A micro plasticity model for pure bending analysis of curved beam-like MEMS devices

Abstract

Computational models are investigated to analyze plane strain pure bending of rectangular cross sectional curved microbeams in elastic and partially plastic states. A generalization of classical von-mises deformation theory of plasticity is adopted to include size effect, by considering intrinsic material length scale parameter, in the modeling. Assuming linear and power-law hardening model, the governing nonlinear equation in elastic-plastic zones are discretized by generalized differential quadrature (GDQ) method and are solved by direct iteration approach. The numerical calculations of proposed model are validated with published literature. Semi-analytical solution is obtained from the special case of curved microbeam with elastic-rigid plastic constitutive model and linear hardening law. The influences of initial curvature and size effect on yielding initiations at the inner and outer surfaces of microstructure are evaluated. Also, distributions of stress components along the microbeam thickness are studied, for different values of the couple moments, at elastic limits and beyond.