Dynamic modeling for incompressible hyperelastic materials with large deformation is an important issue in biomimetic applications. The previously proposed lower-order fully parameterized absolute nodal coordinate for...Dynamic modeling for incompressible hyperelastic materials with large deformation is an important issue in biomimetic applications. The previously proposed lower-order fully parameterized absolute nodal coordinate formulation（ANCF） beam element employs cubic interpolation in the longitudinal direction and linear interpolation in the transverse direction, whereas it cannot accurately describe the large bending deformation. On this account, a novel modeling method for studying the dynamic behavior of nonlinear materials is proposed in this paper. In this formulation, a higher-order beam element characterized by quadratic interpolation in the transverse directions is used in this investigation. Based on the Yeoh model and volumetric energy penalty function, the nonlinear elastic force matrices are derived within the ANCF framework. The feasibility and availability of the Yeoh model are verified through static experiment of nonlinear incompressible materials. Furthermore,dynamic simulation of a silicone cantilever beam under the gravity force is implemented to validate the superiority of the higher-order beam element. The simulation results obtained based on the Yeoh model by employing three different ANCF beam elements are compared with the result achieved from a commercial finite element package as the reference result. It is found that the results acquired utilizing a higher-order beam element are in good agreement with the reference results,while the results obtained using a lower-order beam element are different from the reference results. In addition, the stiffening problem caused by volumetric locking can be resolved effectively by applying a higher-order beam element. It is concluded that the proposed higher-order beam element formulation has satisfying accuracy in simulating dynamic motion process of the silicone beam.展开更多
以粘超弹理论为基础,将L M Yang等提出的本构模型中Rivlin函数改进为Yeoh,提出了一种基于Yeoh函数的描述橡胶材料中高应变率效应的粘超弹本构模型,该模型以左Cauchy变形张量B第一不变量I1B作为唯一变量,简化了原模型结构,并开发了相应...以粘超弹理论为基础,将L M Yang等提出的本构模型中Rivlin函数改进为Yeoh,提出了一种基于Yeoh函数的描述橡胶材料中高应变率效应的粘超弹本构模型,该模型以左Cauchy变形张量B第一不变量I1B作为唯一变量,简化了原模型结构,并开发了相应模型的ABAQUS软件材料用户子程序(VUMAT)。通过高应变率橡胶垫片及中低应变率橡胶缓冲器的冲击试验与数值仿真对比,验证了本构模型及材料用户子程序的有效性与实用性。展开更多
Dielectric elastomers(DEs) are the polymers capable of inducing deformation under electrical stimulation. When subject to a voltage across its thickness, the material reduces in thickness and expands in area. This pap...Dielectric elastomers(DEs) are the polymers capable of inducing deformation under electrical stimulation. When subject to a voltage across its thickness, the material reduces in thickness and expands in area. This paper presents a new method to analyze deformation and stress distribution response of the dielectric elastomer actuator(DEA) model under different applied voltage. An equal-biaxial pre-strained circular actuator model was built. The Yeoh strain energy potential and the collocation method are used for describing the large strain actuation response and stress distribution. The study in this paper has shown that: the stress and the stretch distributions in the passive region of the DE actuator depend on the radial distance from the center at the calculation point of the passive region and the magnitude of the applied voltage; with the same excitation applied voltage, we can get a larger deformation actuation by choosing an appropriate pre-stretch ratio; the influence of the non-ideal material has seriously affected the actual deformation of the DE actuators. This analytical model has a reference potential for the design optimization of high performance DEA systems and the model-based control of the DEA robot.展开更多
In this paper, we present a modified model describing the constitutive relation of viscoelas-tic dielectric elastomer （DE）. The uniform uniaxial tension-recovery experiment was carried out at different stretching ra...In this paper, we present a modified model describing the constitutive relation of viscoelas-tic dielectric elastomer （DE）. The uniform uniaxial tension-recovery experiment was carried out at different stretching rates. Based on Yeoh hyper-elastic model, model-fitting approach is put forward to obtain the relationship between parameters of Yeoh model and stretching rate, thus the modified model was obtained. From the approximate relationship between harmonic motion and uniform reciprocating motion, the stress-strain curve in the recovery process was also identified through the hysteresis between stress and strain. The modified model, with concise form and evident physical concept, can describe the strong nonlinear behavior between deformation and mechanical stress of the material in a common stretching rate range （from 0.01s^-1 to 0.8s^-1 at least）. The accuracy and reliability of the modified model was examined.展开更多
This paper mainly discusses the constitutive laws of incompressible rubber-like materials and the associated finite element analysis method. By a multiplicative decomposition of the deformation gradient into distortio...This paper mainly discusses the constitutive laws of incompressible rubber-like materials and the associated finite element analysis method. By a multiplicative decomposition of the deformation gradient into distortional and dilatational parts, the YEOH mode type constitutive laws of rubber-like materials and their numerical implementation are presented. In order to deal with incompressible problems, a three-field variational principle is developed in which deformation, Jacobian and pressure field are treated independently. The connection between the three-field principle and the Hu-Wasizhu generalized variational principle is established. It is shown that the approach proposed can be degenerated to the B-bar method in the linear case. The derailed FE formulation is given in which deformation is ap proximated by isoparametric conforming element, and Jacobian and pressure by discontinuous approximation. Finally, two numerical examples are presented to show the effectiveness and reliability of the method proposed. The work in this paper provides a corner stone of FEA of this kind of problem. This paper features the combination of the multiplicative decomposition, the three-field principle and YEOH model of rubber-like materials, especially under Lagrangian description, giving an effective way for solving this kind of problems. The Lagrangian description is compatible with usually geometrically nonlinear FEM and the constitutive laws are expressed by the second Kirchhoff stress and the Green strain.展开更多
基金supported by the National Natural Science Foundation of China (11772186 and 11272203)
文摘Dynamic modeling for incompressible hyperelastic materials with large deformation is an important issue in biomimetic applications. The previously proposed lower-order fully parameterized absolute nodal coordinate formulation（ANCF） beam element employs cubic interpolation in the longitudinal direction and linear interpolation in the transverse direction, whereas it cannot accurately describe the large bending deformation. On this account, a novel modeling method for studying the dynamic behavior of nonlinear materials is proposed in this paper. In this formulation, a higher-order beam element characterized by quadratic interpolation in the transverse directions is used in this investigation. Based on the Yeoh model and volumetric energy penalty function, the nonlinear elastic force matrices are derived within the ANCF framework. The feasibility and availability of the Yeoh model are verified through static experiment of nonlinear incompressible materials. Furthermore,dynamic simulation of a silicone cantilever beam under the gravity force is implemented to validate the superiority of the higher-order beam element. The simulation results obtained based on the Yeoh model by employing three different ANCF beam elements are compared with the result achieved from a commercial finite element package as the reference result. It is found that the results acquired utilizing a higher-order beam element are in good agreement with the reference results,while the results obtained using a lower-order beam element are different from the reference results. In addition, the stiffening problem caused by volumetric locking can be resolved effectively by applying a higher-order beam element. It is concluded that the proposed higher-order beam element formulation has satisfying accuracy in simulating dynamic motion process of the silicone beam.
文摘以粘超弹理论为基础,将L M Yang等提出的本构模型中Rivlin函数改进为Yeoh,提出了一种基于Yeoh函数的描述橡胶材料中高应变率效应的粘超弹本构模型,该模型以左Cauchy变形张量B第一不变量I1B作为唯一变量,简化了原模型结构,并开发了相应模型的ABAQUS软件材料用户子程序(VUMAT)。通过高应变率橡胶垫片及中低应变率橡胶缓冲器的冲击试验与数值仿真对比,验证了本构模型及材料用户子程序的有效性与实用性。
基金the National Natural Science Foundation of China(No.51305138)the Research Project of State Key Laboratory of Mechanical System and Vibration(No.MSV201703)
文摘Dielectric elastomers(DEs) are the polymers capable of inducing deformation under electrical stimulation. When subject to a voltage across its thickness, the material reduces in thickness and expands in area. This paper presents a new method to analyze deformation and stress distribution response of the dielectric elastomer actuator(DEA) model under different applied voltage. An equal-biaxial pre-strained circular actuator model was built. The Yeoh strain energy potential and the collocation method are used for describing the large strain actuation response and stress distribution. The study in this paper has shown that: the stress and the stretch distributions in the passive region of the DE actuator depend on the radial distance from the center at the calculation point of the passive region and the magnitude of the applied voltage; with the same excitation applied voltage, we can get a larger deformation actuation by choosing an appropriate pre-stretch ratio; the influence of the non-ideal material has seriously affected the actual deformation of the DE actuators. This analytical model has a reference potential for the design optimization of high performance DEA systems and the model-based control of the DEA robot.
基金supported by the Doctoral Fund of Ministry of Education of China(20120201110030)
文摘In this paper, we present a modified model describing the constitutive relation of viscoelas-tic dielectric elastomer （DE）. The uniform uniaxial tension-recovery experiment was carried out at different stretching rates. Based on Yeoh hyper-elastic model, model-fitting approach is put forward to obtain the relationship between parameters of Yeoh model and stretching rate, thus the modified model was obtained. From the approximate relationship between harmonic motion and uniform reciprocating motion, the stress-strain curve in the recovery process was also identified through the hysteresis between stress and strain. The modified model, with concise form and evident physical concept, can describe the strong nonlinear behavior between deformation and mechanical stress of the material in a common stretching rate range （from 0.01s^-1 to 0.8s^-1 at least）. The accuracy and reliability of the modified model was examined.
基金the National Natural Science Foundation of China(No.19632030)
文摘This paper mainly discusses the constitutive laws of incompressible rubber-like materials and the associated finite element analysis method. By a multiplicative decomposition of the deformation gradient into distortional and dilatational parts, the YEOH mode type constitutive laws of rubber-like materials and their numerical implementation are presented. In order to deal with incompressible problems, a three-field variational principle is developed in which deformation, Jacobian and pressure field are treated independently. The connection between the three-field principle and the Hu-Wasizhu generalized variational principle is established. It is shown that the approach proposed can be degenerated to the B-bar method in the linear case. The derailed FE formulation is given in which deformation is ap proximated by isoparametric conforming element, and Jacobian and pressure by discontinuous approximation. Finally, two numerical examples are presented to show the effectiveness and reliability of the method proposed. The work in this paper provides a corner stone of FEA of this kind of problem. This paper features the combination of the multiplicative decomposition, the three-field principle and YEOH model of rubber-like materials, especially under Lagrangian description, giving an effective way for solving this kind of problems. The Lagrangian description is compatible with usually geometrically nonlinear FEM and the constitutive laws are expressed by the second Kirchhoff stress and the Green strain.
