Convergence of the Finite Element Solution of a Nonlinear Crack Type Problem in Finite Elasticity

摘要

The crack type problem in a hyperelastic body is investigated. The material is assumed to be isotropic, incompressible, and to have a special nonlinear constitutive equation under large deformation. This body is subjected to shear deformation under the action of body force. The problem leads to the nonlinear boundary value problem. The analytical solution of this problem exhibits the singularity at the crack tip. The convergence rate of the Galerkin approximation solution is studied by introducing the weighted Sobolev space in functional analysis technique.