A Size-Dependent Boundary Element Framework for Thermoelastic Simulation of MEMS Microgrippers Based on Couple Stress Theory

Abstract

The proposed work offers a novel Boundary Element Method (BEM) approach to solve the steady-state and transient thermoelastic analyses of thermally activated Micro-Electro-Mechanical Systems (MEMS) microgrippers, which capture size effects using consistent couple stress theory. While MEMS devices move toward the microscale, the traditional thermoelastic theories are no longer sufficient to characterize prominent phenomena such as microrotation, strain gradients, and internal length-scale effects. The resulting formulation integrates these microscale mechanisms through material length-scale parameters and additional rotational degrees of freedom, enabling realistic simulation of thermomechanically loaded bimaterial layer structures under realistic thermal and mechanical boundary conditions. Very good comparison with analytical solutions, finite element models, and experimental measurements confirms the accuracy of the results, with errors of only 2.3% in tip deflection and 1.3% in the maximum temperature increase. Unlike classical theory, size-dependent BEM can predict smaller displacements and greater stiffness and can even resolve microscale effects, which are of utmost importance for the precise prediction of reliable MEMS behavior. Boundary-only discretization, consistency with anisotropic and layered materials, and the ability to model transient and steady-state regimes make this technique an efficient computational and flexible tool for thermal micro-actuator design and optimization.