Method for acquiring strength factor of incompressible material

Abstract

The invention discloses a method for acquiring a strength factor of an incompressible material, and belongs to the technical field of fracture mechanics, and the method comprises the following steps: constructing a virtual grid at a crack tip of the incompressible material containing crack defects; based on a Hellman variational method, carrying out displacement field and strain field finite element calculation on the virtual grid unit to obtain a displacement field and a stress-strain field of the virtual grid unit; according to the displacement field and the stress-strain field of the virtual grid unit, virtual grid convergence calculation is carried out on the energy release rate of the crack tip, and the convergent energy release rate is obtained; and calculating the strength factor of the incompressible material according to the convergent energy release rate. The method can accurately calculate the strength factor of the incompressible material.

Description

Technical Field

[0001] The invention belongs to the technical field of fracture mechanics, and in particular relates to a method for obtaining a strength factor of an incompressible material. Background Art

[0002] Incompressible materials such as rubber, asphalt, and solid propellants are widely used in aerospace and civil engineering.

[0003] However, the Poisson's ratio of incompressible materials is very close to 0.5. When performing structural simulation calculations, there are large errors in the calculation of its displacement field, resulting in a large gap between the calculation of its strength factor and the actual situation. Summary of the invention

[0004] The object of the present invention is to provide a method for obtaining the strength factor of an incompressible material, which can accurately calculate the strength factor of the incompressible material.

[0005] In order to achieve the above object, the present invention provides the following technical solutions: In a first aspect, the present invention provides a method for obtaining a strength factor of an incompressible material, comprising: Constructing a virtual mesh at the crack tip of an incompressible material containing a crack defect; Based on the Hermann variational method, finite element calculations of displacement and strain fields are performed on virtual grid cells to obtain displacement and stress-strain fields of virtual grid cells. According to the displacement field and stress-strain field of the virtual grid unit, the virtual grid convergence calculation is carried out on the energy release rate at the crack tip to obtain the converged energy release rate; Calculates the strength factor for incompressible materials based on the converged energy release rate.

[0006] In combination with the first aspect, further, constructing a virtual grid at a crack tip of an incompressible material containing a crack defect includes: Taking the crack tip of the incompressible material containing crack defects as the center, a ring with an inner diameter of NE and an inner and outer diameter difference of LE is constructed, and the corresponding crack is designed on the ring according to the crack path of the incompressible material; The ring is divided into N equal parts to form N quadrilateral virtual grid units.

[0007] In combination with the first aspect, further, based on the Hermann variational method, finite element calculation of displacement field and stress-strain field is performed on the virtual grid unit, and the displacement field and stress-strain field of the virtual grid unit are obtained, including: Based on the Hermann variational method, the deformation matrix, material matrix and stiffness matrix of the virtual grid unit are constructed, and the average volume deformation parameter of the virtual grid unit is used as the universal displacement. The finite element calculation of the displacement field of the virtual grid unit is carried out to obtain the displacement field of the virtual grid unit. Based on the Hermann variational method, finite element calculation of the stress and strain field of the virtual grid unit is carried out, and the stress and strain field of the virtual grid unit is obtained by difference.

[0008] In combination with the first aspect, further, the displacement field of the virtual grid unit is: ; in, represents the displacement field of the virtual grid cell, represents the stiffness matrix of the virtual mesh element, represents the external force matrix, represents the deformation matrix of the virtual grid cell, Represents the material matrix of the virtual mesh cells.

[0009] Combined with the first aspect, further, the wide displacement is: ; in, Indicates wide displacement, represents the total number of integration points of the virtual grid cell, represents the Poisson distribution, , Indicates that the virtual grid cell is direction, Direction of strain.

[0010] In combination with the first aspect, further, according to the displacement field and strain field of the virtual grid unit, the virtual grid convergence calculation is performed on the energy release rate at the crack tip, and obtaining the converged energy release rate includes: Under different NE, LE and N conditions, the virtual grid convergence calculation of the energy release rate at the crack tip is carried out according to the displacement field and strain field of the virtual grid unit to obtain the converged energy release rate; Among them, NE is 1 to 10 times the average size of the original grid, LE is 1 to 2 times the average size of the original grid, and N is 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 and 104 respectively; The convergent energy release rate is: ; in, , The energy release rate that indicates convergence is direction, The direction component, represents the outer boundary of the virtual grid cell, represents the strain energy density, , Indicates the normal vector outside the outer boundary of the virtual grid cell direction, The direction component, , , , Indicates that the virtual grid cell is direction, direction, direction, The stress tensor in the direction, , Indicates that the virtual grid cell is direction, Direction displacement.

[0011] In combination with the first aspect, further, the calculation formula of the strength factor of the incompressible material is: ; in, , represents the strength factor of the incompressible material, represents the equivalent elastic modulus of incompressible materials under plane strain conditions. , under plane stress conditions, ,in, represents the elastic modulus of the incompressible material, represents a Poisson distribution.

[0012] In a second aspect, the present invention provides a system for obtaining an intensity factor of an incompressible material, comprising: A virtual mesh construction module is used to construct a virtual mesh at the crack tip of an incompressible material containing a crack defect; The finite element calculation module is used to perform finite element calculation of displacement field and strain field on virtual grid cells based on the Hermann variation method, and obtain the displacement field and stress strain field of the virtual grid cells; The energy release rate calculation module is used to perform virtual grid convergence calculation on the energy release rate at the crack tip according to the displacement field and stress-strain field of the virtual grid unit to obtain the converged energy release rate; The strength factor calculation module is used to calculate the strength factor of incompressible materials based on the converged energy release rate.

[0013] In a third aspect, the present invention provides a computer device, comprising: Storage medium: used to store computer programs; Processor: used to execute a computer program to implement the method for obtaining the strength factor of an incompressible material as described in any one of the first aspects.

[0014] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the method for obtaining the strength factor of an incompressible material as described in any one of the first aspects is implemented.

[0015] In a fifth aspect, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the method for obtaining the strength factor of an incompressible material as described in any one of the first aspects.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The method for obtaining the strength factor of incompressible materials provided by the present invention is based on the Hermann variational method, performs finite element calculations of the displacement field and strain field of virtual grid units, obtains the displacement field and stress-strain field of the virtual grid units, and then performs virtual grid convergence calculations on the energy release rate at the crack tip. According to the converged energy release rate, the strength factor of the incompressible material is calculated, and the strength factor of the incompressible material can be accurately obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flow chart of a method for obtaining strength factor of an incompressible material provided by an embodiment of the present invention; Figure 2 It is a schematic diagram of a virtual grid provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The technical solution of the present application is further described in detail below in conjunction with specific implementation methods.

[0019] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and should not be construed as limitations on the present application. In the absence of conflict, the embodiments of the present application and the technical features in the embodiments may be combined with each other.

[0020] An embodiment of the present application provides a method for obtaining the strength factor of an incompressible material. The method for obtaining the strength factor of an incompressible material provided in the embodiment of the present application can be applied to a terminal and can be executed by an incompressible material strength factor obtaining system. The incompressible material strength factor obtaining system can be implemented by software and / or hardware. The incompressible material strength factor obtaining system can be integrated in a terminal, for example: any tablet computer or computer device with communication function.

[0021] Figure 1 is a flow chart of the method for obtaining the strength factor of incompressible materials provided in this embodiment. This flow chart only shows the logical sequence of the method of this embodiment. Different methods can be used without conflict. Figure 1 The steps shown or described are accomplished in the order shown.

[0022] like Figure 1 As shown, the method for obtaining the strength factor of an incompressible material provided in this embodiment includes: Constructing a virtual mesh at the crack tip of an incompressible material containing a crack defect; Based on the Hermann variational method, finite element calculations of displacement and strain fields are performed on virtual grid cells to obtain displacement and stress-strain fields of virtual grid cells. According to the displacement field and stress-strain field of the virtual grid unit, the virtual grid convergence calculation is carried out on the energy release rate at the crack tip to obtain the converged energy release rate; Calculates the strength factor for incompressible materials based on the converged energy release rate.

[0023] The method for obtaining the strength factor of an incompressible material provided in an embodiment of the present application is based on the Hermann variational method, performs finite element calculations of the displacement field and strain field of a virtual grid unit, obtains the displacement field and stress-strain field of the virtual grid unit, and then performs virtual grid convergence calculations on the energy release rate at the crack tip. According to the converged energy release rate, the strength factor of the incompressible material is calculated, and the strength factor of the incompressible material can be accurately obtained.

[0024] In a possible embodiment, constructing a virtual mesh at a crack tip of an incompressible material containing a crack defect includes: Taking the crack tip of the incompressible material containing crack defects as the center, a ring with an inner diameter of NE and an inner and outer diameter difference of LE is constructed, and the corresponding crack is designed on the ring according to the crack path of the incompressible material; The ring is divided into N equal parts to form N quadrilateral virtual grid units.

[0025] Specifically, Figure 2 As shown in the figure, with the crack tip of the incompressible material containing crack defects as the center, a ring with an inner diameter of NE and an inner and outer diameter difference of LE is constructed, and the corresponding crack is designed on the ring according to the crack path of the incompressible material; the ring is divided into N equal parts to form N quadrilateral virtual grid units.

[0026] In a possible embodiment, based on the Hermann variation method, finite element calculation of displacement field and stress-strain field is performed on the virtual grid unit, and obtaining the displacement field and stress-strain field of the virtual grid unit includes: Based on the Hermann variational method, the deformation matrix, material matrix and stiffness matrix of the virtual grid unit are constructed, and the average volume deformation parameter of the virtual grid unit is used as the universal displacement. The finite element calculation of the displacement field of the virtual grid unit is carried out to obtain the displacement field of the virtual grid unit. Based on the Hermann variational method, finite element calculation of the stress and strain field of the virtual grid unit is carried out, and the stress and strain field of the virtual grid unit is obtained by difference.

[0027] In this embodiment, the displacement field of the virtual grid unit is: ; in, represents the displacement field of the virtual grid cell, represents the stiffness matrix of the virtual mesh element, represents the external force matrix, represents the deformation matrix of the virtual grid cell, Represents the material matrix of the virtual mesh cells.

[0028] The wide displacement is: ; in, Indicates wide displacement, represents the total number of integration points of the virtual grid cell, represents the Poisson distribution, , Indicates that the virtual grid cell is direction, Direction of strain.

[0029] In a possible embodiment, a virtual grid convergence calculation is performed on the energy release rate at the crack tip according to the displacement field and strain field of the virtual grid unit, and obtaining the converged energy release rate includes: under different NE, LE and N conditions, a virtual grid convergence calculation is performed on the energy release rate at the crack tip according to the displacement field and strain field of the virtual grid unit to obtain the converged energy release rate.

[0030] The convergent energy release rate is: ; in, , The energy release rate that indicates convergence is direction, The direction component, represents the outer boundary of the virtual grid cell, represents the strain energy density, , Indicates the normal vector outside the outer boundary of the virtual grid cell direction, The direction component, , , , Indicates that the virtual grid cell is direction, direction, direction, The stress tensor in the direction, , Indicates that the virtual grid cell is direction, Direction displacement.

[0031] Specifically, NE is 1 to 10 times the average size of the original grid, LE is 1 to 2 times the average size of the original grid, and N is 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and 104, respectively. , , and draw and The relationship between the change curve.

[0032] In this embodiment, the calculation formula of the strength factor of the incompressible material is: ; in, , represents the strength factor of the incompressible material, represents the equivalent elastic modulus of incompressible materials under plane strain conditions. , under plane stress conditions, ,in, represents the elastic modulus of the incompressible material, represents a Poisson distribution.

[0033] The embodiment of the present application provides a system for obtaining strength factor of an incompressible material, comprising: A virtual mesh construction module is used to construct a virtual mesh at the crack tip of an incompressible material containing a crack defect; The finite element calculation module is used to perform finite element calculation of displacement field and strain field on virtual grid cells based on the Hermann variation method, and obtain the displacement field and stress strain field of the virtual grid cells; The energy release rate calculation module is used to perform virtual grid convergence calculation on the energy release rate at the crack tip according to the displacement field and stress-strain field of the virtual grid unit to obtain the converged energy release rate; The strength factor calculation module is used to calculate the strength factor of incompressible materials based on the converged energy release rate.

[0034] The incompressible material strength factor acquisition system provided in this embodiment can execute the incompressible material strength factor acquisition method provided in the embodiment of the present application, and has the corresponding functional modules and beneficial effects of the execution method.

[0035] An embodiment of the present application provides a computer device, including: Storage medium for storing computer programs; A processor is used to execute a computer program to implement the method for obtaining the strength factor of an incompressible material provided in an embodiment of the present application.

[0036] An embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for obtaining the strength factor of an incompressible material provided in the embodiment of the present application is implemented.

[0037] An embodiment of the present application provides a computer program product, including a computer program. When the computer program is executed by a processor, the method for obtaining the strength factor of an incompressible material provided in the embodiment of the present application is implemented.

[0038] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems or computer program products. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0039] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram and the combination of the processes and / or blocks in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0040] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0041] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0042] The above are only preferred implementations of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for obtaining the strength factor of an incompressible material, characterized in that: include: Constructing a virtual mesh at the crack tip of an incompressible material containing a crack defect; Based on the Herman variational method, finite element calculations of displacement and strain fields are performed on virtual grid cells to obtain displacement and stress-strain fields of virtual grid cells. According to the displacement field and stress-strain field of the virtual grid unit, the virtual grid convergence calculation is carried out on the energy release rate at the crack tip to obtain the converged energy release rate; Calculates the strength factor for incompressible materials based on the converged energy release rate.

2. The method for obtaining the strength factor of an incompressible material according to claim 1, characterized in that: Constructing a virtual mesh at the crack tip of an incompressible material with a crack defect includes: Taking the crack tip of the incompressible material containing crack defects as the center, a ring with an inner diameter of NE and an inner and outer diameter difference of LE is constructed, and the corresponding crack is designed on the ring according to the crack path of the incompressible material; The ring is divided into N equal parts to form N quadrilateral virtual grid units.

3. The method for obtaining the strength factor of incompressible materials according to claim 1, characterized in that: Based on the Hermann variational method, finite element calculations of displacement field and stress-strain field are carried out on the virtual grid unit to obtain the displacement field and stress-strain field of the virtual grid unit, including: Based on the Hermann variational method, the deformation matrix, material matrix and stiffness matrix of the virtual grid unit are constructed, and the average volume deformation parameter of the virtual grid unit is used as the generalized displacement. The finite element calculation of the displacement field of the virtual grid unit is carried out to obtain the displacement field of the virtual grid unit. Based on the Hermann variational method, finite element calculation of the stress and strain field of the virtual grid unit is carried out, and the stress and strain field of the virtual grid unit is obtained by difference.

4. The method for obtaining the strength factor of incompressible materials according to claim 3, characterized in that: The displacement field of the virtual grid element is: ； in, represents the displacement field of the virtual grid cell, represents the stiffness matrix of the virtual mesh element, represents the external force matrix, represents the deformation matrix of the virtual grid cell, Represents the material matrix of the virtual mesh cells.

5. The method for obtaining the strength factor of incompressible materials according to claim 3, characterized in that: The wide displacement is: ； in, Indicates wide displacement, represents the total number of integration points of the virtual grid cell, represents the Poisson distribution, , Indicates that the virtual grid cell is direction, Direction of strain.

6. The method for obtaining the strength factor of incompressible materials according to claim 2, characterized in that: According to the displacement field and strain field of the virtual grid unit, the virtual grid convergence calculation is carried out on the energy release rate at the crack tip. The converged energy release rate is obtained including: Under different NE, LE and N conditions, the virtual grid convergence calculation of the energy release rate at the crack tip is carried out according to the displacement field and strain field of the virtual grid unit to obtain the converged energy release rate; Among them, NE is 1 to 10 times the average size of the original grid, LE is 1 to 2 times the average size of the original grid, and N is 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 and 104 respectively; The convergent energy release rate is: ； in, , The energy release rate that indicates convergence is direction, The direction component, represents the outer boundary of the virtual grid cell, represents the strain energy density, , Indicates the normal vector outside the outer boundary of the virtual grid cell direction, The direction component, , , , Indicates that the virtual grid cell is direction, direction, direction, The stress tensor in the direction, , Indicates that the virtual grid cell is direction, Direction displacement.

7. The method for obtaining the strength factor of incompressible materials according to claim 6, characterized in that: The strength factor of incompressible materials is calculated as: ； in, , represents the strength factor of the incompressible material, represents the equivalent elastic modulus of incompressible materials under plane strain conditions. , under plane stress conditions, ,in, represents the elastic modulus of the incompressible material, represents a Poisson distribution.

8. A system for obtaining strength factors of incompressible materials, characterized in that: include: A virtual mesh construction module is used to construct a virtual mesh at the crack tip of an incompressible material containing a crack defect; The finite element calculation module is used to perform finite element calculation of displacement field and strain field on virtual grid cells based on the Hermann variation method, and obtain the displacement field and stress strain field of the virtual grid cells; The energy release rate calculation module is used to perform virtual grid convergence calculation on the energy release rate at the crack tip according to the displacement field and stress-strain field of the virtual grid unit to obtain the converged energy release rate; The strength factor calculation module is used to calculate the strength factor of incompressible materials based on the converged energy release rate.

9. A computer device comprising: Storage medium for storing computer programs; A processor, used to execute the computer program to implement the method for obtaining the strength factor of an incompressible material according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for obtaining the strength factor of an incompressible material according to any one of claims 1 to 7.

Images