Modelling and simulation of electro-mechanically coupled dielectric elastomers and myocardial tissue using smoothed finite element methods

TL;DR

This study extends smoothed finite element methods to electro-mechanical coupled problems, demonstrating that FSNS-FEM offers a good balance of accuracy and efficiency for simulating dielectric elastomers and myocardial tissue.

Contribution

It introduces and evaluates four S-FEM approaches for electro-mechanical problems, highlighting FSNS-FEM's superior performance over standard FEM in biomedical simulations.

Findings

FSNS-FEM closely matches reference solutions.

NS-FEM overestimates deformation due to softer results.

Standard FEM and FS-FEM exhibit volume locking issues.

Abstract

Computational modelling offers a cost-effective and time-efficient alternative to experimental studies in biomedical engineering. In cardiac electro-mechanics, finite element method (FEM)-based simulations provide valuable insights into diseased tissue behaviour and the development of assistive systems such as di-electric elastomer actuators. However, the use of automatically generated tetrahedral meshes, commonly applied due to geometric complexity, often leads to numerical issues including overly stiff responses and volume locking, particularly in incompressible materials. Smoothed finite element methods (S-FEMs) offer a promising alternative by softening the stiffness matrix through gradient smoothing over defined smoothing domains. This work extends S-FEM formulations to electro-mechanically coupled problems and compares their performance against standard linear FEM. We implement and evaluate four approaches in the Abaqus environment via custom user elements: standard linear FEM, face-based S-FEM (FS-FEM), node-based S-FEM (NS-FEM), and the hybrid face/node-based S-FEM (FSNS-FEM). Two benchmark problems are studied: the electrically induced contraction of a compressible dielectric elastomer and an incompressible, orthotropic myocardial tissue sample. Reference solutions are obtained using a mesh consisting of higher-order elements. Our results demonstrate that FSNS-FEM provides the best balance between accuracy and computational efficiency, closely matching reference data. NS-FEM produces softer results, which leads to an overestimation of the true deformation. FS-FEM and standard FEM consistently exhibit overly stiff behaviour, with pronounced volume locking in the myocardial case. These findings support the potential of S-FEMs, in particular FSNS-FEM, for accurate simulation of coupled electro-mechanical behaviour in complex biomedical applications.