Artificial bone material crack simulation method based on material point method

Abstract

The invention belongs to the technical field of biomedical engineering materials, and particularly provides an artificial bone material crack simulation method based on a material point method. The core of the method is that a spatial derivative is calculated and a momentum equation is solved by discretizing a local material region of an artificial skeleton as a mass point and combining a background grid. The method comprises the following steps: establishing a crack propagation model of a material point method, judging whether a crack begins to expand and judging the crack propagation direction by adopting common two-dimensional crack cracking criteria, stress intensity factor criteria and maximum ring stress criteria, and finally introducing a traction law to simulate the crack surface contact problem between an upper crack surface and a lower crack surface. The material point method not only avoids the problems of mesh distortion and the like during large deformation and crack propagation of a finite element method, but also avoids the problems of numerical fracture and the like easily generated by a discrete element method under high-speed impact.

Description

Technical Field

[0001] The invention belongs to the field of biomedical materials, and in particular relates to an artificial bone material crack simulation method based on a material point method. Background Art

[0002] In the field of medical research and bioengineering, the performance evaluation and optimization design of artificial bone materials have always been regarded as the focus of research. With the advancement of science and technology, the rapid development of materials science and computer simulation technology, the method based on numerical simulation has shown great potential in exploring the crack propagation and fracture behavior of artificial bones.

[0003] Although traditional experimental methods can reveal certain performance characteristics of artificial bone materials to a certain extent, they have great limitations. Experimental testing is not only time-consuming and labor-intensive, but it is often difficult to fully and deeply capture every subtle process of crack propagation. This not only limits our in-depth 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 achieved certain results in simulating crack propagation, fracture behavior, etc. However, they often face severe challenges such as mesh reconstruction, large amount of calculation, and numerical fracture. This not only increases the complexity of the simulation, but also limits its breadth and depth in practical applications.

[0004] In this context, the Material Point Method (MPM), as an emerging Lagrangian particle method, discretizes the material into a series of material points carrying mass and physical properties and performs numerical solutions on the background grid, thus avoiding the grid reconstruction problem of the traditional grid method when dealing with crack propagation. This feature gives MPM a significant advantage in simulating the crack propagation behavior of artificial bones when they are impacted by external forces. It can not only accurately capture the state before the crack propagates, but also simulate the subsequent propagation path of the crack, thus providing us with a new perspective to observe and understand the crack behavior of artificial bones.

[0005] However, although MPM has shown great potential in artificial bone crack simulation, its application still faces some technical difficulties. First, how to reasonably discretize artificial bone materials into material points and give them accurate fracture mechanics parameters is the key to ensuring the accuracy of simulation results. This requires us to have an in-depth understanding of the microstructure and mechanical properties of artificial bone materials, and to be able to reasonably set the properties and parameters of material points based on these characteristics. Secondly, the introduction of prefabricated cracks and the selection of their extension criteria are also crucial. We need to select appropriate prefabricated crack shapes and extension criteria based on the characteristics of artificial bone materials and actual usage 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 crack behavior. In order to accurately simulate this process, we need to establish effective judgment criteria to evaluate the interaction between the upper and lower surfaces of the crack, and determine whether the crack has debonded. Summary of the invention

[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 discretize the artificial bone materials, assign fracture mechanics parameters, define prefabricated cracks, use the stress intensity factor crack extension criterion to determine whether the cracks extend, and use the maximum ring stress criterion to simulate the crack extension path, and finally use the traction law to simulate the contact problem between the upper and lower surfaces of the crack, that is, whether debonding occurs, so as to achieve accurate simulation and prediction of the crack behavior of artificial bone materials. 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 method artificial bone material model and assign mechanical parameters;

[0009] Step 2: Define prefabricated cracks with massless particles;

[0010] Step 3, using the stress intensity factor crack growth criterion as the crack growth criterion;

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

[0012] Step 5: Use the traction law to simulate the contact problem between the upper and lower surfaces of the crack.

[0013] Step 1: distribute the artificial bone material in the background grid in the form of discrete material points. Each material point carries physical information such as mass, volume, position, velocity and stress, as well as fracture mechanics parameters required for crack propagation, including the critical stress intensity factor of the material, the cohesive strength of the crack tip, etc. The material point is associated with the background grid through an interpolation function or a weight function to ensure that the physical information of the material point 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 connect these massless particles through crack segments to set prefabricated cracks. Set the starting and ending massless particles as the two tips of the crack, and judge whether the crack will expand, as well as the direction and speed of expansion based on physical quantities such as the stress intensity factor of the starting and ending particles. These prefabricated crack particles can be dynamically updated and rearranged as the crack expands. Compared with the finite element method, this step does not require re-meshing of the crack tip. This crack processing process greatly improves the efficiency and accuracy of artificial bone material crack simulation.

[0015] Step 3, use the stress intensity factor extension criterion as the criterion for single crack extension and complex crack extension, 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 factor, after a certain exponential weighting, is equal to 1, the crack begins to extend, where the index is used to describe the combined effect of KI and KII on crack extension, 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, using the maximum hoop stress criterion, defines that the propagation direction of the crack in the artificial bone material is the direction where the circumferential stress (or hoop stress) takes the maximum value, and the condition for the unstable crack propagation is that the maximum value of the circumferential stress reaches the critical constant of the material, and the crack begins to propagate in this direction. By calculating the stress intensity factors in different directions at the crack tip, the direction in which the hoop stress is maximum can be found, that is, the crack propagation direction.

[0018] Step 5, by assigning a traction law to one or more crack particles along the crack to achieve the interaction between the crack surfaces, simulating the debonding phenomenon during crack propagation. As the crack opening displacement increases, the traction between the crack surfaces first decreases and then increases until the crack opening displacement reaches the critical opening displacement, the traction disappears, and the crack debonds.

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

[0020] The present invention uses the material point method to simulate the crack extension of artificial bone materials. By distributing the material in the form of discrete material points in the background grid, and using an interpolation function or a weight function to realize the association between the material point and the background grid, the physical information of the material point can be transmitted and obtained more accurately. Compared with the traditional finite element method, the material point method is used to simulate the crack extension, which avoids the extremely high-precision grid division at the crack tip, and does not need to replace the background grid, which greatly reduces the workload of the entire calculation. Compared with the discrete element method, the interpolation function of the material point method is more complete, which avoids the phenomenon of particle aggregation under the action of tension, thereby avoiding problems such as numerical fracture. Therefore, the material point method adopts the characteristics of combining particles with background grids, which is different from the approximation based on the grid of the finite element, and is also different from the discrete element method that simply uses a group of points to discretize the region. It has unique advantages in dealing with problems such as large deformation and crack extension, thereby improving the accuracy of artificial bone crack simulation.

[0021] The present invention is based on the material point method and uses the stress intensity factor extension criterion and the maximum hoop stress criterion as the criterion for crack extension, which can more accurately determine whether the crack extends and the direction and speed of the extension. At the same time, the stress intensity factor extension criterion is not only applicable to crack extension under a single stress scenario, but also to crack extension under complex stress scenarios. Finally, by specifying the traction law for one or more cracks along the crack, the debonding phenomenon during the crack extension process can be simulated, making the simulation of crack extension more realistic and complete. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of the artificial bone material crack simulation method based on the material point method of the present invention;

[0023] Figure 2 It is a schematic diagram of discrete points of materials of the present invention;

[0024] Figure 3 A schematic diagram of a crack model of an artificial bone material of the present invention;

[0025] Figure 4 It is a schematic diagram of the massless prefabricated crack of the present invention;

[0026] Figure 5 It is a schematic diagram of the crack growth direction of the present invention;

[0027] Figure 6 It is a schematic diagram of crack debonding of the artificial bone material of the present invention. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] A method for simulating cracks in artificial bone materials based on the material point method, such as Figure 1 As shown in FIG. 1 , the method includes: discretizing the artificial bone material into material points; assigning fracture mechanics parameters to the discrete points; defining prefabricated cracks with massless particles; using the intensity factor crack extension criterion as the crack extension criterion; using the maximum annular stress criterion to simulate the crack extension path; and finally judging whether debonding occurs on the upper and lower surfaces of the crack by the traction law. Figure 1-4 The present invention provides a method for simulating cracks in artificial bone materials based on a material point method, and the specific steps are as follows:

[0030] Step 1: Establish a material point method artificial bone material model and assign mechanical parameters;

[0031] Step 2: Define prefabricated cracks with massless particles;

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

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

[0034] Step 5: Use the traction law to simulate the contact problem between the upper and lower surfaces of the crack.

[0035] In step 1, the computational material domain is discretized into mass points. The discretization diagram is shown in Figure 2 As shown in the figure, the more discrete mass points there are, the higher the calculation accuracy. The overall shape of the mass points is the shape of the calculation material domain. The background grid accuracy is 0.01mm. The material inside each small grid is discretized into four material points. The sum of the information carried by the four material points is all the information of the material in this area. The information exchange between the material points and the background grid is realized through the interpolation function, so that the information of the material points is updated at each calculation time step. This example uses a single prefabricated crack artificial bone material polylactic acid (PLA) uniaxial compression specimen, as shown in Figure 3 As shown in the figure, the sample is a circular model with a radius of 0.5 mm, and a vertical crack with a length of 0.1 mm is prefabricated in the center of the sample. The density of the material carried by the mass point in this example is 1130 kg / m 3, Young's modulus is 4.02GPa, Poisson's ratio is 0.35, critical stress intensity factor of prefabricated crack is 2.98, cohesive strength is 26MPa, critical opening displacement is 0.00323mm.

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

[0037] In step 3, the commonly used material fracture criterion and stress intensity factor criterion are used to determine whether the crack has expanded. When the stress intensity factor at the crack tip reaches the critical stress intensity factor of 2.98 used in this example, the crack begins to expand.

[0038] In step 4, the maximum annular 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 results in this example are as follows: Figure 5 shown.

[0039] In step 5, the crack is judged by the traction law to simulate the contact problem between the upper and lower surfaces of the crack. As the external stress increases, the upper and lower surfaces of the crack begin to gradually separate. At this time, the upper and lower surfaces of the crack begin to have mutual traction forces, and as the separation distance increases, the traction force increases first and then decreases. When the displacement between the upper and lower surfaces of the crack reaches the critical opening displacement of the crack, the traction force between the upper and lower surfaces of the crack disappears, and finally the crack debonds. Figure 6 Schematic diagram of crack debonding phenomenon in this example.

Claims

1. A crack simulation method for artificial bone materials based on the material point method aims to discretize the local area of ​​the artificial bone material into a series of interacting material points, which will be used for subsequent simulation calculations, and assign fracture mechanics-related parameters to each discrete point. These parameters will affect the initiation, expansion and fracture behavior of the crack. Prefabricated cracks are defined in the model by means of massless particles to simulate the initial defects or damage in the actual material. The intensity factor crack extension criterion is used as the criterion for judging whether the crack extends. This criterion is based on the stress or strain state at the crack tip. The maximum hoop stress criterion is used to simulate the crack extension path, that is, the crack will extend in the direction of the maximum hoop stress. Finally, the traction law is used to judge whether the upper and lower surfaces of the crack are debonded, that is, whether the crack surface is separated due to external force; A method for simulating cracks in artificial bone materials based on a material point method, characterized in that: Step 1: Establish a material point method artificial bone material model and assign mechanical parameters; Step 2: Define prefabricated cracks with massless particles; Step 3, using the intensity factor crack growth criterion as the crack growth criterion; Step 4, using the maximum hoop stress criterion to simulate the crack propagation path; Step 5: Use the traction law to simulate the contact problem between the upper and lower surfaces of the crack.

2. The artificial bone material crack simulation method based on the material point method according to claim 1 is characterized in that: The method for discretizing the artificial bone material region described in step 1 is as follows: The artificial bone material is discretized into a series of interacting particles through the material point method, and each particle is given all the important information of the material area where it is located, such as mass, density, elastic modulus and related fracture mechanics parameters, including material fracture toughness, cohesive strength, etc. At the same time, the background grid is divided, and the material point information is mapped to the background grid for calculation using the interpolation function, and the material point information carried by the calculated grid node is mapped back to the material point to achieve the update of the material state. The material point method combines the advantages of the Lagrangian method and the Euler method, and can effectively avoid the problems of mesh distortion and mesh re-division of the finite element method, as well as the numerical fracture of the discrete element method when facing high-speed impact.

3. The artificial bone material crack simulation method based on the material point method according to claim 1 is characterized in that: The method for defining the prefabricated cracks with massless particles described in step 2 is as follows: Define one or more massless particles and connect them through crack segments to define the prefabricated cracks of artificial bones. The coordinates of the massless particles determine the position of the prefabricated cracks. Among these particles, the first particle serves as the "starting" tip of the crack, and the last particle serves as the "terminating" tip of the crack. These massless particles carry some fracture mechanics parameters, including cohesive strength and critical opening displacement.

4. The artificial bone material crack simulation method based on the material point method according to claim 1 is characterized in that: The stress intensity factor crack growth criterion described in step 3 is as follows: This criterion can be applied to complex stress or single stress conditions. In the simulation of the material point method, when the stress intensity around the crack of the artificial bone material meets this criterion, the crack propagates, where: KI represents the stress intensity factor of type I crack, KIc represents the critical stress intensity factor of type I, KII represents the stress intensity factor of type II crack, and KIIc represents the critical stress intensity factor of type II. p and q are used to describe the combined effect of KI and KII on crack propagation. The material point method simulates crack propagation. In the crack tip area, it does not require extremely high-precision mesh division and frequent mesh replacement like the finite element method. It also avoids the common numerical fracture problem of cracks under tensile force in the discrete element method.

5. The artificial bone material crack simulation method based on the material point method according to claim 1 is characterized in that: The maximum hoop stress criterion described in step 4 is as follows: When the prefabricated crack meets the crack extension criterion, the maximum hoop stress intensity is found by comparing the hoop stress intensity around the crack tip, so that the crack tip extends along this direction.

6. The artificial bone material crack simulation method based on the material point method according to claim 1 is characterized in that: The traction law described in step 5 simulates the contact between the upper and lower surfaces of the crack as follows: After the crack begins to expand, the traction law is used to describe the relationship between the critical opening displacement of the crack tip and the interaction force between the crack surfaces during the loading process, so as to describe 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 increases first and then decreases as the crack tip opening displacement increases. When the crack tip opening displacement reaches the critical opening displacement, the interaction traction force between the crack surfaces disappears, and at this time, debonding occurs between the upper and lower surfaces of the crack.

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