On the accuracy and fitting of transversely isotropic material models

Area of Science:

• Biomechanics and Materials Science
• Computational Solid Mechanics
• Tissue Engineering

Background:

• Biological tissues are complex fiber-reinforced structures essential for form and function.
• Hyperelastic, transversely isotropic material models are widely used for simulating biological tissues.
• Existing models often incorporate pseudo-invariants (I4, I5) to represent fiber energy storage.

Purpose of the Study:

• To evaluate the distinct contributions of pseudo-invariants I4 and I5 in hyperelastic models.
• To identify specific loading scenarios where simplified models (using only I4 or I5) are adequate.
• To determine optimal mechanical tests for fitting transversely isotropic constitutive models.

Main Methods:

• Analysis of relative roles of I4 and I5 under various simple loading conditions.
• Evaluation of model reduction to transversely isotropic linear elasticity for small deformations.
• Identification of mechanical tests with high utility for parameter fitting.

Main Results:

• Specific loading scenarios are identified where models using only I4 or I5 can provide accurate estimations.
• The necessity of including both I4 and I5 for correct reduction to linear elasticity at small strains was confirmed.
• Certain mechanical tests demonstrate particular utility for fitting transversely isotropic constitutive models.

Conclusions:

• Guidance is provided for selecting appropriate constitutive models for fiber-reinforced biological tissues.
• The study offers insights into the interpretation of predictions from transversely isotropic material models.
• Results aid in the accurate parameterization and application of computational models for soft biological matter.