A constituent-based model for the nonlinear viscoelastic behavior of ligaments

Area of Science:

• Biomechanics
• Biomaterials Science
• Computational Biology

Background:

• Soft biological tissues, like ligaments, exhibit complex nonlinear viscoelastic behavior.
• Existing models, such as quasi-linear viscoelastic theory (QLV), have limitations in fully capturing this complexity.
• Understanding tissue mechanics is crucial for injury assessment and treatment.

Purpose of the Study:

• To develop and validate a novel constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues, with a focus on ligaments.
• To generalize the quasi-linear viscoelastic theory (QLV) by independently modeling elastic and time-dependent properties.
• To incorporate constituent-based relaxation behavior using distinct stress relaxation functions for the matrix and collagen fibers.

Main Methods:

• Developed a constitutive law generalizing QLV using an anisotropic strain energy function and a time discretization scheme.
• Modeled time-dependent behavior based on constituent-based relaxation, utilizing separate stress relaxation functions for the isotropic matrix and collagen fibers.
• Estimated model parameters by fitting stress relaxation experiments on medial collateral ligaments (MCLs) from literature.
• Validated the model by simulating creep tests at various stress levels.

Main Results:

• The proposed nonlinear viscoelastic model successfully predicted the time-dependent response of ligaments.
• The model accurately captured nonlinear viscoelastic phenomena, including strain-dependent relaxation rates and stress-dependent creep rates.
• Direction-dependent relaxation behavior was also effectively described by the model.
• Simulations of creep tests demonstrated the model's predictive capabilities for different loading conditions.

Conclusions:

• The developed constitutive model provides a robust framework for predicting the nonlinear viscoelastic behavior of ligaments.
• This model advances the understanding of soft tissue mechanics by accurately accounting for time-dependent and nonlinear responses.
• The findings have implications for biomechanical analysis, injury modeling, and the design of tissue engineering scaffolds.