Size effect in porous slender microbeams: Analytical solutions based on modified strain gradient theory

Resumo

Micro/nano-scale beams, such as micro-electromechanical systems, microactuators, and nanocomposites, are essential in engineering applications. However, classical elasticity theory fails to predict their mechanical behavior accurately due to the pronounced size effects at small scales. To address this limitation, the modified strain gradient theory (MSGT) introduces an additional equilibrium equation and incorporates five elastic constants (three non-classical and two classical) to better capture microstructural phenomena in isotropic linear elastic materials. This work develops analytical solutions for porous slender microbeams based on MSGT, considering various boundary conditions and four different porosity models. The results provide a more accurate framework for analyzing the mechanical behavior of micro-scale porous structures.