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Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue.

Henry W Haslach1

  • 1Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA. haslach@eng.umd.edu

Biomechanics and Modeling in Mechanobiology
|November 13, 2004
PubMed
Summary

This study introduces a new model for soft tissue mechanics using evolution differential equations. This approach simplifies data collection and accurately represents viscoelastic behaviors like creep and stress relaxation.

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Area of Science:

  • Biomechanics
  • Materials Science
  • Thermodynamics

Background:

  • Biological soft tissues exhibit complex nonlinear viscoelastic behavior, unlike simpler elastic models.
  • Existing models often rely on intricate spring-dashpot systems or difficult-to-measure time-dependent coefficients.
  • Accurate modeling is crucial for understanding tissue function and disease.

Purpose of the Study:

  • To develop a novel, thermodynamically consistent model for nonlinear viscoelastic soft tissue.
  • To simplify the data acquisition process for constitutive modeling of biological materials.
  • To accurately represent transient mechanical responses like creep and stress relaxation.

Main Methods:

  • Formulating a system of evolution differential equations based on a maximum energy dissipation principle.

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  • Utilizing time-independent material data derived from an energy function, analogous to elasticity.
  • Supplementing the second law of thermodynamics with a principle of maximum energy dissipation.

    • Main Results:

    • The proposed model successfully represents both creep and stress relaxation with a single set of material constants.
    • It accurately reproduces the loading-unloading hysteresis observed in soft tissues.
    • The model is thermodynamically consistent and can be extended to temperature-dependent behaviors.

    Conclusions:

    • The evolution equation model offers a more accessible and accurate method for describing soft tissue viscoelasticity.
    • It provides a unified framework for understanding various transient mechanical responses.
    • The model's thermodynamic consistency facilitates extensions to more complex biological phenomena.