CAVITATED BIFURCATION FOR INCOMPRESSIBLE HYPERELASTIC MATERIAL

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.

An improved dynamic model for a silicone material beam with large deformation

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.

DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES

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.

Dynamic cavitations in incompressible hyperelastic pre-strained circular sheets

A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value;dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.