Nonlinear material and geometric analysis of thick functionally graded plates with nonlinear strain hardening using nonlinear finite element method

Abstract

The present paper deals with three dimensional nonlinear geometrically and elastoplastic analyses of thick functionally graded plates with nonlinear strain hardening. The boundary conditions are assumed to be general. The plate consists of ceramic (SiC) and metal (Al) phases varying smoothly through the thickness. The effective elastic material properties are obtained by Mori-Tanaka scheme where the plastic behavior of the FG plate is described by the von-Mises yield criterion, nonlinear isotropic strain hardening and the Prandtl-Reuss constitutive equations in combination with the TTO model. The governing equations are obtained from the incremental theory of plasticity in conjunction with the Green-Lagrange nonlinear kinematics. In order to investigate the nonlinear elastoplastic response of the FGM, the nonlinear graded finite element method is developed from three-dimensional continuum concepts that admit arbitrarily large displacements and rotations. This formulation has been implemented and the effect of material gradient index, boundary conditions and thickness-to-length ratio on the nonlinear elastoplastic analysis of the FG plate as well as the development of plastic zone are presented and discussed.