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Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue.
Biomech Model Mechanobiol 2005; 3(3):172-89BM

Abstract

The mechanical behavior of most biological soft tissue is nonlinear viscoelastic rather than elastic. Many of the models previously proposed for soft tissue involve ad hoc systems of springs and dashpots or require measurement of time-dependent constitutive coefficient functions. The model proposed here is a system of evolution differential equations, which are determined by the long-term behavior of the material as represented by an energy function of the type used for elasticity. The necessary empirical data is time independent and therefore easier to obtain. These evolution equations, which represent non-equilibrium, transient responses such as creep, stress relaxation, or variable loading, are derived from a maximum energy dissipation principle, which supplements the second law of thermodynamics. The evolution model can represent both creep and stress relaxation, depending on the choice of control variables, because of the assumption that a unique long-term manifold exists for both processes. It succeeds, with one set of material constants, in reproducing the loading-unloading hysteresis for soft tissue. The models are thermodynamically consistent so that, given data, they may be extended to the temperature-dependent behavior of biological tissue, such as the change in temperature during uniaxial loading. The Holzapfel et al. three-dimensional two-layer elastic model for healthy artery tissue is shown to generate evolution equations by this construction for biaxial loading of a flat specimen. A simplified version of the Shah-Humphrey model for the elastodynamical behavior of a saccular aneurysm is extended to viscoelastic behavior.

Authors+Show Affiliations

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

Pub Type(s)

Comparative Study
Evaluation Study
Journal Article
Validation Study

Language

eng

PubMed ID

15538650

Citation

Haslach, Henry W.. "Nonlinear Viscoelastic, Thermodynamically Consistent, Models for Biological Soft Tissue." Biomechanics and Modeling in Mechanobiology, vol. 3, no. 3, 2005, pp. 172-89.
Haslach HW. Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue. Biomech Model Mechanobiol. 2005;3(3):172-89.
Haslach, H. W. (2005). Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue. Biomechanics and Modeling in Mechanobiology, 3(3), pp. 172-89.
Haslach HW. Nonlinear Viscoelastic, Thermodynamically Consistent, Models for Biological Soft Tissue. Biomech Model Mechanobiol. 2005;3(3):172-89. PubMed PMID: 15538650.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue. A1 - Haslach,Henry W,Jr Y1 - 2004/11/06/ PY - 2002/08/07/received PY - 2004/08/02/accepted PY - 2004/11/13/pubmed PY - 2005/7/20/medline PY - 2004/11/13/entrez SP - 172 EP - 89 JF - Biomechanics and modeling in mechanobiology JO - Biomech Model Mechanobiol VL - 3 IS - 3 N2 - The mechanical behavior of most biological soft tissue is nonlinear viscoelastic rather than elastic. Many of the models previously proposed for soft tissue involve ad hoc systems of springs and dashpots or require measurement of time-dependent constitutive coefficient functions. The model proposed here is a system of evolution differential equations, which are determined by the long-term behavior of the material as represented by an energy function of the type used for elasticity. The necessary empirical data is time independent and therefore easier to obtain. These evolution equations, which represent non-equilibrium, transient responses such as creep, stress relaxation, or variable loading, are derived from a maximum energy dissipation principle, which supplements the second law of thermodynamics. The evolution model can represent both creep and stress relaxation, depending on the choice of control variables, because of the assumption that a unique long-term manifold exists for both processes. It succeeds, with one set of material constants, in reproducing the loading-unloading hysteresis for soft tissue. The models are thermodynamically consistent so that, given data, they may be extended to the temperature-dependent behavior of biological tissue, such as the change in temperature during uniaxial loading. The Holzapfel et al. three-dimensional two-layer elastic model for healthy artery tissue is shown to generate evolution equations by this construction for biaxial loading of a flat specimen. A simplified version of the Shah-Humphrey model for the elastodynamical behavior of a saccular aneurysm is extended to viscoelastic behavior. SN - 1617-7959 UR - https://www.unboundmedicine.com/medline/citation/15538650/Nonlinear_viscoelastic_thermodynamically_consistent_models_for_biological_soft_tissue_ DB - PRIME DP - Unbound Medicine ER -