Reduced-integration hexahedral finite element for static and vibration analysis of micropolar continuum

Abstract

The micropolar elasticity finite element method is widely used for analyzing advanced materials with complex microstructures, but existing implementations often suffer from computational inefficiency due to full integration schemes and shear locking in bending scenarios. This study proposes a high-performance, reduced-integration, first-order hexahedral micropolar element to address these limitations. The formulation combines standard Lagrange interpolation with uniform strain and curvature fields, ensuring patch test satisfaction and accuracy in skewed configurations. An artificial stiffness method is introduced to suppress displacement and rotational hourglass instabilities. Rigorous numerical validations, including force and displacement patch tests, cantilever beam bending, and free vibration analysis, demonstrate the superior accuracy and computational efficiency of the element. Furthermore, applications to star-shaped lattices and 3D chiral metamaterials highlight its effectiveness in capturing microstructure-dependent mechanical behaviors, such as unexpected bending deformation and tension-twist coupling. The proposed element significantly enhances computational efficiency in homogenization simulation, providing a robust and practical tool for the simulation-driven design of advanced mechanical metamaterials with complex deformation mechanisms.