An asymptotic elastic–plastic plate model for moderate displacements and strong strain hardening

Abstract

We propose in this paper to generalize to elastic–plastic plates the constructive asymptotic approach developed by the authors for elastic plates and shells. A dimensional analysis of three-dimensional equations makes appear dimensionless numbers characterizing the problem. Then using the geometric and mechanical data, these dimensionless numbers are linked to the perturbation parameter (the relative thickness of the plate) to obtain a one scale problem. For standard generalized materials with strong strain hardening, subjected to usual force levels, the asymptotic expansion of equations leads to an elastic–plastic plate model valid for moderate displacements. The constructive approach developed enables to specify the domain of validity of the asymptotic elastic–plastic plate model obtained thanks to the dimensional numbers introduced.