Adaptive Finite Element Methods for Variational Inequalitieswith Application to Contact Problems and Plasticity

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The purpose of this research is to develop new and accurate analysis procedures for solving a difficult class of static and dynamic problems in nonlinear solid mechanics, i.e. contact problems in elasticity and plasticity with and without friction. The two year research project involves the development of reliable a-posteriori error estimates of problems described by variational inequalities, development of adaptative strategies based on these error estimates and finally an algorithm development based on the developed strategies. If an efficient method is developed, it will enhance the quality of numerical simulation of manufacturing processes and structural responses.