Finite element design and analysis method for a new type of structural piezoelectric composite material

Abstract

This invention discloses a finite element design and analysis method for a novel structural piezoelectric composite material. The method includes the following steps: extracting the zero level set surface based on the spatial structural equation to create the geometric shapes of a 3D TPMS shell structure, including Schwarz P, Gyroid, Neovius, and Diamond structures; using Matlab to define the frame volume fraction of the geometric shapes and control the unit node information in the 3D TPMS shell structure model; generating the 3D TPMS shell structure model as an inp file, importing the inp file into Abaqus to generate hexahedral elements; using Rhino to smooth the surface of the hexahedral elements, exporting the STL file, and performing remeshing in Hypermesh to convert the hexahedral elements into tetrahedral elements; adding periodic boundary conditions to the tetrahedral element mesh and performing numerical simulation to obtain the TPMS shell structure composite material model. The novel TPMS shell structure piezoelectric composite material designed by this method significantly improves piezoelectric performance compared to existing piezoelectric composite materials.

Description

Technical Field

[0001] The present invention relates to the technical field of piezoelectric composite materials, and in particular to a finite element design and analysis method for a novel structural piezoelectric composite material. Background Art

[0002] With the continuous progress and development of society, people's demand for uninterrupted energy is constantly increasing, and people's awareness of environmental protection is also increasing. Therefore, the development of environmentally friendly, clean, and reliable new energy sources has become a new research hotspot in the world today. Piezoelectric composites can meet the demand for continuous power supply. They provide an effective way to absorb energy from the living environment. They can be used to power mobile electronics, ultrasonic sensors, brakes, speakers, strain gauges, and accelerometers. Generally, the energy conversion properties of piezoelectric composites are partly attributed to the microscopic ceramic structure of these composites. However, the inclusions of existing traditional piezoelectric composites are not carefully designed, and only simple shapes have been tried. The spatial discontinuity of the ceramic phase in these low-dimensional piezoelectric composites results in relatively poor load transfer from the surrounding polymer to the piezoelectric ceramic, thereby limiting the piezoelectric performance. Summary of the Invention

[0003] The present invention provides a finite element design and analysis method for a novel structural piezoelectric composite material, so as to overcome the problem that the existing piezoelectric composite material has low piezoelectric performance due to poor load transfer.

[0004] In order to achieve the above object, the technical solution of the present invention is:

[0005] A finite element design and analysis method for a novel structural piezoelectric composite material includes the following steps:

[0006] S1. Extract the zero level set surface based on the spatial structural equation and create the geometric shape of the 3D model of the TPMS shell structure, including: Schwarz P structure, Gyroid structure, Neovius structure and Diamond structure;

[0007] S2. Using Matlab to define the frame volume fraction of the geometric shape and control the unit node information in the 3D model of the TPMS shell structure to divide multiple unit grids for finite element analysis;

[0008] S3. Generate the TPMS shell structure 3D model as an inp file, and import the inp file into Abaqus to generate hexahedral elements;

[0009] S4. Smoothing the surface of the hexahedral unit using Rhino, exporting the STL file, and performing remeshing in Hypermesh to convert the hexahedral unit into a tetrahedral unit;

[0010] S5. Add periodic boundary conditions to the mesh of the tetrahedral unit and perform numerical simulation to obtain a TPMS shell structure composite material model.

[0011] Furthermore, the spatial structure equation in step S1 includes:

[0012]

[0013]

[0014]

[0015]

[0016] In the formula: x, y, z are spatial coordinates, k = 2π / 1, c is the level set function, is a periodic surface with cubic units.

[0017] Furthermore, the frame volume fraction in step S2 includes the piezoelectric ceramic volume fraction and the external polymer volume fraction, the piezoelectric ceramic volume fraction is 16%, and the external polymer volume fraction is 84%.

[0018] Furthermore, the nodes generated by the re-gridding command in step S4 use a global Cartesian coordinate system.

[0019] Furthermore, the periodic boundary condition in step S5 is to ensure that the variables have the same value at opposite boundary nodes, and is expressed as follows:

[0020] n×(E1-E2)=0;

[0021] Where: n is the normal vector of the opposite interface, E1 and E2 are the electric fields on the surface of the TPMS shell structure composite material model.

[0022] Beneficial effects: Through finite element analysis, the present invention designs a variety of new structures of piezoelectric composite materials for TPMS shell structures, converts hexahedral units into tetrahedral units, enhances the load transfer capacity from polymer to piezoelectric ceramics, and improves the piezoelectric performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0024] Figure 1 This is the overall flow chart of the design and analysis method of the present invention;

[0025] Figure 2 Four TPMS shell structure frames defined by Matlab in the present invention;

[0026] Figure 3 The piezoelectric ceramic polymer created for the present invention using finite element software;

[0027] Figure 4 The TPMS shell structure framework is meshed using finite element software in the present invention;

[0028] Figure 5a The output voltage of 9 piezoelectric composite materials with different structures analyzed by finite element software when the compressive strain is 2%;

[0029] Figure 5b The output voltage of 9 piezoelectric composite materials with different structures analyzed by finite element software when the compressive strain is 5%;

[0030] Figure 5c The output voltage of 9 piezoelectric composite materials with different structures analyzed by finite element software when the compressive strain is 8%;

[0031] Figure 6 This is a potential trend diagram of the TPMS shell structure analyzed by Abaqus in the present invention;

[0032] Figure 7 This is a current trend diagram of the TPMS shell structure analyzed by Abaqus in the present invention. DETAILED DESCRIPTION

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of 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. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0034] This embodiment provides a finite element design and analysis method for a novel structured piezoelectric composite material. Figure 1 As shown, the following steps are included:

[0035] S1. Extract the zero level set surface based on the spatial structural equation and create the geometric shape of the 3D model of the TPMS shell structure, including: Schwarz P structure, Gyroid structure, Neovius structure and Diamond structure;

[0036] S2. Using Matlab to define the frame volume fraction of the geometric shape and control the unit node information in the 3D model of the TPMS shell structure to divide multiple unit grids for finite element analysis;

[0037] S3. Generate the TPMS shell structure 3D model as an inp file, and import the inp file into Abaqus to generate hexahedral elements;

[0038] S4. Smoothing the surface of the hexahedral unit using Rhino, exporting the STL file, and performing remeshing in Hypermesh to convert the hexahedral unit into a tetrahedral unit;

[0039] S5. Add periodic boundary conditions to the mesh of the tetrahedral unit and perform numerical simulation to obtain a TPMS shell structure composite material model.

[0040] The modeling formula used in step S1 to create the 3D model of the TPMS geometry includes:

[0041]

[0042]

[0043]

[0044]

[0045] In the formula: x, y, z are spatial coordinates, k = 2π / 1, c is the level set function, is a periodic surface with cubic units.

[0046] The nodes generated by the remeshing command in step S4 use the global Cartesian coordinate system.

[0047] The periodic boundary condition in step S5 is to ensure that the variables have the same value at opposite boundary nodes, and is expressed as follows:

[0048] n×(E1-E2)=0;

[0049] Where: n is the normal vector of the opposite interface, E1 and E2 are the electric fields on the surface.

[0050] Specifically, the 3D model of the TPMS plate geometry is created by extracting the zero level set surface from the equation, i.e., Defined surfaces, such as Figure 2The following are the frameworks of four TPMS shell structures generated by Matlab using four modeling formulas: Schwarz P structure, Gyroid structure, Neovius structure, and Diamond structure. It is worth noting that the level set function is negative in the area occupied by the piezoelectric material, that is, It is positive in the polymer region, i.e. The volume fraction of the PZT material can be easily adjusted by setting the value of c. The above operations are all implemented in Matlab, and by changing the value of c in the equation, the volume fraction of the piezoelectric ceramic is determined to be 16%, and an inp file is generated for the next step. In Matlab, by changing the value of c, a certain thickness is given to the model, that is, TPMS structures with different volume fractions are obtained. In this embodiment, c = 0 when extracting the zero level set surface. Figure 2 When the volume fraction is 16%, c = 0.32. Complex and logical three-periodic minimal surfaces can be described by mathematical expressions, and the same mathematical expression can be used to obtain countless minimal surfaces by adjusting the parameters.

[0051] Specifically, the numerical simulation of the TPMS shell structure was performed using the commercial FE software package Abaqus / Explicit 2016, a software suite (Dassault Systems 2018) commonly used for finite element modeling and visualization of finite element analysis results. Conventional shell, continuum shell, and solid elements are available for modeling composite structures. During the modeling process, the TPMS shell structure was constructed using cubic elements with a side length of 1 mm, and the ceramic portion accounted for 16% of the volume. For analytical purposes, the structure was divided into small elements. The elements generated by the Abaqus meshing command are in the active element coordinate system, and the nodes generated by the meshing command use the global Cartesian coordinate system. Furthermore, to fully define the numerical model, appropriate periodic boundary conditions must be added to this simulation. Periodic boundary conditions ensure that variables have the same value at opposing boundary nodes. Mathematically, they are defined as n × (E1 - E2) = 0, where n is the normal vector of the opposing interface and E1 and E2 are the electric fields on the surface. To facilitate the implementation of periodic boundary conditions, each pair of nodes on opposing surfaces is assigned the same node number in the finite element analysis. However, since the jagged boundaries in the hexahedral mesh cannot perfectly capture the elegant shape of the TPMS structure, the TPMS shell structure is modeled using three-dimensional tetrahedral elements (C3D4E). The optimization process of the TPMS structure from hexahedral elements to tetrahedral elements is very complicated. The framework and volume fraction of the TPMS shell structure are defined in Matlab, and then the hexahedral elements are generated in Abaqus. Rhino is used to create, edit, analyze and convert NURBS curves, surfaces and solids without restrictions on complexity, angle and size. Therefore, the process of structural surface optimization needs to be completed in Rhino, such as Figure 3The figure shows a piezoelectric ceramic polymer created using Rhino, where the volume fraction of piezoelectric ceramic is 16% and the volume fraction of external polymer is 84%. This step can make the structural surface of the shell smoother and facilitate the next step. Then it is necessary to re-mesh in Hypermesh and generate a tetrahedral mesh on the shell surface. The specific steps are: use Rhino to create, edit, analyze and convert NURBS curves, surfaces and entities, and it can be free from complexity, angle and size restrictions; therefore, the optimization process of the structural surface needs to be completed in Rhino, select the entire hexahedral unit structure, then select the mesh in the tool options, and configure the rendering mesh quality to a smoother and slower property value, then regenerate the STL file and import it into Abaqus for finite element analysis. Under the "model" browser, create a new "component" and name it "mesh" to store the solid mesh. Then under the 3D main menu "tetramesh", select "Volumatetra" and set the mesh size. Then select the entity, and "mesh" will divide the tetrahedral mesh. At this time, the division of the tetrahedral unit mesh is completed, and the number of units is close to 800,000. Figure 4 As shown in Figure 4, it is intuitively illustrated that the surface of the TPMS ceramic structure in the tetrahedral unit model is smoother, which directly affects the output voltage results. At the same time, the calculation error caused by inaccurate geometric structure can be alleviated by fine meshing. In addition, assuming that the interface is seamless, adjacent elements of the ceramic and polymer components share the same nodes. This approach allows the polymer to be continuously distributed throughout the structure to ensure good stress transfer at the interface.

[0052] Specifically, the above is the part of finite element software modeling. The following is the compression response of the model studied through finite element analysis. The calculation of the piezoelectric constitutive equation of the coupled mechanical field and electric field can intuitively reflect the piezoelectric properties of the piezoelectric composite material. Its constitutive equation is: D = d:σ + τ·E; ε = S:σ + d·E.

[0053] In this embodiment, the TPMS shell structure is selected as a benchmark to study the effect of the internal structure on the piezoelectric performance, e.g. Figure 5a 、 5b 5c shows a comparison of the output voltages of several different geometric structures with the same ceramic volume fraction. In Abaqus, 2%, 5%, and 8% compressive deformations are applied to the surface along the polarization direction, i.e., the z direction. Figure 5a 、 5bIn the horizontal coordinates of 5c: a is a 0-3 type piezoelectric composite material; b is a 1-3 type piezoelectric composite material; c is a 3-3 type piezoelectric composite material; d is a Gyroid type hexahedral piezoelectric composite material; e is a Neovius type hexahedral piezoelectric composite material; f is a Schwarz P type tetrahedral shell structure piezoelectric composite material; g is a Gyroid type tetrahedral shell structure piezoelectric composite material; h is a Neovius type tetrahedral shell structure piezoelectric composite material; i is a Diamond type tetrahedral shell structure piezoelectric composite material. Among them, a, b, c, d, and e are five existing piezoelectric composite structures, and f, g, h, and i are four new piezoelectric composite structures of the present invention. The three comparison graphs show the linear relationship between the composite output voltage and compression deformation of the TPMS shell structure. Obviously, the Schwarz P structure, Gyroid structure, Neovius structure, and Diamond structure all exhibit extremely high output voltage. It is also found that at compression deformations of 2%, 5%, and 8%, the Diamond shell structure has the highest output voltage, at 802V, 2007V, and 3211V, respectively. The output voltage of piezoelectric composites characterized by randomly distributed rod-shaped, spherical, and interconnected irregular-shaped ceramic materials is also analyzed. Under 8% compression deformation, the output voltage of the 0-3 type piezoelectric composite material is only 0.2V, which is caused by the discontinuity of the internal ceramic structure. For the 1-3 type piezoelectric composite material, the connectivity of the ceramic has been improved to a certain extent, and its output voltage has increased to 26.87V. The piezoelectric performance is better in the 3-3 type piezoelectric composite material, and the output voltage has increased by nearly 3 times to nearly 84V. The piezoelectric performance of these three piezoelectric composite materials shows that without changing the connectivity, the discontinuity of the ceramic material plays an important role in the piezoelectric effect. Under the same compression deformation, the output voltage of the TPMS shell structure is 13 times to more than 7000 times greater than that of the 3-3 type piezoelectric composite material and the 0-3 type piezoelectric composite material. Therefore, it can be concluded that the shape of the ceramic material also plays an important role in improving the performance of the piezoelectric composite material.

[0054] In this example, in order to explain the superiority of the TPMS shell structure over its homologous structure, the potential distribution on the piezoelectric ceramic surface was also studied, as shown in Figure 2. Figure 6 As shown in the first row, the potential at the top of the TPMS shell structure is negative, and the potential at the bottom gradually increases to about 3×10 4 ; In order to study the electric potential inside the composite material, Figure 6 The second row shows the potential on the cross section when z = 0. It can be seen that the potential difference between the structures corresponding to the third and fourth figures in the second row is the most obvious. The fourth figure in the second row represents the diamond structure composite material, whose maximum potential can reach 2.87×10 4 V, the minimum potential can reach -1.77×10 3V, such a large potential difference will cause a strong current to be generated in the piezoelectric composite material. The structure with a smooth surface usually has the characteristics of low resistance or high conductivity. According to Ohm's law, voltage is inversely proportional to resistance and directly proportional to current. Therefore, it can be proved that the TPMS shell structure can generate a higher output voltage and is the best material choice for piezoelectric composite materials. Figure 7 The figure shows the current on the shell-shaped ceramic surface of these composite materials, where strong electricity is above the z-axis and weak electricity is below. Compressive strain is applied to the piezoelectric composite material in the z-axis direction. The strong current on the TPMS ceramic structure is mainly concentrated at the upper and lower ends, and the current flows evenly on the ceramic surface from top to bottom. The reason is that the smooth surface is conducive to the flow of charge and can more easily penetrate any part of the structure, thereby improving the load transfer ability and greatly improving the piezoelectric performance.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A finite element design and analysis method for a novel structural piezoelectric composite material, characterized in that: The following steps are involved: S1. Extract the zero level set surface based on the spatial structural equation and create the geometric shape of the 3D model of the TPMS shell structure, including: Schwarz P structure, Gyroid structure, Neovius structure and Diamond structure; S2. Using Matlab to define the frame volume fraction of the geometric shape and control the unit node information in the 3D model of the TPMS shell structure to divide multiple unit grids for finite element analysis; S3. Generate the TPMS shell structure 3D model as an inp file, and import the inp file into Abaqus to generate hexahedral elements; S4. Smoothing the surface of the hexahedral unit using Rhino, exporting the STL file, and performing remeshing in Hypermesh to convert the hexahedral unit into a tetrahedral unit; S5. Adding periodic boundary conditions to the mesh of the tetrahedral unit and performing numerical simulation to obtain a TPMS shell structure composite material model; S6. The spatial structure equation in step S1 includes: In the formula: x, y, z are spatial coordinates, k = 2π / 1, c is the level set function, is a periodic surface with cubic units.

2. The finite element design and analysis method for a novel structural piezoelectric composite material according to claim 1, characterized in that: The frame volume fraction in step S2 includes the piezoelectric ceramic volume fraction and the external polymer volume fraction, the piezoelectric ceramic volume fraction is 16%, and the external polymer volume fraction is 84%.

3. The finite element design and analysis method for a novel structural piezoelectric composite material according to claim 1, characterized in that: The nodes generated by the re-gridding command in step S4 use the global Cartesian coordinate system.

4. The finite element design and analysis method for a novel structural piezoelectric composite material according to claim 1, characterized in that: The periodic boundary condition in step S5 is to ensure that the variables have the same value at opposite boundary nodes, and is expressed as follows: n×(E1-E2)=0; Where: n is the normal vector of the opposite interface, E1 and E2 are the electric fields on the surface of the TPMS shell structure composite material model.

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