Thermal-mechanical coupling near-field dynamics simulation method and system for thermal cracking of brittle material, medium and equipment

Abstract

The invention discloses a thermal-mechanical coupling near-field dynamics simulation method and system for thermal cracking of a brittle material, a medium and equipment, and belongs to the technical field of material and structure damage simulation, and the method comprises the following steps: S1, building a solid model, inputting basic information, discretizing the model, building a near-field dynamics material point position matrix and key connection information, and establishing a near-field dynamics model; assembling a near-field dynamic matrix; s2, initial conditions and boundary conditions are set, and an explicit staggered solution method is adopted to iteratively solve the temperature field and the displacement field of the near-field dynamic matrix step by step in sequence; and S3, drawing a temperature field, a displacement field and a result cloud chart of damage according to the solved data. According to the method, the heterogeneous characteristics of the brittle materials are considered, the thermal-mechanical coupling model is established based on the near-field dynamics theory, the adopted coupling model conforms to engineering practice, and simulation and prediction of the cracking problem of the multiple brittle materials under the temperature load effect can be stably and accurately achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of material and structure destruction simulation, and relates to a simulation method for thermal cracking of brittle materials, and in particular to a thermomechanical coupling near-field dynamics simulation method, system, medium and equipment for thermal cracking of brittle materials. Background Art

[0002] It is of great significance to study the fracture of brittle materials caused by thermal deformation and thermal stress. When temperature fluctuations cause thermal stress to exceed the strength threshold of the material, microcracks will be induced in the structure. These microcracks gradually expand and evolve into macro cracks, eventually leading to structural failure. Brittle materials and structures are often subject to a variety of temperature loads, including rapid cooling or heating, which can cause complex heat-driven deformation and fracture, increasing the risk of structural failure. Therefore, it is of great significance to establish a suitable method to evaluate whether brittle materials will crack under the action of temperature and how the cracks will develop.

[0003] In the past few decades, researchers have studied the cracking behavior of brittle materials such as granite ceramics under thermal shock through various experimental, theoretical and numerical methods to predict the thermal shock cracking mode of brittle solids. However, the thermal cracking problem of brittle materials involves the whole process of microcrack initiation, expansion and destruction inside the structure. Traditional numerical simulation methods such as finite element method are based on the theory of classical continuum mechanics. Such methods have bottlenecks in analyzing discontinuous deformation problems and often require the introduction of some external technologies such as re-gridding technology, external failure criteria and additional models. The emerging peridynamics has obvious advantages in describing the discontinuous deformation problem of structures, and some scholars have extended the peridynamic method to the damage and destruction problem of brittle structures under thermal-mechanical coupling. However, due to the complexity of the problem, most of the work is based on the thermally induced deformation model, and the thermal-mechanical coupling model has only been preliminarily studied. There is still a lot of work to be studied in depth. Summary of the invention

[0004] The present invention provides a thermomechanical coupling peridynamic simulation method, system, medium and equipment for thermal cracking of brittle materials, so as to overcome the defects of the prior art.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A thermomechanical coupled peridynamic simulation method for thermal cracking of brittle materials comprises the following steps:

[0007] S1. Establish a solid model, input basic information such as material parameters and model parameters, discretize the model, establish the peridynamic material point position matrix and bond connection information, and assemble the peridynamic matrix;

[0008] S2, setting initial conditions and boundary conditions, and using explicit staggered solution method to iteratively solve the temperature field and displacement field of the peridynamic matrix step by step;

[0009] S3. Draw the temperature field, displacement field and damage result cloud diagram of the calculation model based on the solved data.

[0010] To optimize the above technical solutions, the specific measures taken also include:

[0011] Furthermore, in S1, a uniform orthogonal discrete material point set is generated by a discretization model, which is the peridynamic material point position matrix.

[0012] Further, in S1, the peridynamic matrix is ​​assembled as follows:

[0013] In traditional continuum mechanics, the thermal-mechanical coupling equation is:

[0014]

[0015] Where ρ is the density in kg / m 3 ;c v is the specific heat capacity, the unit is J / (kg·K); T is the temperature, T0 is the reference temperature, the unit is K, is the derivative of temperature with respect to time; k T is the thermal conductivity, the unit is J / (s·m·K); α is the thermal expansion coefficient, the unit is 1 / ℃; is the volume strain rate; S T is the volume heat source term, with the unit of J / (s·m 3 ), u is the displacement tensor, ü is the second-order derivative of the displacement tensor with respect to time, σ is the Cauchy stress tensor, b is the body density vector; is the gradient operator; is the Laplace operator; λ and μ are the Lamé constants, Where E and ν are elastic modulus and Poisson’s ratio, respectively;

[0016] All the first-order and second-order partial derivatives in the traditional thermal-mechanical coupling equations are reconstructed by the peridynamic differential operator, and the peridynamic matrix including the peridynamic differential operator temperature equation and the peridynamic differential operator motion equations in two directions is obtained.

[0017] Furthermore, the peridynamic differential operator temperature equation is:

[0018]

[0019] The equations of motion for the peridynamic differential operators in the two directions are:

[0020]

[0021] Where t is a certain moment; x and x′ represent the coordinate vectors of the material points in the initial configuration; ξ is the relative position vector, ξ = x′-x; u1 and u2 represent the displacement components; b1 and b2 represent the body density components; H x represents the set of material points x' within the near field of material point x with radius δ; V x′ is the equivalent integral volume; is a peridynamic function with orthogonality, through Calculate, where δ is the Kronecker symbol, P1 and P2 are [0,1,2], and n1 and n2 are [0,1,2].

[0022] Furthermore, in S2, the method of using the explicit staggered solution method to iteratively solve the temperature field and displacement field of the peridynamic matrix step by step is:

[0023] The peridynamic differential operator temperature equation is discretized and integrated. The peridynamic differential operator is used in space, and the forward difference method is used in time integration. The time integral of the temperature field of any material point k from the nth step to the n+1th step is obtained as follows:

[0024]

[0025] Where Δt is the calculation time step of the temperature field; n is the time step; j is the material point within the near field range of material point k; N K is the total number of material points within the near field of material point k; V j is the approximate volume of material point j. When orthogonal uniform discretization is used, the actual volume of the two-dimensional material point is V j =|Δx 2 , Δx is the material point (or grid) length;

[0026] The motion equations of the peridynamic differential operators in two directions are discretized and integrated. The peridynamic differential operator is used in space, and the forward difference method is used in time integration. The time integral of the displacement field of any material point from step t to step t is obtained as follows:

[0027]

[0028]

[0029] Furthermore, in S2, an explicit multiscale time integration scheme is used to use different time steps for the temperature equation and the equation of motion.

[0030] Furthermore, in S3, the damage result cloud map is drawn by using a scalar function μ with history dependence to describe the fracture behavior of the material at time t′:

[0031]

[0032] In the formula, s is the elongation, which indicates the degree of relative displacement between material points. Where ξ is the relative position vector and η is the relative displacement vector.

[0033] The present invention also provides a thermomechanically coupled peridynamic simulation system for thermal cracking of brittle materials, which is used to execute the above method, including: a pre-processing module, which is used to establish a peridynamic material point position matrix and bond connection information, and assemble a peridynamic matrix; a calculation and analysis module: which gradually and sequentially iteratively solves the temperature field and displacement field of the peridynamic matrix; and a post-processing module: which draws a result cloud map of the temperature field, displacement field and damage based on the solved data.

[0034] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the thermo-mechanical coupling peridynamic simulation method for thermal cracking of brittle materials as described above.

[0035] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the thermomechanical coupling near-field dynamics simulation method for thermal cracking of brittle materials as described above is implemented.

[0036] The beneficial effects of the present invention are:

[0037] 1. The model has high accuracy. The peridynamic theory and method adopted in the present invention can naturally describe the whole process of structural damage accumulation, crack propagation and fracture. The method is complete and reliable, and has excellent effect on the analysis of damage and destruction problems.

[0038] Second, it is highly adaptable. The present invention uses the peridynamic method to simulate the thermal cracking and failure process of brittle materials under temperature conditions. It can adjust the loading quantity and loading form of boundary particles to ensure that the simulation process is closer to the actual situation and enhance the accuracy of the model in predicting mechanical properties. Moreover, this prediction method is not limited to a certain brittle structure and is suitable for simulating the thermal cracking and failure process of brittle materials such as granite and ceramic plates. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is the main flow chart of the thermo-mechanical coupled peridynamic simulation method for thermal cracking of brittle materials;

[0040] Figure 2 It is a program flow chart of the thermo-mechanical coupled peridynamic simulation method for thermal cracking of brittle materials;

[0041] Figure 3It is a schematic diagram of the structure of heterogeneous granite;

[0042] Figure 4 is a schematic diagram of the explicit multiscale time integration scheme;

[0043] Figure 5 Graphs showing the temperature distribution (left), damage distribution (middle), and horizontal displacement distribution caused by temperature (right) obtained in the embodiment. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0045] This embodiment takes the thermal cycle test simulation of heterogeneous granite material as an example, and uses the thermomechanical coupling peridynamic simulation method for thermal cracking of brittle materials provided by the present invention to perform peridynamic modeling and analysis. The main process is as follows: Figure 1 The specific procedure flow is as shown in Figure 2 As shown, including:

[0046] S1. Establish a solid model, input basic information such as material parameters and model parameters, discretize the model, establish the peridynamic material point position matrix and bond connection information, and assemble the peridynamic matrix.

[0047] Specifically, a uniform orthogonal set of discrete material points is generated by the discretization model, which is the peridynamic material point position matrix. The size of the material points should meet the calculation accuracy requirements. In this embodiment, the granite specimen to be tested is 10 mm long and 20 mm high. Its four boundaries are only subject to temperature load and are not subject to any displacement constraints. In addition, the heterogeneity of rock materials needs to be considered. The mineral content and the corresponding thermal expansion coefficient listed in Table 1 are processed using the Shuffle algorithm to obtain the following: Figure 3 Schematic diagram of the heterogeneous granite structure shown.

[0048] Table 1

[0049] Mineral Name Volume content (%) Thermal expansion coefficient (1 / ℃) Feldspar 43.5 <![CDATA[9.7×10 -6 ]]> Quartz 30 <![CDATA[24.3×10 -6 ]]> Biotite 26.5 <![CDATA[3.0×10 -6 ]]>

[0050] The peridynamic matrix is ​​assembled as follows:

[0051] In traditional continuum mechanics, the thermal-mechanical coupling equation is:

[0052]

[0053] Where ρ is the density in kg / m 3 ;c v is the specific heat capacity, the unit is J / (kg·K); T is the temperature, T0 is the reference temperature, the unit is K, is the derivative of temperature with respect to time; k T is the thermal conductivity, the unit is J / (s·m·K); α is the thermal expansion coefficient, the unit is 1 / ℃; is the volume strain rate; S T is the volume heat source term, with the unit of J / (s·m 3 ), u is the displacement tensor, ü is the second-order derivative of the displacement tensor with respect to time, σ is the Cauchy stress tensor, b is the body density vector; is the gradient operator; is the Laplace operator; λ and μ are the Lamé constants, where E and ν are the elastic modulus and Poisson's ratio, respectively.

[0054] All the first-order and second-order partial derivatives in the traditional thermal-mechanical coupling equations are reconstructed by peridynamic differential operators to obtain the thermal-mechanical coupling equations based on peridynamic differential operators, which is the peridynamic matrix including the peridynamic differential operator temperature equation and the peridynamic differential operator motion equations in two directions.

[0055] The peridynamic differential operator temperature equation is:

[0056]

[0057] The equations of motion for the peridynamic differential operators in two directions are:

[0058]

[0059] Where t is a certain moment; x and x′ represent the coordinate vectors of the material points in the initial configuration; ξ is the relative position vector, ξ = x′-x; u1 and u2 represent the displacement components; b1 and b2 represent the body density components; H x represents the set of material points x' within the near field of material point x with radius δ; V x′ is the equivalent integral volume; is a peridynamic function with orthogonality, through Calculate, where δ is the Kronecker symbol, P1 and P2 are [0,1,2], and n1 and n2 are [0,1,2].

[0060] The peridynamic differential operator model replaces the differential in the original equation by spatial integration. When brittle materials are damaged and cracks occur under the action of thermal stress, the singularity problem in the traditional thermal-mechanical coupling equilibrium equation can be effectively avoided.

[0061] S2. Set initial conditions and boundary conditions, and use explicit staggered solution method to iteratively solve the temperature field and displacement field of the peridynamic matrix (i.e., numerical model) step by step.

[0062] Specifically, the peridynamic differential operator temperature equation is discretized and integrated. The peridynamic differential operator is used in space, and the forward difference method is used in time integration. The time integral of the temperature field of any material point k from the nth step to the n+1th step is obtained as follows:

[0063]

[0064] Where Δt is the calculation time step of the temperature field; n is the time step; j is the material point within the near field range of material point k; N K is the total number of material points within the near field of material point k; V j is the approximate volume of material point j. When orthogonal uniform discretization is used, the actual volume of the two-dimensional material point is V j =|Δx 2 , Δx is the material point (or grid) length.

[0065] By solving this formula for each material point, we can obtain the temperature field.

[0066] The motion equations of the peridynamic differential operators in two directions are discretized and integrated. The peridynamic differential operator is used in space, and the forward difference method is used in time integration. The time integral of the displacement field of any material point k from the nth step to the n+1th step is:

[0067]

[0068] By solving this formula for each material point, we can obtain the displacement field.

[0069] When using the explicit staggered solution method to solve multi-physics field coupling problems, there is a problem of unequal time steps for each field. Among them, the time step applicable to the temperature equation is much larger than that of the motion equation. Therefore, it is necessary to introduce Figure 4 The explicit multiscale time integration scheme shown is used to handle the unequal time steps in the coupled thermal-mechanical problem, using different time steps Δt for the temperature equation and the equation of motion.

[0070] S3. Draw the temperature field, displacement field and damage cloud diagram of the calculation model based on the solved data, such as Figure 5 shown.

[0071] Among them, the method of drawing the damage result cloud map is as follows: In order to describe the failure phenomenon of crack initiation or expansion inside the material, a scalar function μ with history dependence is used to describe the fracture behavior of the material at t′:

[0072]

[0073] In the formula, s is the elongation, which indicates the degree of relative displacement between material points. Where ξ is the relative position vector and η is the relative displacement vector.

[0074] In another embodiment, a thermomechanically coupled peridynamic simulation system for thermal cracking of brittle materials is provided, which is used to execute the above method, including: a pre-processing module, which is used to establish a peridynamic material point position matrix and bond connection information, and assemble a peridynamic matrix; a calculation and analysis module: which gradually and sequentially iteratively solves the temperature field and displacement field of the peridynamic matrix; and a post-processing module: which draws a result cloud map of the temperature field, displacement field and damage based on the solved data.

[0075] In another embodiment, a computer-readable storage medium is provided, storing a computer program, characterized in that: the computer program enables a computer to execute the thermo-mechanical coupling peridynamic simulation method for thermal cracking of brittle materials as described above.

[0076] In another embodiment, an electronic device is provided, characterized in that it includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the thermo-mechanically coupled near-field dynamics simulation method for thermal cracking of brittle materials as described above is implemented.

[0077] In the embodiments disclosed in the present application, the computer storage medium can be a tangible medium that can contain or store a program for use by or in conjunction with an instruction execution system, device or equipment. The computer storage medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or equipment, or any suitable combination of the above. More specific examples of computer storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above.

[0078] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0079] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A thermomechanical coupled peridynamic simulation method for thermal cracking of brittle materials, characterized by: The following steps are involved: S1. Establish a solid model, input basic information, discretize the model, establish the peridynamic material point position matrix and bond connection information, and assemble the peridynamic matrix; S2, setting initial conditions and boundary conditions, and using explicit staggered solution method to iteratively solve the temperature field and displacement field of the peridynamic matrix step by step; S3. Draw the cloud diagram of temperature field, displacement field and damage results based on the solved data.

2. The thermomechanical coupling peridynamic simulation method for thermal cracking of brittle materials according to claim 1, characterized in that: In S1, a uniform orthogonal discrete material point set is generated by a discretization model, which is the peridynamic material point position matrix.

3. The thermomechanical coupling peridynamic simulation method for thermal cracking of brittle materials according to claim 1, characterized in that: In S1, the peridynamic matrix is ​​assembled as follows: In traditional continuum mechanics, the thermal-mechanical coupling equation is: Where ρ is the density; c v is the specific heat capacity; T is the temperature, T0 is the reference temperature; k T is the thermal conductivity; α is the thermal expansion coefficient; is the volume strain rate; S T is the volume heat source term; u is the displacement tensor; σ is the Cauchy stress tensor; b is the body density vector; is the gradient operator; is the Laplace operator; λ and μ are the Lamé constants, Where E and ν are elastic modulus and Poisson’s ratio, respectively; All the first-order and second-order partial derivatives in the traditional thermal-mechanical coupling equations are reconstructed by the peridynamic differential operator, and the peridynamic matrix including the peridynamic differential operator temperature equation and the peridynamic differential operator motion equations in two directions is obtained.

4. The method for thermal-mechanical coupling peridynamic simulation of thermal cracking of brittle materials according to claim 3, characterized in that: The peridynamic differential operator temperature equation is: The equations of motion for the peridynamic differential operators in the two directions are: Where t is a certain moment; x and x′ represent the coordinate vectors of the material points in the initial configuration; ξ is the relative position vector, ξ = x′-x; u1 and u2 represent the displacement components; b1 and b2 represent the body density components; H x represents the set of material points x' within the near field of material point x with radius δ; V x′ is the equivalent integral volume; is a peridynamic function with orthogonality, through Calculate, where δ is the Kronecker symbol, P1 and P2 are [0,1,2], and n1 and n2 are [0,1,2].

5. The thermomechanical coupling peridynamic simulation method for thermal cracking of brittle materials according to claim 4, characterized in that: In S2, the method of using explicit staggered solution method to iteratively solve the temperature field and displacement field of the peridynamic matrix step by step is: The peridynamic differential operator temperature equation is discretized and integrated. The peridynamic differential operator is used in space, and the forward difference method is used in time integration. The time integral of the temperature field of any material point k from the nth step to the n+1th step is obtained as follows: Where Δt is the calculation time step of the temperature field; n is the time step; j is the material point within the near field range of material point k; N K is the total number of material points within the near field of material point k; V j is the approximate volume of material point j. When orthogonal uniform discretization is used, the actual volume of the two-dimensional material point is V j =|Δx 2 , Δx is the material point length; The motion equations of the peridynamic differential operators in two directions are discretized and integrated. The peridynamic differential operator is used in space, and the forward difference method is used in time integration. The time integral of the displacement field of any material point k from the nth step to the n+1th step is obtained as follows:

6. The thermomechanical coupling peridynamic simulation method for thermal cracking of brittle materials according to claim 5, characterized in that: In S2, an explicit multiscale time integration scheme is used to use different time steps for the temperature equation and the equation of motion.

7. The thermomechanical coupling peridynamic simulation method for thermal cracking of brittle materials according to claim 1, characterized in that: In S3, the method for drawing the damage result cloud map is: The fracture behavior of the material at time t′ is described by a history-dependent scalar function μ: In the formula, s is the elongation, which indicates the degree of relative displacement between material points. Where ξ is the relative position vector and η is the relative displacement vector.

8. A thermomechanical coupled peridynamic simulation system for thermal cracking of brittle materials, characterized by: Used to perform the method according to any one of claims 1 to 7, comprising: Pre-processing module, used to establish the peridynamic material point position matrix and bond connection information, and assemble the peridynamic matrix; Computational analysis module: Iteratively solves the temperature field and displacement field of the peridynamic matrix step by step; Post-processing module: Draw the temperature field, displacement field and damage result cloud map based on the solved data.

9. A computer-readable storage medium storing a computer program, characterized in that: The computer program enables a computer to execute the thermal-mechanical coupled peridynamic simulation method for thermal cracking of brittle materials according to any one of claims 1 to 7.

10. An electronic device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for thermal-mechanical coupling peridynamic simulation of thermal cracking of brittle materials as claimed in any one of claims 1 to 7 is implemented.

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