Nonlinear plastic buckling analysis of Micro–Scale thin plates established on higher order mechanism-based strain gradient plasticity framework

Abstract

The present study investigates a nonlinear plastic buckling analysis of microplate by using the Mechanism-based Strain Gradient (MSG) plasticity. The MSG as a higher order theory is based on the Taylor model of dislocation interaction, consisting a multiple plastic work hardening. It extends a virtual work postulating the existence of higher-order stress work-conjugate at the in-plane traction of the microplate to the plastic strain gradient. The energy minimizing method is applied to obtain plastic buckling critical forces per each length scales and plastic hardening exponents. An iterative quadratic extrapolation (IQE) is implemented for linearization of nonlinear terms generated due to spatial variations of constitutive equations. The results indicate significant dependence of the critical force on the length scale as well as plastic work hardening exponent. Verifications are carefully done among two limit states of the elastic case and particular plastic analysis of a macro plate.