A bimodular polyconvex anisotropic strain energy function for articular cartilage.

Area of Science:

• Biomechanics
• Materials Science
• Orthopedics

Background:

• Articular cartilage exhibits complex nonlinear, anisotropic, and asymmetric mechanical properties.
• Existing models often struggle to fully capture these characteristics, particularly the bimodular behavior.

Purpose of the Study:

• To develop a novel strain energy function for finite deformations.
• To accurately describe the nonlinear, anisotropic, and asymmetric mechanical response of articular cartilage.
• To incorporate bimodular and polyconvex features for enhanced material stability and behavior modeling.

Main Methods:

• Developed a strain energy function incorporating bimodular features, activating strain energy terms only in tension.
• Ensured the function is polyconvex with respect to the deformation gradient tensor for material stability.
• Introduced novel bimodular and polyconvex 'strong interaction terms' for orthotropic material strain invariants.

Main Results:

• The developed model effectively describes nonlinear, anisotropic, and asymmetric mechanical responses.
• Regression analyses on hypothetical data confirmed the model's capability.
• Demonstrated the ability to model anisotropic and asymmetric Poisson's ratios and stress-strain responses in tension and compression.

Conclusions:

• The novel strain energy function provides a robust framework for modeling articular cartilage.
• The inclusion of strong interaction terms significantly enhances the model's predictive power for complex mechanical behaviors.
• This approach offers improved accuracy for finite deformation analysis in biomechanical applications.