Application of the multigrid method to nonlinear solid computational mechanics

The multigrid method has recently been used to aid in the convergence rate of linear elastic finite element problems. Presented in this thesis is background information on the linear multigrid method, the dynamic relaxation solver and the Jacobi-iteration solver. An overview of quasistatic nonlinear finite element mechanics is also presented. This thesis presents modification to the multigrid algorithm which gives the multigrid method the ability to aid the convergence rates of nonlinear structural finite element problems. The modified multigrid method is used with both a Jacobian and a dynamic relaxation solver to solve Goel-Malvern plasticity model problems in one and two dimensions. Results show that the convergence rate is always at least doubled by using the modified multigrid algorithm.