The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obta...The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obtained. The catastrophe and concentration of stresses are discussed. The stability of solutions is discussed through the energy comparison. And the growth of a pre-existing micro-void is also observed.展开更多
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
In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inn...In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.展开更多
文摘The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obtained. The catastrophe and concentration of stresses are discussed. The stability of solutions is discussed through the energy comparison. And the growth of a pre-existing micro-void is also observed.
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.
基金Project supported by the National Natural Science Foundation of China (Nos. 10872045 and 10772104)the Program for New Century Excellent Talents in University (No. NCET-09-0096)the Fundamental Research Funds for the Central Universities (No. DC10030104)
文摘In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.
