture energy release rate of the material. The bilinear damage constitutive relation is as Figure 3 shown.

[0138] The method of the interaction force between material points adopts the unconventional state-type axisymmetric peridynamic model as follows.

[0139] Based on the peridynamic differential operator method (PDDO) and the axisymmetric model of elasticity in space, an axisymmetric unconventional state-type peridynamic model is established. At the same time, the non-spherical influence function method is introduced to solve the numerical instability problem in the model. The following bond-associated non-local strain tensor is defined:

[0140]

[0141] Among them, u m = u m (x (i) ), u′ m = u′ m (x (i) + ξ (ij) )(m = z, r) are the displacement components of the material point, r represents the radial distance of the material point from the axis of symmetry. and are peridynamic functions, which can be constructed by polynomials and contain the non-spherical influence function ω(|ξ (ip) |, θ) term. The subscript on the left side of the equation indicates that the bond-associated integral is used on the right side of the equation. The bond-associated integral and the point-associated integral share the same peridynamic range and simultaneously consider the influence of the bond length and the angle change between bonds, as Figure 4 shown. ξ (ip) = x (p) - x (i) is the initial relative position vector between the material points of other bonds during the bond-associated integral and it also contains the target bond ξ (ij) . θ is the angle between ξ (ij) and ξ (ip) . The specific form of the non-spherical influence function is:

[0142]

[0143] Among them, n1, n2, and n3 are constant coefficients. The magnitude of n1 represents the influence degree of the key length change, and n2n3 controls the influence of other keys ξ (ip) on the target key ξ (ij) The contribution degree of the influence. In this embodiment, n1 = n2 = 10 and n3 = 3 are taken.

[0144] When damage occurs to the material point, the following damage reduction model is adopted for the influence function in the bond - associated non - local strain tensor,

[0145]

[0146] Among them, s ij is the elongation rate of the bond, is the critical elongation rate, D(x (i) , t) is the damage parameter of the material point x (i) , D critical is the critical damage value, which takes the value of 0.9 in this embodiment. This model can prevent the matrix singularity problem that may occur in the calculation of unconventional - state peridynamics.

[0147] In the constitutive model part, the stress - strain relationship is updated using Hooke's law in general form, expressed as:

[0148] σ mn = λθδ mn + 2με mn

[0149] Among them, the subscripts m and n represent z and r, and the volumetric strain is The Lamé constants are and When damage occurs to the material point, each stress component is multiplied by a reduction coefficient 1 - D(x (i) , t).

[0150] The energy - equivalence method is used to derive and establish a new bond - associated force vector t or force - vector state T[x (i) , t], expressed as:

[0151]

[0152] Among them, t is the time variable, is the bond - associated Cauchy stress tensor. Under the small - deformation condition, the Cauchy stress tensor σ(x (i) ) is equal to the first Piola - Kirchhoff stress tensor P. The square brackets <·> indicate that the force - vector state acts on a certain bond to obtain a force vector, is the material point x (i) all material points x within the peridynamic range of the material point x(j) Sum of volumes;

[0153] Furthermore, a new axisymmetric unconventional state-based peridynamic motion equation in integral form is constructed as

[0154]

[0155] where ρ is the material mass density and b is the body force density vector acting on the material point.

[0156] The strengthening method of material mechanics parameters is as follows:

[0157] Firstly, the strain rate conditions of different impact velocity groups are obtained from the strain data collected through experiments. Then, combined with the existing experimental studies, the material mechanics parameters of the above model are strengthened using DIF, including the tensile strength σ T and the fracture energy release rate G F . The strengthening method is to directly multiply the above mechanical parameters by the dynamic enhancement factor DIF. Based on the existing experimental studies on DIF and the above material parameters, in this embodiment, the DIF values for the impact velocities of 5 m / s, 6 m / s, and 7 m / s are 2.2, 2.7, and 3.5 respectively.

[0158] S103: The mutual forces between the material points in the contact area between different SHPB bars are simulated using the bond force density function in step two. The mutual forces between the material points in the contact areas between the incident bar and the specimen and between the specimen and the transmission bar are simulated using the contact model of rigid bodies and deformable bodies. For the mutual forces between severely damaged material points or between severely damaged material points and the intact part of the specimen, the short-range repulsive force model is used for simulation;

[0159] The contact model of rigid bodies and deformable bodies and the short-range repulsive force model are as follows:

[0160] During the impact contact process, from time step t to the next time step t + Δt, the position update process of the material point x (k) and the update process of the mutual forces between the rigid body and the deformable body are involved, which are respectively expressed as:

[0161]

[0162] where and v (k) represent the displacement and velocity of the material point x (k) , F (k) is the force exerted by the material point x (k) on the rigid impact body, F is the resultant force received by the rigid impact body. When contact occurs Conversely

[0163] To describe the interaction force between severely damaged material points or between severely damaged material points and the intact part of the specimen, the short-range repulsive force is expressed as:

[0164]

[0165] where is the repulsive force constant, and \(d = \min\{|x (i) - x (j) |, 1.414|\Delta x|\}\) is the maximum action distance of the repulsive force.

[0166] S104: Assign a uniform initial velocity to the impact bar, and the other parts of the SHPB system are initially at rest, so as to simulate the impact bar being launched by the bullet launcher and realize the impact process of the impact bar on the incident bar. In this embodiment, the initial velocities of the impact bars in the one-dimensional model and the axisymmetric model of the SHPB non-damaging impact test without specimens are both 7 m / s, and the initial velocities of the impact bars in the SHPB impact spallation test model with specimens are 5 m / s, 6 m / s, and 7 m / s in three groups respectively.

[0167] S105: Corresponding to the positions of the strain gauges in the experiment, select strain measurement points in the incident bar, the transmitted bar, and the specimen, and record the strain time history of different components of the SHPB during the impact spallation simulation process; select velocity measurement points in the incident bar and the specimen, and record the velocity of the material points of the incident bar and the flying-out velocity of the spallation section; assign initial values to strain, stress, resultant force, and damage variables, set the initial conditions, and apply body force, stress, and displacement boundary conditions;

[0168] To obtain strain data, it is necessary to select the corresponding material points in the geometric models of the bars and the specimen for strain calculation and output according to the pasting positions of the strain gauges in the test device. The strain calculation formula for the material point \(x (k) is expressed as:

[0169]

[0170] where \(x (k+d) and \(x (k-d) are adjacent material points with a distance of \(d\) from the material point \(x (k) . In this embodiment, the selection of the strain measurement points in the one-dimensional model and the axisymmetric model of the SHPB non-damaging impact test without specimens is specifically as follows, for example Figure 5As shown, assuming that the left end point of the impact rod is the starting point with a coordinate value of 0, the coordinate values of the strain test points on the incident rod and the transmission rod are 3m and 4m. Additionally, it should be noted that three strain test points are selected for both the incident rod and the transmission rod in the axisymmetric model, and they have the same axial coordinate value (4m) and different radial coordinate values (0, 0.0088m, and 0.0184m); in this embodiment, the strain test selection for the SHPB impact spallation test model of the specimen is specifically as follows: there is one test point on the incident rod, which is 2.6m away from the left end point of the impact rod, and there are three test points on the specimen with the same interval distance, which are 3.67m, 3.72m, and 3.77m away from the left end point of the impact rod respectively.

[0171] To obtain velocity data, five to six material points need to be selected at the non-impact ends of the incident rod and the specimen, and the velocity data throughout the impact process is output and recorded. Then, the weighted average value of the velocities of these material points is calculated to represent the velocities of the incident rod and the spallation section of the specimen. The specific material points can be selected according to the situation and will not be introduced here.

[0172] In this embodiment, for the initial condition part, except for the impact rod, the initial velocities of the material points in other rods and the specimen model All the initial displacements u of the material points are 0; for the boundary condition part, in the axisymmetric model, a radial displacement constraint condition needs to be applied to the material points on the axis of symmetry to restrict their radial displacement u r = 0, that is, the axisymmetric boundary.

[0173] S106: Perform explicit dynamic calculations. Through iterative loops, the positions, velocities, and accelerations of the material points are updated in real time; specifically, for the dynamic deformation and cracking failure problems in this embodiment, time stepping is achieved through the difference algorithm of the explicit Verlet velocity format to obtain the velocities and displacements at time t + Δt, which are:

[0174]

[0175] Among them, t is the current deformation moment, Δt is the time step, the subscripts n and n + 1 correspond to the moments t and t + Δt respectively, and n is the number of calculation steps; are the velocities of the material points at times t + Δt and t respectively, u (n+1) , u (n) are the displacements of the material points at times t + Δt and t respectively; for transient problems, the velocity field needs to be smoothed using the weighted average method, and the formula is:

[0176]

[0177] Among them, ω(|ξ (ij) |) is the influence function, which is only related to the length of the bond. Additionally, the material point x (i)Taking its own speed into account.

[0178] S107: After obtaining the explicit dynamics calculation results, the critical elongation rate bond-breaking criterion is used to describe damage cracking, and the strain-time history data of the one-dimensional model and the axisymmetric model of the SHPB non-damaged impact test without specimens in this embodiment are output. As Figure 6 shown, the spall damage results and strain-time history data of the SHPB spallation test model with specimens in this embodiment are output, and the strain-time history curve is plotted. As Figure 7 and 8 shown, and the thickness and flying-out speed of the spallation section are recorded, and thus the analysis of problems such as the wave propagation process of the bar and the spallation failure of typical SHPB impact specimens in the split Hopkinson bar impact test is carried out.

[0179] Example 2:

[0180] This embodiment provides a terminal device, which includes a processor and a memory. The memory is used to store a computer program, and the computer program includes program instructions. The processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function. The processor described in the embodiment of the present invention can be used for the operation of a peridynamics simulation method based on a split Hopkinson bar impact test, including the following steps:

[0181] S1: Establish a geometric model of the split Hopkinson pressure bar (SHPB) test system and perform simplification processing, divide the position areas of the bar system and the specimen, and respectively determine the corresponding material properties and configurations;

[0182] S2: Generate a set of discrete material points with uniform orthogonal distribution on the model simplified in step S1, and based on the bond-type peridynamics model or the axisymmetric peridynamics model, establish the interaction relationship between the material points in the bar and the specimen. Combine the experimental data to introduce a dynamic enhancement factor to dynamically strengthen the constitutive parameters of the material, and obtain a well-defined set of material points and the interaction force model;

[0183] S3: For the contact interaction behaviors between various parts in the test system, the following strategies are respectively adopted to establish a contact force model, including: adopting a bond force density function model between bars, adopting a rigid body and deformable body contact model between a bar and a specimen, and adopting a short-range repulsive force model between material points in the damage evolution region, so as to completely describe the interaction mechanical behaviors of each contact region in the system, and output the contact force model and the interaction force between contact regions;

[0184] S4: Determine the uniform initial velocity of the impact bar. Other parts in the system are initially in a static state. Simulate the process of the bullet device impacting and loading in the real test. Through dynamic simulation, output the evolution information of the velocity and displacement states of each bar during the impact process, and establish the basis of the dynamic response under the initial loading conditions, that is, obtain the preliminary simulation results of the impact process;

[0185] S5: Select corresponding material points in the geometric models of the bars and the specimen to calculate and output the strain. Select velocity test points on the incident bar and the specimen, output and record the velocity data of the entire impact process, and determine the flying-out velocity of the spallation section of the specimen and the velocity of the incident bar;

[0186] S6: Initially assign values to the strain, stress, resultant force, and damage variable, set the initial conditions, and apply body force, stress, and displacement boundary conditions;

[0187] S7: Conduct explicit dynamics calculations, and update the positions, velocities, and accelerations of the material points in real time; adopt the critical elongation rate bond-breaking criterion to describe damage cracking; output the displacement results and damage results at different times, and record the velocity of the incident bar, the flying-out velocity of the spallation section, and the strain time-history data of the test points on the specimen, calculate the relationship between the flying-out velocity of the spallation section and the velocity of the incident bar, the spallation occurrence position and the spallation thickness, and draw the strain time-history curve of the test points, and carry out the analysis of the propagation behavior of stress waves in the bar and the evolution mechanism of the spallation failure process of a typical SHPB impact specimen in the split Hopkinson bar impact test.

[0188] Example 3:

[0189] This embodiment provides a storage medium, specifically a computer-readable storage medium (Memory). The computer-readable storage medium is a memory device in a terminal device and is used to store programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and, of course, the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, and the operating system of the terminal is stored in this storage space. Moreover, one or more instructions suitable for being loaded and executed by a processor are stored in this storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory.

[0190] One or more instructions stored in the computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps in the above-mentioned embodiment regarding a peridynamic simulation method based on a split Hopkinson bar impact test; one or more instructions in the computer-readable storage medium are loaded and executed by a processor to perform the following steps:

[0191] S1: Establish a geometric model of the split Hopkinson pressure bar (SHPB) test system and perform simplification processing, divide the position areas of the bar system and the specimen, and respectively determine the corresponding material properties and configurations;

[0192] S2: Generate a set of discrete material points with a uniform orthogonal distribution on the model simplified in step S1, and based on the bond-type peridynamic model or the axisymmetric peridynamic model, establish the interaction relationship between the material points in the bar and the specimen. Combine the experimental data to introduce a dynamic enhancement factor to perform dynamic strengthening processing on the constitutive parameters of the material, and obtain a well-defined set of material points and the interaction force model;

[0193] S3: For the contact interaction behavior between various parts in the test system, respectively adopt the following strategies to establish a contact force model, including: using a bond force density function model between bars, using a rigid body and deformable body contact model between the bar and the specimen, and using a short-range repulsive force model between the material points in the damage evolution region, so as to completely describe the interaction mechanical behavior of each contact area in the system, and output the contact force model and the interaction force between the contact areas;

[0194] S4: Determine the uniform initial velocity of the impact bar, and the other parts in the system are initially in a stationary state. Simulate the process of the bullet device impacting and loading in a real test, and output the evolution information of the velocity and displacement states of each bar during the impact process through dynamic simulation, and establish the dynamic response basis under the initial loading conditions, that is, obtain the preliminary simulation result of the impact process;

[0195] S5: Select corresponding material points in the geometric models of the bar and the specimen for strain calculation and output. Select velocity measurement points on the incident bar and the specimen, output and record the velocity data throughout the impact process, and determine the flying velocity of the spallation section of the specimen and the velocity of the incident bar.

[0196] S6: Initialize the strain, stress, resultant force, and damage variable, set the initial conditions, and apply body force, stress, and displacement boundary conditions.

[0197] S7: Perform explicit dynamic calculations to update the positions, velocities, and accelerations of the material points in real time. Use the critical elongation rate bond-breaking criterion to describe damage cracking. Output the displacement results and damage results at different times, record the velocity of the incident bar and the flying velocity of the spallation section, as well as the strain time history data of the measurement points on the specimen, calculate the relationship between the flying velocity of the spallation section and the velocity of the incident bar, the spallation occurrence position, and the spallation thickness, and plot the strain time history curve of the measurement points to analyze the propagation behavior of stress waves in the bar and the evolution mechanism of the spallation failure process of typical SHPB impact specimens in the split Hopkinson bar impact test.

[0198] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0199] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the specified functions in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0200] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device implements the specified functions in the flow Figure 1One or more processes and / or boxes Figure 1 The functions specified in one box or more boxes.

[0201] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 One or more processes and / or boxes Figure 1 The steps of the functions specified in one box or more boxes.

[0202] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the knowledge scope of those of ordinary skill in the art, various changes can be made without departing from the gist of the present invention.

[0203] Many other changes and modifications can be made without departing from the concept and scope of the present invention. It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A peridynamic simulation method based on split Hopkinson bar impact test, characterized in that, The method includes: S1: Establish a geometric model of the Split Hopkinson Pressure Bar (SHPB) test system and simplify it. Divide the position areas of the rod system and the specimen, and determine the corresponding material properties and configurations respectively. S2: Generate a set of discrete material points with a uniform orthogonal distribution on the simplified model in step S1. Based on the bond-type peridynamic model or the axisymmetric peridynamic model, establish the interaction relationship between the material points in the rod and the specimen. Combine the experimental data to introduce a dynamic enhancement factor to dynamically strengthen the constitutive parameters of the material, and obtain a well-defined set of material points and the interaction force model. S3: For the contact interaction behavior between various parts of the test system, adopt the following strategies to establish the contact force model respectively, including: using the bond force density function model between the rods, using the rigid body and deformable body contact model between the rod and the specimen, and using the short-range repulsive force model between the material points in the damage evolution area, so as to completely describe the interaction mechanical behavior of each contact area in the system, and output the contact force model and the interaction force between the contact areas. S4: Determine the uniform initial velocity of the impact rod. The other parts of the system are initially in a stationary state. Simulate the process of the bullet device impacting and loading in the real test. Output the evolution information of the velocity and displacement states of each rod during the impact process through dynamic simulation, and establish the dynamic response basis under the initial loading conditions, that is, obtain the preliminary simulation results of the impact process. S5: Select the corresponding material points in the geometric models of the rod and the specimen to calculate and output the strain. Select the velocity test points on the incident rod and the specimen, output and record the velocity data throughout the impact process, and determine the flying-out velocity of the spallation section of the specimen and the velocity of the incident rod. S6: Assign initial values to the strain, stress, resultant force, and damage variables, set the initial conditions, and apply the body force, stress, and displacement boundary conditions. S7: Perform explicit dynamic calculations to update the positions, velocities, and accelerations of the material points in real time. Use the critical elongation rate bond-breaking criterion to describe damage cracking. Output the displacement results and damage results at different times, record the velocity of the incident rod and the flying-out velocity of the spallation section, as well as the strain time history data of the test points on the specimen, calculate the relationship between the flying-out velocity of the spallation section and the velocity of the incident rod, the spallation occurrence position and the spallation thickness, and draw the strain time history curve of the test points to analyze the propagation behavior of the stress wave in the rod and the evolution mechanism of the spallation failure process of the typical SHPB impact specimen in the Split Hopkinson bar impact test.

2. The near-field dynamics simulation method based on the split Hopkinson bar impact test according to claim 1, wherein In step S2, generating the set of discrete material points includes: Perform a uniform orthogonal meshless particle division on the geometric model of the entire SHPB system. The size of the material points meets the calculation accuracy requirements. There are a total of N material points. The geometric model uses square material points. The size of the material points is d. For the SHPB rod, d = L / 6000 - L / 1000, and for the specimen, d = l / 1500 - l / 200, where L and l are the maximum side lengths of the physical models of the rod system and the specimen. According to the material point size d and the characteristic scale of the loaded material structure, the radius of the near-field range is determined to be δ = m×d, where m is the ratio of the near-field range to the material point size; according to the initial position coordinates of the material point and the radius of the near-field range, the near-field range associated with the point is determined It is expressed as: where x (i) and x (j) are the coordinates of the material points in the initial configuration.

3. A peridynamic simulation method based on a split Hopkinson bar impact test according to claim 1, characterized in that In step S2, using the bond-type peridynamic model to establish the interaction relationship between the material points in the rod and the specimen includes: The motion equation of peridynamics is: where, u (i) and u (j) are displacement vectors, ρ is the material point density, f (ij) is the non-local interaction force density vector between any two material points, with the unit of N / (m 3 ·m 3 ), b is the body force density, and the initial relative position vector and the current relative position vector are defined as ξ (ij) = x (j) - x (i) and η (ij) = u (j) - u (i) ; The bilinear damage constitutive model is introduced into the improved microelastic-brittle model, and the bond force density vector of the bond-type peridynamics is obtained as follows: where the relative elongation of the bond is s = (|ξ (ij) + η (ij) | - |ξ (ij) |) / |ξ (ij) |, μ is a scalar function describing the history-dependence of the fracture behavior, expressed as c(ξ (ij) , δ) is the micro-modulus function, g(ξ (ij) , δ) and c(0, δ) are the kernel function and the micro-modulus constant of the cubic polynomial respectively, d is a parameter used to describe the bilinear damage of the bond, and they are expressed as follows: Among them, E is the elastic modulus, v is the Poisson's ratio, and the critical elongation σ T is the tensile strength of the specimen, and G F is the fracture energy release rate of the material.

4. A peridynamic simulation method based on a split Hopkinson bar impact test according to claim 1, characterized in that In step S2, an axisymmetric peridynamics model is used to establish the interaction relationship between the rod and the material points in the specimen, including: Based on the peridynamic differential operator method PDDO and the axisymmetric model of elasticity in space, an axisymmetric unconventional state peridynamics model is established. At the same time, the non-spherical influence function method is introduced to solve the numerical instability problem in the model, and the following bond-associated nonlocal strain tensor is defined: wherein, u m = u m (x (i) ), u' m = u' m (x (i) + ξ (ij) )(m = z, r) are the displacement components of the material point, and r represents the radial distance of the material point from the axis of symmetry, and are peridynamic functions, which can be constructed by polynomials and contain the non-spherical influence function ω(|ξ (ip) |, θ) term. The subscript on the left side of the equation indicates that the bond-based integral on the right side is used. The bond-based integral and the point-based integral share the same peridynamic range and simultaneously consider the effects of bond length and the change in the angle between bonds. ξ (ip) = x (p) - x (i) is the initial relative position vector between the material points of other bonds within during the bond-based integral. It also includes the target bond ξ (ij) , θ is the angle between ξ (ij) and ξ (ip) . The specific form of the non-spherical influence function is: Among them, n1, n2, and n3 are constant coefficients. The magnitude of n1 represents the degree of influence of the key length change, and n1 can take values from 5 to 15. n2n3 controls other keys ξ (ip) within on the target key ξ (ij) the contribution degree of the influence, and n2n3 can take values from 10 to 30. n3 is an odd number; When damage occurs to the material points, the following damage reduction model is adopted for the influence function in the bond-associated nonlocal strain tensor: Among them, s ij is the elongation rate of the key, is the critical elongation rate, D(x (i) , t) is the damage degree of the material point x (i) , D critical is the critical damage value, which can be taken as 0.

9. This damage reduction model can prevent the matrix singularity problem that may occur during the calculation of non-conventional state peridynamics; In the constitutive model part, the stress-strain relationship is updated using the generalized Hooke's law, expressed as: σ mn = λθδ mn + 2με mn where the subscripts m and n represent z and r, and the volumetric strain should be The Lamé constants are and When damage occurs to a material point, each stress component is multiplied by a reduction factor 1 - D(x (i) , t); Derive and establish a new bond-associated force vector t or force vector state T[x (i) ,t] using the energy equivalence method, expressed as: where t is the time variable, is the key-associated Cauchy stress tensor. Under small deformation conditions, the Cauchy stress tensor σ(x (i) ) and the first Piola-Kirchhoff stress tensor P are equal. The square brackets <·> indicate that a force vector state acts on a certain key to obtain a force vector. is the sum of the volumes of all material points x (i) in the near-field range of the material point x (j) ; Furthermore, a new integral-type strong-form axisymmetric unconventional state peridynamics motion equation is constructed as: where ρ is the material mass density and b is the body force density vector acting on the material points.

5. A peridynamic simulation method based on a split Hopkinson bar impact test according to claim 1, characterized in that In step S2, the constitutive parameters of the material are dynamically strengthened, including: The strain rate conditions of different impact velocity groups are obtained from the strain data collected through experiments. Then, combined with the existing experimental studies, the dynamic increase factor DIF is used to strengthen the material mechanical parameters of the geometric model, including the tensile strength σ T and the fracture energy release rate G F . The strengthening method is to directly multiply the above mechanical parameters by the dynamic increase factor DIF.

6. The near-field dynamics simulation method based on the split Hopkinson bar impact test according to claim 1, characterized in that In step S3, a rigid body and deformable body contact model is used between the rod and the specimen, and a short-range repulsive force model is used between the material points in the damage evolution region, including: During the impact contact process, from time step t to the next time step t+Δt, it involves the position update process of the material point x (k) and the update process of the interaction force between the rigid body and the deformable body, which are respectively expressed as: Among them, and v (k) represent the displacement and velocity of the material point x (k) , F (k) is the force exerted by the material point x (k) on the rigid impact body, and F is the resultant force received by the rigid impact body. When contact occurs On the contrary To describe the interaction force between severely damaged material points or between severely damaged material points and the intact part of the specimen, the short-range repulsive force is expressed as: Among them, is the repulsive force constant, and d = min{|x (i) - x (j) |, 1.414|Δx|} is the maximum acting distance of the repulsive force.

7. A peridynamic simulation method based on a split Hopkinson bar impact test according to claim 1, characterized in that In step S5, in order to obtain strain data, corresponding material points need to be selected in the geometric models of the rod and the specimen for strain calculation and output according to the pasting positions of the strain gauges in the test device. The strain of material point x (k) is expressed by the following strain calculation formula: where x (k+d) and x (k-d) are neighboring material points at a distance d from the material point x (k) ; To obtain the velocity data, five to six material points need to be selected at the non-impact ends of the incident rod and the specimen, and the velocity data throughout the impact process is output and recorded. Then, the weighted average of the velocities of these material points is calculated to represent the velocities of the incident rod and the spallation section of the specimen.

8. A peridynamic simulation method based on a split Hopkinson bar impact test according to claim 1, characterized in that In step S6, the initial conditions and boundary conditions are set as follows: In the initial conditions, the initial velocities of the material points in the incident rod, the transmitted rod, and the specimen model are set to zero, and the initial displacements of the entire model are set to zero; In the boundary conditions, displacement and force boundaries can be applied to one or more layers of material points at the boundary positions as needed. In the unconventional state axisymmetric peridynamics elastic model, a radial displacement constraint condition is applied to the material points on the axis of symmetry to restrict their radial displacements, i.e., the axisymmetric boundary.

9. A peridynamic simulation method based on a split Hopkinson bar impact test according to claim 1, characterized in that In step S7, explicit dynamics Velocity-Verlet calculations are performed, including: Given the displacements and velocities at the initial moment, and applying time-dependent body forces as well as stress and displacement boundary conditions, a time-stepping iterative loop calculation is realized through the difference algorithm of the explicit Verlet velocity format to obtain the velocities and displacements at time t + Δt, namely: where \(t\) is the current deformation time, \(\Delta t\) is the time step, subscripts \(n\) and \(n + 1\) correspond to times \(t\) and \(t+\Delta t\) respectively, and \(n\) is the number of calculation steps; are the velocities of the material points at times \(t+\Delta t\) and \(t\) respectively, \(u\) (n+1) , \(u\) (n) are the displacements of the material points at times \(t+\Delta t\) and \(t\) respectively; for transient problems, the weighted average method needs to be used to smooth the velocity field, and the formula is: Among them, ω(|ξ (ij) |) is the influence function, which is only related to the length of the key; in addition, the velocity of the material point x (i) itself needs to be taken into account.

10. A non-local dynamics simulation system based on a split Hopkinson bar impact test, characterized in that, The system is applied to the method according to any one of claims 1-9, and the system includes: Geometric modeling module: Establish a geometric model of the split Hopkinson pressure bar SHPB test system and perform simplification processing, divide the position areas of the rod system and the specimen, and determine the corresponding material properties and configurations respectively; Discrete material point distribution module: Generate a set of uniformly orthogonally distributed discrete material points on the model simplified by the geometric modeling module, and based on the bond-type peridynamics model or the axisymmetric peridynamics model, establish the interaction relationship between the rod and the material points in the specimen, and dynamically strengthen the constitutive parameters of the material by introducing a dynamic enhancement factor in combination with experimental data to obtain a well-defined set of material points and the interaction force model; Contact force model construction module: For the contact interaction behaviors between various parts in the test system, the following strategies are respectively adopted to establish a contact force model, including: using a bond force density function model between bars, using a rigid body and deformable body contact model between bars and specimens, and using a short-range repulsive force model between material points in the damage evolution region, so as to completely describe the interaction mechanical behaviors of each contact region in the system, and output the contact force model and the mutual forces of the contact regions; Impact loading simulation module: Determine the uniform initial velocity of the impact bar, and other parts in the system are initially in a stationary state. Simulate the process of the bullet device impacting and loading in the real test. Through dynamic simulation, output the evolution information of the velocity and displacement states of each bar during the impact process, and establish the basis for the dynamic response under the initial loading conditions, that is, obtain the preliminary simulation results of the impact process; Strain and velocity output module: Select corresponding material points in the geometric models of the bars and specimens for strain calculation and output. Select velocity test points on the incident bar and the specimen, output and record the velocity data throughout the impact process, and determine the flying-out velocity of the spallation section of the specimen and the velocity of the incident bar; Initial condition setting module: Assign initial values to strain, stress, resultant force, and damage variables, set initial conditions, and apply body force, stress, and displacement boundary conditions; Explicit dynamics calculation module: Conduct explicit dynamics calculations, and update the positions, velocities, and accelerations of material points in real time; use the critical elongation rate bond-breaking criterion to describe damage cracking; output the displacement results and damage results at different times, and record the velocity of the incident bar and the flying-out velocity of the spallation section, as well as the strain time-history data of the test points on the specimen, calculate the relationship between the flying-out velocity of the spallation section and the velocity of the incident bar, the spallation occurrence position and the spallation thickness, and draw the strain time-history curve of the test points, and conduct an analysis of the propagation behavior of stress waves in the bar and the evolution mechanism of the spallation failure process of typical SHPB impact specimens in the split Hopkinson bar impact test.

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