CN114818404A - Prediction method for crack propagation of brittle material - Google Patents
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Abstract
The invention discloses a method for predicting crack propagation of a brittle material, which comprises the following steps: dispersing the brittle material solid model into a series of space material points through space grid multi-stage division; obtaining parameters of the brittle material, and taking the parameters as input of a prediction model; constructing a constitutive relation of a prototype micro-brittle model based on the space coordinates, setting the sizes of a near field domain and a dual domain, and determining a bond force action range; determining an initial boundary condition, and applying an external force by adopting progressive loading; updating physical and mechanical information such as material point position, speed, acceleration and the like in real time by adopting an explicit iteration method, and describing damage cracking by adopting a critical elongation bond breaking rule; and outputting the displacement result and the damage result at different moments, recording the position and time of damage and fracture, and acquiring the crack propagation paths at different moments. The method solves the problem of false stress waves caused by variable near field domain size, and can effectively predict and analyze the mechanical behavior and the damage problem of the brittle material under the action of load.
Description
Technical Field
The invention relates to a prediction method for crack propagation of a brittle material, in particular to a prediction method for predicting and analyzing the whole process from generation, propagation and destruction of a microscopic crack of the brittle material under the action of load based on a dual-domain near-field dynamics method, and belongs to the technical field of material structure destruction simulation. The invention can effectively predict and analyze the mechanical behavior and the fracture damage problem of the brittle material under the load action.
Background
The research on impact damage and fracture of materials has important guiding significance in the field of engineering application, and fracture analysis of materials or engineering structures cannot be avoided as long as the safety and reliability of the materials are involved, no matter in aerospace, mechanical manufacturing and civil construction.
The failure of brittle materials is due to the creation of numerous microscopic defects within the material under the influence of external stresses and environmental factors, either alone or in combination, which are not visible to the naked eye, but which continue to propagate and merge with each other as the external forces or environmental factors continue to influence, resulting in visible cracking of the material and ultimately failure and complete failure of the material. Cracks are an important manifestation of failure and often are characterized by: on one hand, the occurrence of macrocracks is very likely to cause low-stress brittle fracture of the material, i.e. although the stress is far lower than the yield strength, the material can be subjected to sudden fracture, which is related to the fact that the stress field distribution in the material is changed by the occurrence of the macrocracks, and part of the regions are subjected to stress concentration due to the occurrence of the macrocracks; on the other hand, the occurrence of the crack is a material discontinuity problem, and in the conventional mechanical theory, for example, the theory related to the elastic mechanics makes a continuity assumption in theoretical establishment, so that the conventional mechanical theory has a plurality of complex problems in the research of the material discontinuity problem of the crack.
The cracking of the brittle material is researched, and research methods are divided into two types according to different research means: physical testing and numerical simulation. Physical testing can yield partially reliable data, but requires significant labor, financial and time costs. Compared with a test method, the numerical simulation method is low in cost and high in efficiency, has no special requirements on the shape and the size of a calculation model, is free in setting of boundary conditions and loads, and breaks through the limitations of test equipment conditions and a test piece preparation method. When solving the non-continuous problem, the finite element method based on the continuous theory needs to preset a crack path and a crack propagation criterion, and has the problems of inaccurate fracture description, insufficient calculation precision and the like.
Near-field dynamics (Peridynamics) is an emerging numerical calculation method for describing material characteristics based on non-local models. Its advantage is avoiding the singularity of traditional partial differential equation solving when facing the discontinuity (crack) problem and the complexity of existing multi-scale algorithm. Therefore, it has a unique advantage in simulating the cracking problem of the material. As shown in fig. 1, a substance body occupying a space region R is dispersed into closely arranged substance dots, and a circular (spherical) region in which a substance dot x itself is a circular dot and a radius is δ is referred to as a near field region H δ . Other arbitrary object point x 'in the near field domain (x' e H) δ ) The interaction force existing therebetween is called a bond. At any time t, the equation of motion for any mass point x within the mass is:
where f is the point-to-force function between the object points x and x'; ρ is the density of the material; b (x, t) is the external load density; u is the displacement vector field of the mass point, ξ ═ x '-x, η ═ u' -u; integral field H x Is the area occupied by the object in the reference configuration and has H x And d is the radius of the non-local near-field region of the material point.
This method is similar to the meshless method, requiring discretization of the solid model into individual particles with material properties. When the interaction force among the particles is analyzed, the number of the material points in the near-field domain can be increased along with the radius of the near-field domain in a square relationship; in the process of simulating the loading action of the substance, a large number of numerical iteration steps are needed, and the calculation parameters of each substance point are continuously solved and updated. The non-ideal computational efficiency of the near field dynamics algorithm has always been the primary reason for restricting the application universality. In order to take advantage of the specific advantages of near-field dynamics in analyzing the discontinuous problem and guide future engineering practices more effectively and efficiently, it is necessary to develop a near-field dynamics model and optimize derived algorithms.
In view of the foregoing, it is desirable to establish a method for predicting crack propagation in brittle materials that accurately predicts cracks while minimizing computational complexity.
Disclosure of Invention
The invention aims to solve the problem that the calculation efficiency of crack development under the load action of a near field dynamics simulation material in the prior art is not ideal, provides a concept of dual field corresponding to the near field in the near field dynamics theory, splits the constitutive force between particles into two forces, expands the near field dynamics theory to the dual field near field dynamics theory, and realizes the non-uniform dispersion of an entity model because the expanded theoretical limit that the size of the near field is a fixed value does not exist any more. The numerical method thoroughly solves the problem of false stress waves caused by variable near field domain size, provides a new idea for the research of multi-material, self-adaptive and composite materials, and specifically realizes the following technical scheme:
a method of predicting crack propagation in a brittle material, comprising the steps of:
the method comprises the following steps: through space grid multi-stage division, a brittle material solid model is dispersed into a series of space material points, and a non-uniform discretization model is allowed;
step two: obtaining structural parameters, material performance parameters and external load parameters of the brittle material, and taking the parameters as the input of a pre-constructed near-field dynamics cracking path prediction model based on dual domains;
step three: based on the space coordinates, constructing a prototype micro-brittle model constitutive relation considering the brittle characteristics of the material, and setting the sizes of a near field domain and a dual domain to determine the acting range of the bond force;
step four: determining an initial boundary condition of a brittle material solid model, and applying an external force in a progressive loading mode;
step five: performing dynamic calculation by adopting an explicit iteration method, updating physical and mechanical information such as material point position, speed, acceleration and the like in real time, and describing damage cracking by adopting a critical elongation bond breaking rule;
step six: and outputting the displacement result and the damage result at different moments, and recording the position and time of damage and fracture so as to obtain crack propagation paths at different moments.
Further, the spatial grid multilevel division method of the brittle material solid model in the first step is as follows:
a particle in the material, which contains a series of related particles with certain physical information in its vicinity, may be discretized into a finite number of cubes spaced at Δ x for numerical calculations. The cubes are equal in size and are arranged uniformly and occupy a certain volume, and physical parameters of the dividing units are represented by geometric centers of the small cubes. The concept of the dual field, which is derived from the near-field and understood as a collection of points, the elements of which are all the points in the own near-field containing the target particle, is presented and applied to the governing equations. Near field dynamics based on the dual-domain theory allows variable near field domain sizes, so that a concerned detail region can be divided by smaller discrete particle spacing, and non-uniform division of near field domains with different sizes can be carried out in the same physical body. The division is carried out step by step, the space is firstly dispersed into uniform material points with the same size, then secondary division is carried out in a key area, coordinates of the secondary division are reversely deduced by utilizing the coordinates of the first-level points and the geometric relation after the secondary division, for example, in a two-dimensional plane, four coordinate points can be derived from one coordinate point and replace the original first-level coordinates, and the operation of the tertiary division is also carried out.
The force term in the control equation after integrating the near field domain and the dual domain is also expanded into two terms, as follows:
after the model is dispersed, the integral term is a summation form considered as a certain area in numerical realization, and the dispersion of the control equation is given as follows:
it is noted that the micro-modulus c in the construction of the force term depends on the radius of the material point x and is half the corresponding micro-modulus in conventional near-field dynamics theory. Wherein, V x′ Is the volume of the material point x'; hx is the near field range of the material point x, and other physical quantities have the same meanings as above.
Further, the prototype micro-brittle model constitutive relation of the brittle characteristics of the material in the third step and the bond fracture criterion are as follows:
the bond elongation of the material point bond in near field dynamics is:
s(η,ξ)＝(‖ζ‖-‖ξ‖)/‖ξ‖.
wherein s is bond elongation; eta is the relative displacement between the material points x and x'; xi is the relative position between the substance points x and x' in the reference configuration, the vector zeta is eta + xi, the | xi | and | zeta | are the lengths of the bond before and after deformation respectively, and s is larger than the critical elongation s c When the force is lost, the point representing the object point.
Therefore, the bond damage factor can describe the fracture condition of the material point pair, and the damage of any one local material point x in the material can be defined by a local damage function on the level of the material point pair
And (4) showing. Local damage function
The local damage range is 0-1. When the local damage is 1, all interactions associated with that point are eliminated, whereas when the local damage is 0, all interactions are complete.
Further, in the fifth step, when performing explicit dynamics calculation, the acceleration and the velocity are approximated by finite difference form of displacement. And obtaining the speed and the displacement of the next time step by utilizing the finite difference approximation of the displacement and the speed at the given initial moment to the second derivative of the material point k:
wherein, Δ t is a time step length, and n is a calculation step number;
the velocity of the material point at time t + deltat and t respectively,
the displacement of the mass point at time t + Δ t and t, respectively. To ensure the stability of the integration process, the time step Δ t needs to be as small as possible.
Preferably, in practical simulations, to guarantee the accuracy requirement, the present invention reduces the numerical error by applying volume correction factors and surface correction terms to the material points of the particles in the near-field domain, but not all in the near-field domain, and the particles themselves at the physical boundary, respectively.
Compared with the prior art, the invention has the following obvious and prominent substantive characteristics and remarkable advantages:
1. the invention provides the specific implementation of the near field dynamics model based on the dual domain, develops and perfects the near field dynamics model and a numerical solving system, and introduces the near field dynamics engineering application into a wider field.
2. The invention adopts the constitutive relation of the brittle characteristics of the material and the bond fracture criterion, inherits the nature of the natural description structure damage of the near field dynamics and the direct penetration of the crack propagation, and effectively improves the calculation precision of the structure deformation by adding the volume correction factor and the surface correction term.
3. The invention provides the idea of space multistage division, and can efficiently and accurately solve the problems of structure static dynamic deformation, elastic wave propagation and brittle fracture damage.
Drawings
FIG. 1 is a diagram of a near field dynamics model of the present invention;
FIG. 2 is a schematic diagram of a multi-level spatial partitioning algorithm implementation of the present invention;
FIG. 3 is the constitutive relation of the prototype micro-fragile model and the local damage factor adopted by the present invention;
FIG. 4 is a schematic diagram of the near field dynamics local damage function in the present invention;
FIG. 5 is a schematic diagram of the dual-domain near-field dynamics modeling and solving process of the present invention;
FIG. 6 is a schematic diagram of a solid model provided by an embodiment of the invention;
FIG. 7 is a schematic diagram illustrating progressive application of mockup boundaries according to an embodiment of the invention;
fig. 8 is a schematic diagram illustrating comparison of damage distribution in the damage cracking process according to the calculation result provided by the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
A method of predicting crack propagation in a brittle material, comprising the steps of:
the method comprises the following steps: through space grid multi-stage division, a brittle material solid model is dispersed into a series of space material points, and a non-uniform discretization model is allowed;
step two: obtaining structural parameters, material performance parameters and external load parameters of the brittle material, and taking the parameters as the input of a pre-constructed near-field dynamics cracking path prediction model based on dual domains;
step three: based on the space coordinates, constructing a prototype micro-brittle model constitutive relation considering the brittle characteristics of the material, and setting the sizes of a near field domain and a dual domain to determine the acting range of the bond force;
step four: determining an initial boundary condition of a brittle material solid model, and applying an external force in a progressive loading mode;
step five: performing dynamic calculation by adopting an explicit iteration method, updating physical and mechanical information such as material point position, speed, acceleration and the like in real time, and describing damage cracking by adopting a critical elongation bond breaking rule;
step six: and outputting the displacement result and the damage result at different moments, and recording the position and time of damage and fracture so as to obtain crack propagation paths at different moments.
Further, the spatial grid multilevel division method of the brittle material solid model in the first step is as follows:
a particle in the material, which contains a series of related particles with certain physical information in its vicinity, may be discretized into a finite number of cubes spaced at Δ x for numerical calculations. The cubes are equal in size and are arranged uniformly and occupy a certain volume, and physical parameters of the dividing units are represented by geometric centers of the small cubes. The concept of the dual domain, derived from the near-field domain, is proposed and applied to the governing equation, with the understanding that the set of points, whose elements are all the points in the own near-field domain that contain the target particle. Near field dynamics based on the dual-domain theory allows variable near field domain sizes, so that a concerned detail region can be divided by smaller discrete particle spacing, and non-uniform division of near field domains with different sizes can be carried out in the same physical body. The division is carried out step by step, the space is firstly dispersed into uniform material points with the same size, then secondary division is carried out in a key area, coordinates of the secondary division are reversely deduced by utilizing the coordinates of the first-level points and the geometric relation after the secondary division, for example, in a two-dimensional plane, four coordinate points can be derived from one coordinate point and replace the original first-level coordinates, the operation of the three-level division is also carried out, and the division idea is shown in figure 2.
The force term in the control equation after integrating the near field domain and the dual domain is also expanded into two terms, as follows:
after the model is dispersed, the integral term is a summation form considered as a certain area in numerical realization, and the dispersion of the control equation is given as follows:
it is noted that the micro-modulus c in the construction of the force term depends on the radius of the material point x and is half the corresponding micro-modulus in conventional near-field dynamics theory. Wherein, V x′ Is the volume of the material point x'; hx is the near field range of the material point x, and other physical quantities have the same meanings as above.
Further, the prototype micro-brittle model constitutive relation of the brittle characteristics of the material in the third step and the bond fracture criterion are as follows:
the bond elongation of the material point bond in near field dynamics is:
s(η,ξ)＝(‖ζ‖-‖ξ‖)/‖ξ‖.
wherein s is bond elongation; eta is the relative displacement between the material points x and x'; xi is the relative position between the substance points x and x' in the reference configuration, the vector zeta is eta + xi, the | xi | and | zeta | are the lengths of the bond before and after deformation respectively, and s is larger than the critical elongation s c When the point pair force of the object point disappears, the constitutive relation of the prototype micro brittle model is shown in FIG. 3.
Therefore, the bond damage factor can describe the breaking condition of the material point pair, and the damage of any one local material point x in the material can be defined by a local damage function on the level of the material point pair
And (4) showing. As shown in fig. 4, the local damage function
The local damage range is 0-1. When the local damage is 1, all interactions associated with that point are eliminated, whereas when the local damage is 0, all interactions are complete.
Further, in the fifth step, when performing explicit dynamics calculation, the acceleration and the velocity are approximated by finite difference form of displacement. And obtaining the speed and the displacement of the next time step by utilizing the finite difference approximation of the displacement and the speed at the given initial moment to the second derivative of the material point k:
wherein, Δ t is a time step length, and n is a calculation step number;
the velocity of the material point at time t + deltat and t respectively,
the displacement of the mass point at time t + Δ t and t, respectively. To ensure the stability of the integration process, the time step Δ t needs to be as small as possible.
Preferably, in practical simulations, to guarantee the accuracy requirement, the present invention reduces the numerical error by applying volume correction factors and surface correction terms to the material points of the particles in the near-field domain, but not all in the near-field domain, and the particles themselves at the physical boundary, respectively.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
As shown in fig. 5, in this embodiment, the dynamic deformation and crack failure of a concrete plane slab with dimensions of 200mm × 200mm under the mixed action of shear load and tensile load are taken as an example, and the near field dynamics modeling and analysis are performed by using the method of the present invention; young modulus is E-30 GPa, Poisson ratio is upsilon-0.2, and mass density is rho-2265 kg/m 3 Type I energy release rate G Ιc ＝110J/m 2 Type II energy Release Rate G IIc ＝10G Ic Uniformly distributed loads p with the resultant force of 5kN are applied to the horizontal direction of the upper left half part and the lower right half part of the thin plate, and then a speed load with the v being 10mm/s is applied to the upper and lower boundaries of the thin plate. The specific implementation comprises the following steps:
s1: through the multi-stage division of the spatial grid, the brittle material solid model is discretized into a series of spatial material points, and a non-uniform discretization model is allowed. The size of the material point meets the calculation accuracy requirement, and the delta x is 1.25mm as follows: uniformly and orthogonally carrying out non-grid particle division on the whole structure solid model, wherein 6360 material points with the interval of 1.25mm are in total, 1320 material points in an encryption region are subjected to secondary division based on the multi-level space division idea to obtain 5280 material points of fine particles, and the solid model is dispersed into 10320 material points. If a uniform Δ x of 1.25mm is used, the sample is divided into 25440 sample points.
S2: obtaining the structural parameters of the brittle material,And (3) material performance parameters and external load parameters, and taking the parameters as the input of a pre-constructed near-field dynamics cracking path prediction model based on dual domains. Determining a near field domain H associated with the point according to the initial position coordinate and the near field range radius of the material point x And dual domain H' x Expressed as:
H x ＝{x'∈R|‖x'-x‖≤δ}
H' x ＝{x'∈R|x∈H x' }
wherein x, x' are coordinates of the material point in the initial configuration.
Furthermore, all the various geometric parameters and attribute parameters in the previous steps are input into the dual-domain near-field dynamics model as input items.
S3: based on the space coordinates, a prototype micro-brittle model constitutive relation considering the brittle characteristics of the material is constructed, and the sizes of a near field domain and a dual domain are set to determine the acting range of the bond force. The constitutive relation of the prototype micro-brittle model of the brittle material is as follows:
wherein f is xx′ Is the constitutive part of bond xx', f x′x The constitutive force portion being the dual bond x' x; both constitutive forces are a function of the elongation of the respective bond s, s being greater than the critical elongation s c When the point of the object point is opposite to the point of the object point, the point of the object point is opposite to the point of the object point; μ is a local damage function; eta is the relative displacement between the material points x and x'; xi is the relative position between the substance points x and x' in the reference configuration, the vector zeta is eta + xi, and | xi | and | ζ | are the lengths of the bond before and after deformation, respectively.
And generating a near field range associated with the point and a near field range associated with the bond according to the size of the substance point and the characteristic scale of the loaded material structure, specifically, determining that the radius of the near field range is delta 3.015 delta x according to the size delta x of the substance point and the characteristic scale of the loaded material structure.
S4: and determining the initial boundary condition of the brittle material solid model, and applying an external force in a progressive loading mode. In this embodiment, the initial conditions are set as follows: all the initial displacement and the initial speed of the nodes are 0; with a uniform velocity boundary and loading pattern over time, the action time was the first 2000 time steps, Δ t 0.1 μ s, as shown in fig. 7.
S5: and (3) performing dynamic calculation by adopting an explicit iteration method, updating physical and mechanical information such as material point position, speed, acceleration and the like in real time, and describing damage cracking by adopting a critical elongation bond breaking rule. Updating the position, the speed and the acceleration of a material point in real time by applying the simplest explicit time integral and iterative loop calculation; specifically, for the dynamic deformation and cracking damage problem of this embodiment, time stepping is implemented by using a differential algorithm in an explicit Verlet speed format, and the speed and displacement of t + Δ t time are obtained, that is:
wherein, delta t is a time step length, and n is the number of calculation steps;
the velocity of the material point at time t + deltat and t respectively,
the displacement of the mass point at time t + Δ t and t, respectively.
S6: and outputting the displacement result and the damage result at different moments, and recording the position and time of damage and fracture so as to obtain crack propagation paths at different moments. After an explicit dynamics calculation result is obtained, a critical elongation breaking key criterion is adopted to describe damage cracking, displacement results and damage cloud chart results at different moments are output, for example, as shown in fig. 8, the position and time of damage close to a critical value of 0.5 are recorded, the time, position and cracking speed of cracking are calculated, the accuracy of the method is demonstrated with an experiment or other numerical methods, the high efficiency of an even domain near field dynamics model is verified with a uniformly divided near field dynamics model, and in fact, in the problem, the efficiency is improved by 119.49%, and therefore crack extension prediction analysis of the brittle material is carried out.
The embodiments of the present invention have been described with reference to the accompanying drawings, but the present invention is not limited to the embodiments, and various changes and modifications can be made according to the purpose of the invention, and any changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention shall be equivalent substitutions, as long as the purpose of the present invention is met, and the present invention shall fall within the protection scope of the present invention without departing from the technical principle and inventive concept of the present invention.
Claims (5)
1. A method of predicting crack propagation in a brittle material, comprising the steps of:
(1) dispersing a brittle material solid model into a series of spatial material points by a spatial grid multistage division method, and allowing a non-uniform discretization model;
(2) obtaining structural parameters, material performance parameters and external load parameters of the brittle material, and taking the structural parameters, the material performance parameters and the external load parameters as the input of a pre-constructed near-field dynamics cracking path prediction model based on dual domains;
(3) based on the space coordinates, constructing a prototype micro-brittle model constitutive relation considering the brittle characteristics of the material, setting the sizes of a near field domain and a dual domain, and determining the acting range of the bond force;
(4) determining an initial boundary condition of a brittle material solid model, and applying an external force in a progressive loading mode;
(5) performing dynamic calculation by adopting an explicit iteration method, updating physical and mechanical information of the position, the speed and the acceleration of a substance point in real time, and describing the damage and the cracking of the material by adopting a critical elongation bond breaking rule;
(6) and outputting the displacement result and the damage result at different moments, and recording the position and time of damage and fracture so as to obtain crack propagation paths at different moments.
2. The method of predicting crack propagation in a brittle material as claimed in claim 1, characterized in that the discretization of the brittle material solid model in step (1) is: a certain material point in the material is in a nearby area and comprises a series of related material points with certain physical information, and the material is dispersed into a finite number of cubes with the distance delta x for convenience of numerical calculation; each cube is equal in size, uniform in arrangement mode and occupies a certain volume, and physical parameters of the dividing units are represented by the geometric centers of the small cubes; the concept of a dual domain is put forward and applied to a control equation, wherein the dual domain is derived from a near-field domain and is understood as a set of a series of points, and the elements of the set are all points containing target particles in the own near-field domain; the near field dynamics based on the dual-domain theory allows the variable size of the near field domain, so that a concerned detail region is divided by smaller discrete particle spacing, and the near field domains with different sizes are non-uniformly divided in the same physical body; the division is carried out step by step, the space is firstly dispersed into uniform material points with equal size, and then secondary division is carried out in a key area;
the force term in the control equation after integrating the near field domain and the dual domain is also expanded into two terms, as follows:
after the model is dispersed, the integral term is a summation form considered as a certain area in numerical realization, and the dispersion of the control equation is given as follows:
it is to be noted that the micro-modulus c in the composition of the force term depends on the radius of the material point x and is half of the corresponding micro-modulus in the conventional near-field dynamics theory; wherein Vx 'is the volume of the material point x'; hx is the near field range of the material point x.
3. The method of predicting crack propagation in a brittle material as claimed in claim 1, wherein the prototype micro-brittle model constitutive relation of the brittle characteristic in the step (3) and the bond rupture criterion are as follows:
the bond elongation of the material point bond in near field dynamics is:
s(η,ξ)＝(‖ζ‖|-‖ξ‖)/‖ξ‖.
wherein s is bond elongation; eta is the relative displacement between the material points x and x'; xi is the relative position between the substance points x and x' in the reference configuration, the vector zeta is eta + xi, the | xi | and | zeta | are the lengths of the bond before and after deformation respectively, and s is larger than the critical elongation s c When the point of the object point is opposite to the point of the object point, the point of the object point is opposite to the point of the object point;
thus, the bond damage factor describes the breaking of a material point pair, and the damage at any one local material point x in the material is defined by a local damage function at the level of the material point pair
Represents:
local damage function
The local damage range is 0-1.
4. The method of predicting crack propagation of a brittle material as claimed in claim 1, characterized in that, in the explicit kinetic calculation in step (5), acceleration and velocity are approximated in the form of finite difference of displacement; and obtaining the speed and the displacement of the next time step by utilizing the finite difference approximation of the displacement and the speed at the given initial moment to the second derivative of the material point k:
wherein, Δ t is a time step length, and n is a calculation step number;
the velocity of the material point at time t + deltat and t respectively,
respectively displacement of the material point at t + delta t and t moment; in order to ensure the stability of the integration process, the time step Δ t needs to be as small as possible.
5. The method of predicting crack propagation in brittle material as claimed in claim 4, characterized in that in the explicit dynamics calculation, in order to guarantee the accuracy requirement, the volume correction factor and the surface correction term are respectively adopted for the material points of the particles in the near field but not all in the near field and the self particles at the physical boundary to reduce the numerical error.
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