Quantitative justification of linearization in nonlinear hencky material problems

Abstract

The classical linear elasticity theory is based on the assumption that the size of the displacement gradient tensor is small. In many engineering applications, although the basic assumption is violated due to, e.g., corner singularities, the linear elasticity system is still used to approximate the reality. In this paper, we give a-posteriori error analysis for the effect of the linearization on solutions of nonlinear Hencky materials. A-posteriori error estimates for the effect of idealizations on solutions of more realistic materials will be given in forthcoming papers