Cavitation Computation in Nonlnear Elasticity

Zhiping Li
LMAM and School of Mathematical Sciences
Peking University
P. R. China
E-mail address: lizp@math.pku.edu.cn


ABSTRACT

Many nonlinear elastic materials, such as rubbers, exhibit cavitation phenomenon under large traction. The occurrence of cavities is considered closely related to nonlinear instability and bifurcation of the total elastic energy of the system. One of the main difficulties in the finite element computations of a cavity growth is that it is hard to approximate the locally extremely large expansion dominant deformation with an orientation preserving finite element deformation. Another main difficulty is that the strain field is extremely anisotropic and varies in large scale, that causes the iterative method for solving the nonlinear system converges very slowly. To overcome the first difficulty, we apply a rectangular dual-parametric finite element. To overcome the second difficulty, we employ a domain decomposition method.

The research was supported by the NSFC project 11171008.