Use and Analysis of Finite Element Methods for Problems of Solid Mechanics and Fracture

Abstract

Abstract : In this project the principal investigator and his co-workers wish to exploit their expertise in the theoretical analysis, particularly regarding superconvergence, and practical application of finite element methods to produce and analyze new finite element schemes for treating difficult linear and nonlinear problems of solid mechanics and fracture mechanics. The difficulties arise from the presence of effects such as material nonlinearities, nonhomogeneity, time dependence and stationary and moving cracks. In particular they wish to apply new retrieval techniques of finite elements to define new adaptive procedures for producing numerical solutions with enhanced properties for some problems of linear elasticity and linear elastic fracture, elasto- plasticity and nonlinear fracture, viscoelasticity and viscoelastic fracture. Contexts in which these new techniques will be applied include the deformation and fracture of timbers, and elasto-plastic deformation and fracture of metals with work hardening and the viscoelastic deformation and fracture of various polymers. Attention will also be given to some composite structures in these contexts. Whenever possible the numerical results will be compared with experimental results.