Stabilized Mixed Formulations for Incompressible Finite Strain Electromechanics Including Stress Accurate Analysis

ABSTRACT In this study, we introduce a novel methodology for finite strain electromechanics that effectively addresses the incompressible limit. The primary innovation of this work is the first‐time application of robust and accurate stabilized mixed formulations, previously developed by the authors for hyperelasticity, within the realm of electromechanics. These formulations incorporate the pressure field as an unknown variable, thereby facilitating the automatic attainment of the incompressible limit. Additionally, we consider the mechanical deviatoric stress tensor as a primary unknown, allowing for the design of finite element technology capable of managing incompressible behavior while ensuring high accuracy in the stress field and avoiding shear locking of thin solids. To enable the use of equal‐order interpolations, we employ the orthogonal subgrid scale method for stabilization. Furthermore, the electromechanical problem is approached through a block‐iterative staggered method. We present a series of numerical examples to assess the robustness and applicability of these formulations in solving complex finite strain electromechanics problems.