A robust anisotropic hyperelastic formulation for the modelling of soft tissue

Area of Science:

• Biomechanics
• Computational mechanics
• Materials science

Background:

• The Holzapfel-Gasser-Ogden (HGO) model is widely used for anisotropic hyperelastic soft biological tissues.
• A common compressible formulation (HGO-C) uses isochoric invariants for the anisotropic component.
• This formulation may not accurately capture compressible anisotropic material behavior.

Purpose of the Study:

• To evaluate the accuracy of the compressible HGO-C model for anisotropic soft tissues.
• To develop and present a modified anisotropic (MA) model that correctly accounts for volumetric effects.
• To assess the impact of the new model in simulating stent deployment in arteries.

Main Methods:

• Analysis of three simple deformations (pure dilatation, pure shear, uniaxial stretch) using the HGO-C model.
• Development of the modified anisotropic (MA) model incorporating full anisotropic invariants.
• Implementation of the MA model in a finite element subroutine for stent deployment simulation.

Main Results:

• The HGO-C model's anisotropic component is insensitive to volumetric deformation, leading to inaccurate predictions.
• The MA model correctly predicts anisotropic responses to hydrostatic tensile loading and computes accurate stress states for pure shear and uniaxial deformations.
• Simulations of stent deployment show significantly higher stress triaxiality and arterial compliance with the MA model compared to the HGO-C model.

Conclusions:

• The standard HGO-C model fails to accurately represent compressible anisotropic soft tissue behavior due to its use of isochoric invariants.
• The proposed MA model, utilizing full anisotropic invariants, accurately captures volumetric effects and anisotropic responses.
• The MA model offers improved accuracy for simulations involving soft biological tissues, such as stent deployment in arteries.