Cavitation Computation in Nonlnear Elasticity
Zhiping Li
LMAM and School of Mathematical Sciences
Peking University
P. R. China
Email 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 dualparametric finite
element. To overcome the second difficulty, we employ a domain decomposition
method.
The research was supported by the NSFC project 11171008.
