Abaqus Anisotropic Hyperelasticity

Fiber-driven stress patterns in arterial tissue simulation with Abaqus.

Modeling Anisotropic Hyperelasticity in Abaqus 

Many modern materials, from fiber-reinforced elastomers to soft biological tissues, exhibit direction-dependent, nonlinear elastic behavior. These materials don’t deform uniformly; instead, their mechanical response varies along preferred directions and becomes increasingly complex under large strains. 

Simulating these effects accurately requires more than conventional material models. That’s where Abaqus excels, with robust, built-in formulations for anisotropic  hyperelasticity and the flexibility to implement custom behavior via user subroutines. 

Why Anisotropic Hyperelasticity Matters 

At small strains, anisotropic materials can often be approximated using linear elasticity. But once strains exceed 5–10%, microstructural effects, like fiber stretching, rotation, or uncrimping, introduce significant nonlinearity. 

To model this, Abaqus uses hyperelastic formulations based on strain energy potentials: mathematical functions that define how much energy the material stores during deformation. 

Two Mathematical Approaches in Abaqus 

Abaqus supports two core formulations for anisotropic hyperelasticity: 

• Strain-based Formulation 

• Based on strain tensor components (e.g., Green-Lagrange strain) 

• Assumes orthogonal preferred directions 

• Suitable for engineering composites and structured materials 

• Invariant-based Formulation 

• Based on deformation tensor invariants and fiber orientations 

• Supports non-orthogonal fiber layouts 

• Preferred for biomechanics and soft tissue modeling 

Built-in Material Models in Abaqus 

Abaqus/Standard and Abaqus/Explicit offer four predefined anisotropic hyperelastic  strain energy potentials: 

• Generalized Fung model – Phenomenological, fully anisotropic or orthotropic 

• Holzapfel-Gasser-Ogden (HGO) model – Designed for arterial wall behavior 

• Holzapfel-Ogden model – Tailored for myocardium simulation 

• Kaliske-Schmidt model – Effective for fiber-reinforced polymers and biomaterials 

These models are optimized for nearly incompressible materials and handle large strains effectively. 

User Subroutines for Custom Material Models 

Abaqus supports full customization via user subroutines, allowing engineers to implement specific anisotropic material responses: 

• Strain-based: UANISOHYPER_STRAIN (Standard) or VUANISOHYPER_STRAIN (Explicit) 

• Invariant-based: UANISOHYPER_INV (Standard) or VUANISOHYPER_INV (Explicit) 

Users define the strain energy potential and its derivatives, enabling the modeling of novel or proprietary material systems with complex anisotropic behavior. 

Modeling Additional Effects 

• Compressibility Most relevant in 3D models or confined geometries. Nearly incompressible behavior is default in Abaqus/Explicit; full incompressibility is supported in Abaqus/Standard. 

• Thermal expansion Both isotropic and orthotropic thermal expansion can be included. 

• Viscoelasticity Anisotropic hyperelasticity can be paired with isotropic time-domain viscoelasticity for rate-dependent effects. Directionally dependent relaxation is not supported, so this approach requires engineering judgment. 

• Stress softening (Mullins effect) Captures the softening observed during cyclic loading of elastomers or biological tissues. Available through a pseudo-elasticity framework. 

Application Example: Arterial Layer Simulation 

A benchmark application of this modeling technique is the mechanical response of the adventitial layer of human iliac arteries, as investigated by Gasser, Holzapfel, and Ogden. Numerical simulations modeled strips cut in axial, circumferential, and oblique directions (15° offset) to assess how fiber orientation affects tissue mechanics. 

This study showed that fiber dispersion significantly alters stiffness and strain response, reinforcing the importance of directional modeling in biomechanics. These insights are critical in vascular and soft tissue simulation, where precise mechanical representation informs both design and diagnosis. 

Simulation of arterial wall behavior using Abaqus, illustrating stress distribution along different fiber directions.

Effect of fiber orientation on arterial mechanics: Abaqus simulation of axial, circumferential, and oblique cut samples.

Why Work With 4RealSim 

Implementing anisotropic hyperelasticity in Abaqus is powerful, but complex. At 4RealSim, we support engineering teams through: 

• Hands-on model implementation 

• Custom subroutine development 

• Simulation troubleshooting via phone, email, and remote sessions 

• Up-to-date insights from ongoing Abaqus development and roadmap 

As a certified SIMULIA partner with deep material modeling experience, 4RealSim helps you unlock the full capabilities of Abaqus for advanced applications in engineering, biomedical, and composite simulation.  

Acknowledgement: This blog is based on a Dassault Systemes Abaqus Manual chapter. 

Need Help With Anisotropic Hyperelasticity in Abaqus?

If you have questions about implementing anisotropic hyperelasticity in Abaqus, or need guidance on choosing the right material model, we’re here to help. Whether you're looking to get started with built-in formulations or require assistance developing custom user subroutines, our team can support you. Contact us by filling in the contact form or email us directly at support@4realsim.com for personalized advice and simulation assistance.