Simulation and prediction method for instability phenomenon of dielectric high-elastic thin shell

Abstract

The invention discloses a simulation and prediction method for an instability phenomenon of a dielectric high-elastic thin shell. The method comprises the following steps: S1, constructing a mechanical-electric coupling constitutive model of a dielectric high-elastic material; s2, developing a numerical analysis method of the nonlinear response of the dielectric high-elastic thin shell; s3, simulating the overall instability phenomenon of the structure under large deformation; and S4, outputting the complex mechanical behavior under the predicted force-electricity coupling effect. Compared with the prior art, the method for simulating and predicting the instability phenomenon of the dielectric high-elastic thin shell has the advantages that the method can be used for capturing the complex shape and geometric change of the dielectric high-elastic thin shell and simulating the complex behavior of the thin shell under the force-electricity coupling effect.

Description

Technical Field

[0001] The invention relates to the technical field of dielectric high-elastic thin shell instability phenomenon analysis, and in particular to a simulation prediction method for dielectric high-elastic thin shell instability phenomenon. Background Art

[0002] Intelligent soft robots are a new type of robot system that integrates advanced material science, robotics technology, control algorithms, and complex mechanical structures. The field of intelligent soft robots is undergoing a rapid evolution and development from single materials to multiple materials and then to intelligent materials. At present, dielectric polymer elastic (dielectric polymer elastic) materials widely used in intelligent soft robots are a commonly used intelligent material. Applications include soft robots, soft grippers, artificial muscles and other intelligent devices. They will deform when subjected to electric fields, and will also produce charge distribution changes under the action of mechanical forces, showing a strong electromechanical coupling effect.

[0003] However, the mechanical response of this type of dielectric highly elastic soft intelligent device has electromechanical coupling characteristics, as well as strong nonlinearity of materials and geometry. Based on large deformation, local morphological instability phenomena such as wrinkles and creases may occur, and overall instability phenomena such as volume mutation and symmetry breaking may also occur. These instabilities may cause defects and damage to robotic devices, but the morphological changes associated with instability can also be cleverly utilized as the electric drive function of soft robots. Therefore, systematically simulating and accurately analyzing the various instability phenomena of dielectric highly elastic thin shell structures is crucial to the design, optimization and manufacturing of intelligent soft robots.

[0004] At present, the relevant analysis theory of dielectric highly elastic thin shells is still in the development stage, and the research on their mechanical properties is also mainly based on experiments. The industry still lacks numerical methods to simulate the large deformation and instability of the structure under the action of electromechanical coupling, which has seriously restricted the large-scale engineering application of dielectric highly elastic thin shell structures in the field of intelligent soft robots. Mathematical modeling of dielectric highly elastic thin shell structures and establishment of accurate and efficient numerical simulation methods can save a lot of experimental materials, time and manpower, accelerate the revelation of the electromechanical coupling response law of the structure, and provide a basis for the design and manufacture of intelligent materials and structures. Summary of the invention

[0005] The technical problem to be solved by the present invention is to overcome the above technical defects and provide a simulation and prediction method for the instability phenomenon of dielectric highly elastic thin shells, which can be used to capture the complex shape and geometric changes of dielectric highly elastic thin shells and simulate the complex behavior of the thin shells under the action of electromechanical coupling.

[0006] In order to solve the above technical problems, the technical solution provided by the present invention is: a simulation and prediction method for the instability phenomenon of dielectric highly elastic thin shells, comprising the following steps: S1: constructing a mechanoelectric coupling constitutive model of dielectric highly elastic materials; S2: developing an isogeometric analysis method for the nonlinear response of dielectric highly elastic thin shells; S3: simulating the overall instability phenomenon of the structure under large deformation; S4: outputting the predicted complex mechanical behavior under the action of mechanoelectric coupling.

[0007] Preferably, constructing the constitutive model in S1 includes establishing a nonlinear Kirchhoff-Love thin shell theory under electromechanical coupling, deriving control equations of the thin shell structure under different electrical loading modes, and establishing a dielectric highly elastic thin shell electromechanical coupling theoretical model.

[0008] Preferably, the numerical analysis method in S2 includes a method based on finite element analysis of geometric thin shells such as subdivision surfaces, combined with a multi-physics field coupling analysis method and a nonlinear numerical analysis tool.

[0009] Preferably, the energy density of electromechanical coupling is added to the free energy density of the Mooney-Rivlin polymer hyperelastic constitutive model to construct the nominal energy density of the dielectric hyperelastic material.

[0010] Preferably, the instability phenomenon in S3 includes volume jump and symmetry breaking.

[0011] Preferably, the isogeometric analysis method includes Catmull-Clark subdivision surface and adaptive arc length method.

[0012] The advantages of the present invention over the prior art are that the method provided by the present invention has a clear and progressive technical route, and is carried out in sequence according to the technical route of establishing a theoretical model, developing an analysis method, simulating and predicting instability phenomena. Based on the electroelasticity theory and the thin shell theory, a mechanoelectric coupling theoretical model of a dielectric highly elastic thin shell is established, and an isogeometric analysis model is established using the subdivision surface method to simulate the nonlinear large deformation of the mechanoelectric coupling thin shell structure, simulate and predict various instability phenomena of the dielectric highly elastic thin shell structure, thereby revealing the mechanical properties of the dielectric highly elastic soft robot under the influence of multi-physical fields, and promoting the application and development of the dielectric highly elastic thin shell structure in the field of intelligent soft robots. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a structural diagram of the patent name of this invention.

[0014] Figure 2 This is a schematic diagram of the Kirchhoff-Love thin shell.

[0015] Figure 3 It is the electric field loading method of some dielectric highly elastic thin shells.

[0016] Figure 4 It is a schematic diagram of the algorithm steps.

[0017] Figure 5 This is a schematic diagram of volume and pressure in a polymer elastic thin shell structure.

[0018] Figure 6 It is a schematic diagram of the electroelastic circular ring shell after it is inflated to near the limit point.

[0019] Figure 7 It is a flow chart of the segmentation algorithm.

[0020] Figure 8 It is the Catmull-Clark subdivision surface and its spline interpolation function.

[0021] Fig. 9 is a schematic diagram of a subdivision surface unit with singular vertices.

[0022] Fig.10 It is a schematic diagram of how adaptive arc length improves calculation efficiency and reliability by dynamically adjusting the step size. DETAILED DESCRIPTION

[0023] The following is combined with Figure 1-10 The present invention is described in further detail.

[0024] A simulation and prediction method for the instability phenomenon of dielectric highly elastic thin shells:

[0025] (1) Construct a mechanical-electric coupling constitutive model for dielectric hyperelastic materials, establish the nonlinear Kirchhoff-Love thin shell theory under mechanical-electric coupling, derive the control equations of the thin shell structure under different electrical loading modes, and establish a complete mechanical-electric coupling theoretical model for dielectric hyperelastic thin shells;

[0026] (2) Based on the finite element analysis of thin geometric shells such as subdivision surfaces, combined with multi-physics field coupling analysis methods and nonlinear numerical analysis tools, develop a numerical analysis method for the nonlinear response of dielectric highly elastic thin shells;

[0027] (3) Simulate the local and overall instability of the structure under large deformation and predict the complex mechanical behavior under electromechanical coupling. The technical route of the scheme is clear and progressive, following the technical route of establishing theoretical models, developing analysis methods, simulating and predicting instability phenomena.

[0028] The present invention is specifically implemented:

[0029] 1. Electromechanical coupling constitutive model of dielectric hyperelastic materials

[0030] The electromechanical coupling of materials is added to the hyperelastic constitutive model, and the constitutive model of dielectric polymer materials is derived.

[0031] The Mooney-Rivlin model is selected as the constitutive model of polymer hyperelastic materials, and on this basis it can be extended to more complex constitutive models such as Ogden, Gent, and Arruda-Boyce.

[0032] The energy density part of the electromechanical coupling is added to the free energy density expression of the constitutive model (the electric field energy density part is ignored here) to construct the nominal energy density of the dielectric high elastic material, which is expressed as:

[0033]

[0034] in is the elastic energy density part. Taking the Mooney-Rivlin constitutive model as an example, it is expressed as:

[0035]

[0036] Where I1, I2 are the first and second invariants of the stress tensor, C1, C2 are material parameters, is the energy density of electromechanical coupling. Here we only give a simple solution, namely:

[0037]

[0038] In the formula is the stress tensor, D is the nominal electric displacement, and b is the electromechanical coupling coefficient, which is a material parameter. The energy density is given by coupling stress and electric displacement. However, dielectric polymer materials are mostly incompressible materials, so the incompressible condition needs to be introduced in the nominal energy density function.

[0039] 2. Nonlinear Kirchhoff-Love shell theory under electromechanical coupling

[0040] The work of linear elastic Kirchhoff-Love thin shell analysis is extended to nonlinear large deformation analysis of thin shell structures. Figure 2 (a) The thin shell structure satisfying the Kirchhoff-Love assumption is defined and the parameter domain coordinates (θ1, θ2, θ3) and global coordinates (x, y, z) are given.

[0041] The Kirchhoff-Love thin shell theory assumes that the lines perpendicular to the neutral plane in the shell remain straight and perpendicular to the neutral plane after deformation, thus converting the solution of the three-dimensional problem to the neutral surface of the shell.

[0042] Figure 2(a) The thickness of the Kirchhoff-Love shell is h, and any point on the shell can be converted from the corresponding parameter domain coordinates (θ1, θ2, θ3); (b) the reference configuration of the neutral surface is converted into the deformed configuration through motion, and both can also be converted from the parameter coordinates (θ1, θ2).

[0043] Figure 2 (b) Defines the relationship between the reference and deformation configurations of the shell neutral surface

[0044] In this method, the nonlinear finite element framework uses the full Lagrangian format to calculate the strain of a point in the thin shell, that is, the reference configuration is always the initial geometric position of the thin shell structure. and a i are the covariant basis vectors on the neutral plane of the reference and deformed configurations, respectively. The covariant basis vectors of the reference and deformed configurations at other locations in the shell are defined as:

[0045]

[0046] Unlike the thin shell with small deformation, the thickness of the shell with large deformation will change significantly after large deformation. Therefore, it is necessary to introduce the thickness stretch λ3 to describe the change of thickness. α and β are indices ranging from 1 to 2. The Cauchy-Green strain tensor C is defined as:

[0047]

[0048] The corresponding Green-Lagrange strain tensor E is

[0049]

[0050] in is the contravariant basis vector under the reference configuration. ij and are the components of the covariant metric tensor, defined as:

[0051]

[0052] The Green-Lagrange strain tensor can be expanded with respect to the thickness coordinate θ3 to obtain the linear expansion of the Green-Lagrange strain tensor:

[0053] E=A+θ3B (8)

[0054] The tensors A and B are the membrane strain tensor and the bending strain tensor, respectively, with components α αβ and β αβ .

[0055] After considering the electromechanical coupling, the total energy of the Kirchhoff-Love shell system has the following form:

[0056]

[0057] in is the mid-surface under the reference configuration, W is the nominal energy density, and v is the Jacobi in the thickness direction. When the system is in equilibrium, the total energy of the system takes a stationary value, so taking a first variation of it, we have

[0058] ε∏=ε∏ int -δ∏ ext =0 (10)

[0059] where Π int and Π ext They are the internal potential energy and external potential energy of the system respectively, both of which contain mechanical energy and electrical energy, that is, they are functions of displacement and electric potential.

[0060] When in use, if only the large deformation of the dielectric high-elastic thin shell structure after the voltage is applied to the upper and lower surface electrodes is considered, and the change in the dielectric properties of the material caused by the mechanical deformation is ignored, the problem can be regarded as a one-way coupling problem of applying an electrical load to the structure to generate mechanical deformation, that is:

[0061] The electric load, while considered as an external force, changes the mechanical properties of the material through coupling effects, with only the displacement being an unknown;

[0062] If the effect of mechanical force on the internal electric field of the material is considered, it becomes a two-way coupling problem, and the electric potential is solved as an unknown variable.

[0063] 3. Control equations of dielectric high-elastic thin shell under different electrical loading modes

[0064] The thin shell theory expands the strain series in the thickness direction, retaining the membrane strain (zero-order term) and the bending strain (first-order term) to describe the deformation of the shell.

[0065] Expand the electric potential of a thin shell structure through the thickness direction and keep the first three terms:

[0066]

[0067] Then the electric field strength can be expressed as:

[0068]

[0069] Substituting the expression of electric field intensity into the electromechanical coupling model of thin shells, it is found that the membrane strain of the thin shell is coupled with the first-order potential, while the bending strain is coupled with the zero-order and second-order potentials. If the 0th, 1st, and 2nd order potentials are regarded as independent variables, corresponding control equations can be established for different electrical boundary conditions. For example, if an electrode coating is applied to the upper and lower surfaces and a voltage is applied, the zero-order and first-order potentials satisfy:

[0070]

[0071] Taking the electrical boundary condition of symmetrically applied voltage as an example, V2=-V1, and the solution is φ (0) =0,φ (1) =2V1 / h

[0072] Its zero-order potential is zero, the first-order potential is known, and only the second-order potential that changes parabolically along the thickness direction is unknown.

[0073] 4. Efficient solution algorithm for electromechanical coupling system equations

[0074] In the nonlinear finite element method, the load will be applied in steps, and any load step will be linearized using the Newton iteration method. In each Newton iteration, there is a linearized mechanical system equation:

[0075] KΔu=-R u (14)

[0076] Where K is the linear stiffness matrix, Δu is the displacement increment, R u is the residual vector of mechanical energy. At the same time, the corresponding linearized dielectric system equation inside the structure is introduced:

[0077]

[0078] Where H is the dielectric coefficient matrix, is the potential increment, is the residual vector of electric energy. When the mechanical energy of the dielectric thin shell structure is coupled with the electric energy, the equation is modified as follows:

[0079]

[0080] in is the linear forward electromechanical coupling matrix. When a potential difference is applied to the thin shell, strain is generated inside the structure, which is equivalent to the shell structure being subjected to additional energy generated by the electromechanical coupling effect. The mechanical system equation can be expressed as:

[0081]

[0082] in is the inverse electromechanical coupling matrix. The two equations can be combined to solve the coupling system equation in Newton iteration:

[0083]

[0084] The coupled system matrix is ​​a block matrix, and the system equation can be reduced to the following form using the Schur complement form of the matrix:

[0085]

[0086] The inverse operation of matrix D requires a lot of computing power. To improve efficiency, we can use the line operator method in the open source linear algebra library to approximate it. We use an efficient solver to perform double iterative solutions to reduce computational complexity. After solving the displacement increment, we can calculate the increment of the electric potential:

[0087]

[0088] 5. Efficient solution algorithm for linear systems

[0089] A nonlinear isogeometric finite element analysis model based on the subdivision surface method is established to solve the equation

[0090] The external force is applied in steps. In each loading step, the geometric and physical domains of the Kirchhoff-Love hyperelastic shell are discretized using the spline function of the subdivision surface with C1 continuity. The variation δΠ of the internal energy and the external energy is calculated using the subdivision surface spline basis function as the test function. int and δΠ ext Discretize into vector F int and F ext .

[0091] Define the residual vector of energy:

[0092] R=F int -F ext (twenty one)

[0093] When the residual R=0, the system reaches equilibrium. After linearizing the equation, the Newton iteration method is used to solve it to achieve large deformation analysis of thin shell problems.

[0094] The first-order approximation is obtained by performing Taylor series expansion on the nonlinear system equation to obtain a linearized equation. Based on this linear approximation equation, the load is applied step by step. In each load step, the Newton iteration method is used to gradually approach the true solution. The algorithm steps are as follows: Figure 4 As shown, it mainly includes 1. Initializing variables: at the beginning of each load step, provide a guess value of the initial solution. 2. Constructing a linear system: using the linear approximate equation obtained in this load step, establish a linear stiffness matrix. 3. Solving the linear system: Solve the constructed linear system to obtain the iterative increment. 4. Update variables: add the iterative increment to the solution of the current load step to obtain a new approximate solution. 5. Check convergence: verify whether the new approximate solution meets the predetermined convergence criteria. If it does, end the iteration; otherwise, re-establish the linear system and continue the iteration. 6. Iteration termination: when the solution meets the convergence criteria, it is considered that a sufficiently accurate solution has been obtained, the iterative process terminates, and the next load step begins.

[0095] 6. Numerical simulation of nonlinear post-buckling response of dielectric highly elastic thin shells

[0096] The arc length method is used to introduce the "arc length" that represents the nonlinear response in the load (mechanical field and electric field)-displacement space. The arc length is used as a parameter to control the step size on the curve to ensure the accuracy and stability of the nonlinear solution.

[0097] 7. Simulation of various instability phenomena of dielectric high-elastic thin shells under large deformation

[0098] The volume and pressure in a closed polymer elastic thin shell structure exist as follows Figure 5 In the relationship between the elastic thin shell structure and the pressure inside the thin shell structure, the initial stiffness is relatively large at the beginning of the inflation stage, and it is not easy to deform. As the internal pressure of the thin shell structure increases, the structure deforms, the internal gas volume increases, and the stiffness gradually decreases. When the internal pressure of the thin shell structure exceeds the Maxwell load and approaches the limit point,

[0099] The structure is in an unstable state. The electric load of the dielectric high-elastic thin shell structure will change the relationship between the pressure and volume inside the structure.

[0100] like Figure 5 (b) as shown.

[0101] When the pressure is near the limit point, the system can be in three equilibrium states, such as Figure 5 There are three points A, B and C in the diagram, and the overall energy of the system in these three states is different. When the pressure exceeds the Maxwell load, the energy added from point A to point B is less than the energy released from point B to point C. Under a slight disturbance, the system may suddenly jump from point A directly to point C.

[0102] Methods for dealing with incompressible conditions of dielectric high elastic materials include

[0103] The Lagrange multiplier method commonly used in numerical methods is used to introduce incompressible conditions into the internal energy equation and construct the Lagrangian function:

[0104]

[0105] in is the hydrostatic pressure in the incompressible material, i.e. the Lagrange multiplier, and [J tot -1] is the incompressible condition of the material. Taking the variation of the internal energy function, we get

[0106]

[0107] In the mechanical response analysis of dielectric high elastic membranes, in order to simplify the problem, the electric field is usually regarded as a known condition. Therefore, after introducing the Green-Lagrange strain, the variation of the internal energy function can be simplified to

[0108]

[0109] Where S is the Piola-Kirchhoff stress expressed as

[0110]

[0111] The first two terms can be regarded as the mechanical part of stress, and the third term is the stress part excited by the electric field, which can be expressed as:

[0112]

[0113] In the finite element method, the hydrostatic pressure can be Discretized as independent degrees of freedom, it can also be processed using the plane stress state of the Kirchhoff-Love thin shell structure, that is, the stress component in the thickness direction is zero:

[0114]

[0115] So as to find The expression

[0116]

[0117] The in-plane stress can be expressed as

[0118]

[0119] After the stress in the thickness direction is released, the equilibrium equation can be established in the neutral plane of the shell. In the equilibrium state, the variation of the Lagrangian function is zero. To solve this equation, we need to linearize it and solve it iteratively using Newton's method. That is, we need to use the derivative of stress with respect to strain to define the fourth-order elastic tensor: That is, the stress-strain relationship is expressed as

[0120] The subdivision surface geometry representation method can use a simple mesh to construct a single surface to represent a complex geometric topology, while having high continuity at any position on the surface. It uses Catmull-Clark subdivision surfaces including quadrilateral structured meshes and Loop subdivision surfaces including triangular unstructured meshes. Figure 7 shown.

[0121] The limit surface generated by the Catmull-Clark subdivision algorithm is exactly the same as the third-order B-spline surface, so the limit surface can also be obtained by interpolating the B-spline curve and the control points, as shown below:

[0122]

[0123] Where x is the limit surface point, P is the control point of the grid, and (ξ, η) is the coordinate of the parameter domain. The limit surface can be obtained by interpolating the control grid at any subdivision level. Figure 8The control points and basis functions required for interpolating the gray cells are shown. The 16 interpolation basis functions of Catmull-Clark are the tensor products of two one-dimensional third-order B-spline functions. The one-dimensional third-order B-spline function is:

[0124]

[0125] Cells on boundaries and corners require either truncating the basis functions or setting additional control points on the boundaries.

[0126] Figure 8 (a) Regular cell: 16 control points and interpolation basis functions. (b) Boundary cell: 12 control points and interpolation basis functions. (c) Corner cell: 9 control points and interpolation basis functions.

[0127] For subdivision surface elements with singular vertices, the number of control points and basis functions becomes 2κ+7, where κ is the vertex valence. Fig. 9 As shown in (a), the unit is locally subdivided until the integral point to be calculated falls into the regular unit, as shown in Fig. 9 (b) and Fig. 9 (c) as shown.

[0128] Subdivision surface spline function is used as the interpolation function of the electromechanical coupling large deformation control equation of dielectric highly elastic thin shell, and a numerical analysis model is established. Classic examples of shell problems including hemispherical shells and cylindrical shells are used to verify the effectiveness and accuracy of the shell structure analysis method.

[0129] The ability of subdivision surfaces to describe complex geometric shapes is used to perform mechanical analysis on thin shells with complex surface topology. The electromechanical coupling theory is introduced based on the geometric model of thin shell structures. While solving the large deformation nonlinear equations of the thin shell structure, the method needs to use the same nonlinear isogeometric finite element method framework to construct the system equations of the dielectric problem inside the structure. At the same time, the relationship between strain and electric field intensity derived from the electromechanical coupling constitutive method is used to establish two system equations, thereby establishing a system matrix for calculating the coupling problem.

[0130] Adaptive Arc Length Method

[0131] Take a reference pressure value p to construct the external force vector under the current configuration, introduce the load coefficient λ as a variable, and the system equation is that the residual vector is zero, expressed as

[0132] R(u,λ)=F int (u)-λF ext (u)=0 (32)

[0133] The internal force vector F int With the external force vector F extare functions of displacement. In the incremental method, the displacement and load factor of the current loading step are expressed as u n+1 and λ n+1 , is the value u from the previous converged loading step n and λ n Calculated by increasing Δu and Δλ respectively:

[0134]

[0135] where the subscripts n+1 and n denote the current and previous converged load steps, respectively. The residual of the current load step can be written as

[0136] R(u n+1 ,λ n+1 )=F int (u n+1 )-λ n+1 F ext (u n+1 )=0 (34)

[0137] Add an extra arc length equation to the nonlinear system of equations:

[0138] [Δu] T [Δu]+ψ[Δλ] 2 F T F=[Δs] 2 (35)

[0139] Δs is the arc length increment, F = F ext ψ is a scalar coefficient that controls the ratio of the load-displacement space. Using Newton's method, we can solve the above two equations to obtain Δu and Δλ. (1) ,Δλ (1) ), the increments of Δu and Δλ are calculated iteratively, expressed as δu and δλ. The increment of the k+1th Newton iteration can be expressed as

[0140]

[0141] The displacement and load coefficient after the k+1th Newton iteration in the n+1th step loading can be expressed as:

[0142]

[0143] After substituting it into the control equation, the system equation of the arc length method can be obtained:

[0144]

[0145] in is the structural stiffness matrix of the current iteration step, and the vector a=2[Δu (k)], scalar b = 2ψ[Δλ (k) ][F T F], the residual of the arc length equation is expressed as

[0146]

[0147] The system matrix equation can be solved to obtain δu and δλ, and the Newton iteration is continued until the preset convergence condition is met, thus ending this load step.

[0148] For the inflated dielectric high-elastic thin shell structure, in the initial stage of air pressure loading, the displacement increment is smaller than the increment of air pressure inside the structure. However, as the air pressure continues to increase, the structure gradually loses its stiffness, causing the displacement increment within the same arc length to gradually dominate, while the air pressure increment gradually decreases. When the air pressure reaches the limit value, the structural stiffness drops to zero, and then the load-displacement curve shows a downward trend.

[0149] In the solution of each loading step, the coefficient of the arc length method is adjusted according to the ratio of displacement to pressure increment, and the value of the determinant of the stiffness matrix is ​​calculated to determine the increase or decrease of the structural stiffness. Based on this, the step size of the arc length method can be adjusted dynamically. Therefore, an adaptive parameter α is introduced in the arc length method, and the solution based on two previously converged loading steps (n and n-1 steps) is used to predict the first iteration of the arc length method in the next loading step (n+1):

[0150]

[0151] Where α = Δs / Δs n is the ratio of the arc length increment, Δs is the arc length of the first loading step, Δs n is the arc length of the nth loading step. Then the increment in the prediction step can be expressed as

[0152]

[0153] like Fig.10 As shown in the figure, the value of α can be automatically adjusted to control the increment at different stages of the load-displacement curve. After each loading step converges, the determinant value of the stiffness matrix is ​​calculated and compared with the value of the previous loading step to determine the increase and decrease of the structural stiffness, and then adjust the value of α to achieve the adaptive arc length increment. If the value of the determinant gradually approaches zero, it means that the curve is about to reach the limit point. At this time, the arc length increment needs to be significantly reduced to ensure that the loading step can converge smoothly. If the value of the determinant changes its sign, the arc has experienced a stationary point, which can be used to determine the direction of the arc. At the same time, in the further improvement of the adaptive arc length method, a rollback mechanism is introduced to deal with the situation where convergence fails in a certain loading step. If the current loading step fails to meet the convergence conditions, the program will roll back to the solution of the previous loading step, and recalculate the new loading step after adjusting the arc length increment.

[0154] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

[0155] The present invention and its embodiments are described above, and such description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. In short, if ordinary technicians in the field are inspired by it, without departing from the purpose of the invention, they can design a structure and embodiment similar to the technical solution without creativity, which should belong to the protection scope of the present invention.

Claims

1. A simulation and prediction method for the instability phenomenon of dielectric high-elastic thin shells, characterized by: The following steps are involved: S1: Construct the electromechanical coupling constitutive model of dielectric high elastic materials; S2: Develop an isogeometric analysis method for the nonlinear response of dielectric highly elastic thin shells; S3: Simulate the overall instability of the structure under large deformation; S4: Output predicts complex mechanical behavior under electromechanical coupling.

2. The method for simulating and predicting the instability phenomenon of a dielectric high-elastic thin shell according to claim 1, characterized in that: The constitutive model constructed in S1 includes establishing the nonlinear Kirchhoff-Love thin shell theory under electromechanical coupling, deriving the control equations of the thin shell structure under different electrical loading modes, and establishing a dielectric highly elastic thin shell electromechanical coupling theoretical model.

3. The method for simulating and predicting the instability phenomenon of a dielectric high-elastic thin shell according to claim 2, characterized in that: The numerical analysis method in S2 includes the development of a multi-physics coupling analysis method and a nonlinear numerical analysis tool based on the finite element analysis of geometric thin shells such as subdivision surfaces.

4. The method for simulating and predicting the instability phenomenon of a dielectric high-elastic thin shell according to claim 2, characterized in that: The energy density of electromechanical coupling is added to the free energy density of the Mooney-Rivlin polymer hyperelastic constitutive model to construct the nominal energy density of dielectric hyperelastic materials.

5. The method for simulating and predicting the instability phenomenon of a dielectric high-elastic thin shell according to claim 3, characterized in that: The instability phenomena in S3 include volume jump and symmetry breaking.

6. The method for simulating and predicting the instability phenomenon of a dielectric high-elastic thin shell according to claim 3, characterized in that: The isogeometric analysis methods include Catmull-Clark subdivision surface and adaptive arc length method.

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