Finite element implementation of anisotropic quasi-linear viscoelasticity using a discrete spectrum approximation

Area of Science:

• Biomechanics
• Computational mechanics
• Materials science

Background:

• Soft tissues exhibit complex anisotropic and viscoelastic properties.
• Accurate modeling of these properties is crucial for understanding joint mechanics.

Purpose of the Study:

• Develop a computational framework for finite element analysis of anisotropic, viscoelastic soft tissues.
• Implement quasilinear viscoelastic (QLV) theory with a discrete spectrum approximation.
• Validate the model's accuracy in simulating soft tissue behavior.

Main Methods:

• Utilized quasilinear viscoelastic (QLV) theory.
• Developed a discrete spectrum approximation for the QLV relaxation function.
• Integrated a transversely isotropic hyperelastic material model for elastic response.
• Implemented the model in a general-purpose nonlinear finite element program.

Main Results:

• The discrete spectrum approximation effectively fits experimental data with an exponential series.
• The finite element formulation accurately reproduces tissue anisotropy and time-dependent behavior.
• The model successfully analyzed large 3D problems, such as the femur-medial collateral ligament-tibia complex.

Conclusions:

• The developed framework provides a robust method for analyzing anisotropic, viscoelastic soft tissues.
• This computational approach enhances the understanding of biological joint mechanics.
• The formulation is capable of handling complex, large-scale biomechanical simulations.