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.

This work was supported by the MICIU/AEI/10.13039/501100011033, Spain grant PID2022-141957OA-C22, and by “ERDF A way of making Europe.” Autonomous Community of the Region of Murcia, Spain, through the programme for the development of scientific and technical research by competitive groups (21996/PI/22), included in the Regional Programme for the Promotion of Scientific and Technical Research of Fundación Séneca – Agencia de Ciencia y Tecnología de la Región de Murcia. Institució Catalana de Recerca i Estudis Avançats (ICREA) Acadèmia Research Program of the Generalitat de Catalunya.

Peer Reviewed

Postprint (published version)