A new model for permanent flexural deflection of cantilever MEMS actuator by conventional mechanism-based strain gradient plasticity framework

Abstract

In two past decades, there are so many works representing to elastic behaviors of cantilever MEMS actuators in the micro and nanoscales for various loading conditions and geometries. However, there are little efforts available for the permanent plastic behavior of the MEMS structures and actuators. In addition, the most size—dependent plasticity considerations based on gradient models have been limited to primary concepts on material modeling or microstructural evolution as compared with structural analyses. In this paper, a conventional mechanism-based strain gradient (CMSG) plasticity theory is applied to investigate permanent behavior of the cantilever micro-beam actuators, by determining the effect of length scale on flexural displacement. If the beam is scaled to micron size, mechanical behavior follows from material dimension or length scale. While the model consisted of a multiple plastic work hardening, its kinematics is established on the Euler–Bernoulli hypothesis. The deflection of cantilever MEMS actuator is determined for different cases of the loading and length scales, compared with other relevant theoretical and experimental observations. Also, the effect of the elastic medium of the environmental foundation is considered for the actuator, dedicatedly.