A method for simulating crack of artificial bone material based on material point method

Abstract

The present application belongs to the technical field of biomedical engineering materials, and specifically provides a kind of artificial bone material crack simulation method based on material point method.The core of the method is to discretize the local material area of artificial bone as a particle, and to calculate the spatial derivative and solve the momentum equation by combining the background grid.The crack propagation model of the material point method is established, and by using the common two-dimensional crack opening criterion, stress intensity factor criterion and maximum hoop stress criterion, it is determined whether the crack starts to expand and the crack propagation direction, and finally the traction law is introduced to simulate the crack surface contact problem between the upper and lower crack surfaces.The material point method not only avoids the grid distortion problems faced by the finite element method under large deformation and crack propagation, but also avoids the numerical fracture problems easily produced by the discrete element method under high-speed impact.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of biomedical materials, and particularly relates to a crack simulation method for artificial bone materials based on a material point method. BACKGROUND

[0002] In the field of medical research and bioengineering, the performance evaluation and optimal design of artificial bone materials have always been the focus of research. With the progress of science and technology, the rapid development of material science and computer simulation technology, numerical simulation-based methods have shown great potential in exploring the crack propagation and fracture behavior of artificial bone.

[0003] Traditional experimental methods, although to some extent can reveal some performance characteristics of artificial bone materials, have great limitations. Experimental testing not only consumes time and effort, but also often fails to fully and deeply capture every subtle process of crack propagation. This not only limits our understanding of the crack behavior of artificial bone materials, but also increases the difficulty of predicting their service life and optimizing structural design. In order to overcome these challenges, researchers have begun to turn their attention to numerical simulation methods. At present, in the field of crack simulation, a variety of numerical methods have been widely used, among which the finite element method and the discrete element method are particularly prominent. These methods have made certain achievements in simulating crack propagation and fracture behavior. However, they often face the challenges of mesh reconstruction, large amount of calculation and numerical fracture. This not only increases the complexity of simulation, but also limits its breadth and depth in practical applications.

[0004] Under this background, the material point method (MPM) as a new Lagrangian particle method, by discretizing the material into a series of material points carrying mass and physical properties, and solving numerically on a background grid, avoids the mesh reconstruction problem of traditional grid methods in dealing with crack propagation. This feature makes MPM have significant advantages in simulating the crack propagation behavior of artificial bone under external force impact. It not only can accurately capture the state before the crack occurs and expands, but also can simulate the subsequent crack propagation path, thereby providing us with a new perspective to observe and understand the crack behavior of artificial bone.

[0005] However, despite the great potential of MPM in artificial bone crack simulation, its application still faces some technical challenges. First, how to reasonably discretize artificial bone material into material points and assign accurate fracture mechanics parameters is the key to ensuring the accuracy of the simulation results. This requires us to have a deep understanding of the microstructure and mechanical properties of artificial bone material and be able to set the attributes and parameters of the material points reasonably according to these characteristics. Second, the introduction of pre-existing cracks and the selection of their propagation criteria are also crucial. We need to choose the appropriate pre-existing crack shape and propagation criteria according to the characteristics of artificial bone material and actual use conditions to ensure the authenticity and reliability of the simulation. In addition, the debonding phenomenon of the upper and lower contact surfaces of the crack during crack propagation is one of the important factors affecting the crack behavior. In order to accurately simulate this process, we need to establish effective criteria to evaluate the interaction between the upper and lower surfaces of the crack and determine whether the crack has debonding phenomenon. SUMMARY

[0006] In view of the above background, the present invention proposes a method for simulating cracks in artificial bone materials based on the material point method, which aims to accurately simulate and predict the crack behavior of artificial bone materials by discretizing artificial bone materials, assigning fracture mechanics parameters, defining pre-existing cracks, using stress intensity factor crack propagation criteria to determine whether the crack has propagated, using maximum hoop stress criteria to simulate the crack propagation path, and finally simulating the contact problem between the upper and lower surfaces of the crack, i.e., whether debonding occurs, through the traction law. The technical solution of the present invention is as follows:

[0007] The method for simulating cracks in artificial bone materials based on the material point method comprises the following steps:

[0008] Step 1, establish a material point artificial bone material model and assign mechanical parameters;

[0009] Step 2, define pre-existing cracks with massless particles;

[0010] Step 3, use stress intensity factor crack propagation criteria as the crack propagation criteria;

[0011] Step 4, use maximum hoop stress criteria to simulate the crack propagation path;

[0012] Step 5, simulate the contact problem between the upper and lower surfaces of the crack through the traction law.

[0013] Step 1, distribute artificial bone material in the form of discrete material points in the background grid. Each material point carries physical information such as mass, volume, position, velocity and stress, and fracture mechanics parameters required for crack propagation, including the critical stress intensity factor of the material, the crack tip cohesive strength, etc. The association between material points and background grid is realized through interpolation function or weight function, to ensure that the physical information of material points can be accurately transmitted to the background grid, and the necessary calculation information can be obtained from the background grid.

[0014] Step 2, define a series of massless particles in the artificial bone material model, and set pre-cracks by connecting these massless particles through crack segments. Set the starting and ending massless particles as the two crack tips, and judge whether the crack propagates, the direction and speed of propagation according to the stress intensity factor and other physical quantities received by the two particles. These pre-crack particles can be dynamically updated and rearranged as the crack propagates. Compared with the finite element method, this step does not need to re-divide the crack tip into fine grid, and this crack processing process greatly improves the efficiency and accuracy of artificial bone material crack simulation.

[0015] Step 3, use the stress intensity factor expansion criterion as the criterion for single crack propagation and complex crack propagation, that is, when the ratio of the type I and type II stress intensity factors at the crack tip of the artificial bone material to the corresponding critical stress intensity factors is equal to 1 after a certain exponential weighting, the crack begins to expand, wherein the exponential is used to describe the comprehensive influence of KI and KII on crack propagation, and their values depend on factors such as the geometry of the crack, the mechanical properties of the material, and the external load conditions. Stress intensity factor criterion:

[0016]

[0017] Step 4, adopt the maximum hoop stress criterion to define that the propagation direction of the artificial bone material crack is the direction in which the maximum hoop stress (or called circumferential stress) is taken, and the condition for crack unstable propagation is that the maximum value of the hoop stress reaches the critical constant of the material, and the crack begins to expand in that direction. By calculating the stress intensity factors in different directions of the crack tip, the direction with the maximum hoop stress, i.e. the crack propagation direction, can be found.

[0018] Step 5, realize the interaction between crack surfaces by assigning a traction law to one or more crack particles along the crack, to simulate the debonding phenomenon in the crack propagation process. With the increase of crack opening displacement, the traction between crack surfaces first decreases and then increases, until the crack opening displacement reaches the critical opening displacement, the traction disappears, and the crack debonding phenomenon occurs.

[0019] The present application has the following beneficial effects:

[0020] The present application uses the material point method to simulate the crack propagation of artificial bone material, and can more accurately transmit and obtain the physical information of the material point by distributing the material in the form of discrete material points in the background grid and using interpolation function or weight function to realize the association of the material point and the background grid.

[0021] The present application uses the material point method, uses the stress intensity factor expansion criterion and the maximum ring stress criterion as the criterion of crack propagation, and can more accurately judge whether the crack propagates and the direction and speed of propagation. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 The flow chart of the artificial bone material crack simulation method based on the material point method of the present application is shown in the figure.

[0023] Figure 2 The material discrete point schematic diagram of the present application is shown in the figure.

[0024] Figure 3 The artificial bone material crack model schematic diagram of the present application is shown in the figure.

[0025] Figure 4 The pre-crack without mass schematic diagram of the present application is shown in the figure.

[0026] Figure 5 The crack growth direction schematic diagram of the present application is shown in the figure.

[0027] Figure 6 The artificial bone material crack debonding schematic diagram of the present application is shown in the figure. DETAILED DESCRIPTION

[0028] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described, obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present application.

[0029] A material point method-based artificial bone material crack simulation method, as shown in Figure 1 , the method comprises: discretizing the artificial bone material into material points. The discrete points are endowed with fracture mechanics parameters. The pre-crack is defined by the massless particles. The strength factor crack propagation criterion is used as the crack propagation standard. The maximum ring stress criterion is used to simulate the crack propagation path. Finally, the debonding phenomenon of the upper and lower surfaces of the crack is judged by the traction law. In combination with the Figures 1-4 , the present application provides a material point method-based artificial bone material crack simulation method, and the specific steps are as follows:

[0030] Step 1, establishing a material point artificial bone material model and endowing it with mechanical parameters;

[0031] Step 2, defining the pre-crack by the massless particles;

[0032] Step 3, using the stress intensity factor crack propagation criterion as the crack propagation standard;

[0033] Step 4, using the maximum ring stress criterion to simulate the crack propagation path;

[0034] Step 5, simulating the crack upper and lower surface contact problem by the traction law.

[0035] In step 1, the material domain is discretized into particles, and the discrete schematic diagram is as shown in Figure 2 , the more the number of discrete particles, the higher the calculation accuracy. The overall shape of the particles is the shape of the calculation material domain, the background grid accuracy is 0.01mm, and the material inside each small grid is discretized into four material points. The information carried by the four material points is the total information of the material in this region. Through the interpolation function, the information exchange between the material points and the background grid is realized, so as to update the information of the material points at each calculation time step. In this example, a single pre-crack artificial bone material polylactic acid (PLA) uniaxial compression specimen is used, as shown in Figure 3 , the specimen is a circular model with a radius of 0.5mm, and a vertical crack with a length of 0.1mm is pre-prepared in the center of the specimen. In this example, the material density carried by the particles is 1130kg / m 3, the Young's modulus is 4.02 GPa, and the Poisson's ratio is 0.35. The critical stress intensity factor of the pre-crack is 2.98. The cohesive strength is 26 MPa, and the critical opening displacement is 0.00323 mm.

[0036] In step 2, the pre-crack is defined using massless particles, and a schematic diagram of the pre-crack is shown in FIG. 4. One or more massless particles carrying the crack traction law are defined, and the particles are connected to construct a complete pre-crack of any shape. In this example, two massless particles at the same vertical position are defined and connected to construct a vertical pre-crack located at the center of the entire model.

[0037] In step 3, the commonly used material fracture criterion, stress intensity factor criterion, is used to determine whether the crack propagates. When the stress intensity factor at the crack tip reaches the critical stress intensity factor 2.98 used in this example, the crack begins to propagate.

[0038] In step 4, the maximum hoop stress criterion is used to define the crack propagation direction. When the stress intensity in a certain direction around the crack tip reaches the critical stress intensity, the crack begins to grow in that direction. The crack growth result in this example is shown in FIG. 5. Figure 5

[0039] In step 5, the traction law is used to determine the contact problem between the upper and lower surfaces of the simulated crack. As the external stress increases, the upper and lower surfaces of the crack begin to separate. At this time, the upper and lower surfaces of the crack begin to exert traction on each other. As the separation distance increases, the traction force first increases and then decreases. When the displacement between the upper and lower surfaces of the crack reaches the critical opening displacement, the traction force between the upper and lower surfaces of the crack disappears, and finally the crack debonds, Figure 6 which is a schematic diagram of the crack debonding phenomenon in this example.​

Claims

1. A method for simulating cracks in artificial bone materials based on the material point method, characterized in that: Step 1: Establish a material point method artificial bone model and assign mechanical parameters; Step 2: Define pre-cracks using massless particles; Step 3: Use the strength factor crack propagation criterion as the crack propagation standard; Step 4: Simulate the crack propagation path using the maximum ring stress criterion; Step 5: Simulate the contact problem between the upper and lower surfaces of the crack using the traction law; The aim is to discretize local regions of artificial bone materials into a series of interacting material points, which will be used for subsequent simulation calculations. Each discrete point is assigned fracture mechanics-related parameters that will affect crack initiation, propagation, and fracture behavior. Pre-existing cracks are defined in the model using massless particles to simulate initial defects or damage in real materials. The strength factor crack propagation criterion is used as the standard for judging whether a crack will propagate. This criterion is based on the stress or strain state at the crack tip. The maximum circumferential stress criterion is used to simulate the crack propagation path, i.e., the crack will propagate along the direction that generates the maximum circumferential stress. Finally, the traction law is used to determine whether the upper and lower surfaces of the crack debond, i.e., whether the crack surface separates due to external forces. The discretization method for the artificial bone material region described in step 1 is as follows: The artificial bone material is discretized into a series of interacting particles using the material point method. Each particle is assigned all important information about its material region, including mass, density, elastic modulus, and related fracture mechanics parameters such as fracture toughness and cohesive strength. Simultaneously, a background mesh is created, and an interpolation function is used to map the material point information onto the background mesh for calculation. The calculated material point information from the mesh nodes is then mapped back to the material points, thus updating the material state. The material point method combines the advantages of the Lagrange method and the Eulerian method, effectively avoiding the mesh limitations of the finite element method. The problems of distortion and mesh re-division, and the numerical fracture problem of the discrete element method under high-speed impact; among them, the method of defining pre-cracks using massless particles in step 2 is as follows: one or more massless particles are defined and connected by crack segments to define pre-cracks in the artificial skeleton. The coordinates of the massless particles determine the position of the pre-crack. Among these particles, the first particle is the "starting" tip of the crack, and the last particle is the "terminating" tip of the crack. These massless particles carry some fracture mechanics parameters, including cohesive strength and critical opening displacement; among them, the stress intensity factor crack propagation criterion in step 3 is as follows: This criterion is applicable to complex or single stress conditions. In the material point method simulation, when the stress intensity around the crack in the artificial bone material satisfies this criterion, crack propagation occurs. Here, KI represents the Type I crack stress intensity factor, KIc represents the Type I critical stress intensity factor, KII represents the Type II crack stress intensity factor, and KIIc represents the Type II critical stress intensity factor; p and q are used to describe the combined effect of KI and KII on crack propagation. The material point method simulates crack propagation without requiring extremely high-precision meshing and frequent mesh replacements in the crack tip region, unlike the finite element method. It also avoids the limitations of the discrete element method in tensile stress simulation. Numerical fracture problems of cracks under tensile loading are discussed. Step 5 describes the traction law simulating the contact between the upper and lower surfaces of the crack as follows: After the crack begins to propagate, during continued loading, the traction law describes the relationship between the critical opening displacement of the crack tip and the interaction force between the crack surfaces, thus describing the contact problem between the upper and lower surfaces of the crack. As the external stress increases, the traction force between the upper and lower surfaces of the crack tip first increases and then decreases with the increase of the crack tip opening displacement. When the crack tip opening displacement reaches the critical opening displacement, the traction force between the crack surfaces disappears, and at this point, debonding occurs between the upper and lower surfaces of the crack.

2. The method for simulating cracks in artificial bone materials based on the material point method according to claim 1, characterized in that, The maximum circumferential stress criterion described in step 4 is as follows: when the pre-crack satisfies the crack propagation criterion, the maximum circumferential stress intensity is found by comparing the circumferential stress intensity around the crack tip, so that the crack tip propagates along this direction.

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