Modeling the biomechanical properties of soft biological tissues: Constitutive theories

In the past few years significant progress has been made in determining the biomechanical properties and the structure of soft biomechanical tissues which have been the basis of improved constitutive model descriptions. This paper provides a review of nonlinear isotropic and anisotropic constitutive models appropriate for description of the solid mechanical properties of soft biological tissues. The properties involve elastic, and inelastic responses including viscoelasticity, damage and poroviscoelasticity. In particular, the kinematics and stress and the required mathematical framework for constitutive equations for soft tissues including residual stresses, collagen fiber recruitment and dispersion are reviewed. Also included are test protocols required for the determination of the mechanical properties. A special note is also devoted to the important influence of the microstructure within the tissues. As a key representative example the extension and inflation of an artery wall is analyzed with a specific focus on consideration of fiber recruitment and damage. Finally, open problems are highlighted along with future directions that point to innovative approaches which may enable biomechanics research to be translated into tools for use in clinical practice. • This paper provides a review of nonlinear isotropic and anisotropic constitutive models appropriate for description of the solid mechanical properties of soft biological tissues. • The properties involve elastic, and inelastic responses including viscoelasticity, damage and poroviscoelasticity. In particular, the kinematics and stress and the required mathematical framework for constitutive equations for soft tissues including residual stresses, collagen fiber recruitment and dispersion are reviewed. Also included are test protocols required for the determination of the mechanical properties. A special note is also devoted to the important influence of the microstructure within the tissues. As a key representative example the extension and inflation of an artery wall is analyzed with a specific focus on consideration of fiber recruitment and damage. • Finally, open problems are highlighted along with future directions that point to innovative approaches which may enable biomechanics research to be translated into tools for use in clinical practice.