A polyconvex anisotropic strain-energy function for soft collagenous tissues

Area of Science:

• Continuum Mechanics
• Computational Solid Mechanics
• Biomechanics

Background:

• Polyconvexity of strain-energy functions is crucial for the mathematical stability of boundary-value problems in solid mechanics.
• Existing models may not adequately capture the complex behavior of soft biological tissues under deformation.

Purpose of the Study:

• To propose a novel exponential polyconvex anisotropic strain-energy function.
• To ensure the function inherently satisfies energy- and stress-free natural state conditions.
• To validate the model's suitability for soft biological tissues through experimental comparison.

Main Methods:

• Development of an exponential strain-energy function represented by a series expansion.
• Incorporation of material constants to define anisotropic properties.
• Each term in the series is designed to a priori satisfy natural state conditions.

Main Results:

• The proposed function exhibits polyconvexity, ensuring mathematical well-posedness.
• The exponential form is particularly well-suited for the hyperelastic behavior of soft tissues.
• The model demonstrates good agreement with experimental data from various biological tissues.

Conclusions:

• The novel exponential polyconvex anisotropic strain-energy function offers a robust framework for biomechanical modeling.
• This model provides a more accurate representation of soft biological tissue mechanics.
• The inherent satisfaction of natural state conditions simplifies model implementation and analysis.