An accurate, robust, and efficient finite element framework for anisotropic, nearly and fully incompressible elasticity

TL;DR

This paper introduces a new finite element framework with stabilization techniques for simulating anisotropic, nearly incompressible biological tissues, overcoming locking issues and improving accuracy and efficiency.

Contribution

The paper presents novel stabilization methods for P1-P1 elements to effectively simulate anisotropic, incompressible materials, reducing locking and enhancing computational robustness.

Findings

Demonstrates high accuracy in benchmark tests

Shows improved stability over standard methods

Enables faster simulations of biological tissues

Abstract

Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an isochoric part is a very common approach. However, due to the high stiffness of anisotropic materials in the preferred directions, the finite element analysis of such problems often suffers from severe locking effects and numerical instabilities. In this paper, we present novel methods to overcome locking phenomena for anisotropic materials using stabilized P1-P1 elements. We introduce different stabilization techniques and demonstrate the high robustness and computational efficiency of the chosen methods. In several benchmark problems we compare the approach to standard linear elements and show the accuracy and versatility of the methods to simulate anisotropic, nearly and fully incompressible materials. We are convinced that this numerical framework offers the possibility to accelerate accurate simulations of biological tissues, enabling patient-specfic parameterization studies, which require numerous forward simulations.