A new constitutive formulation for characterizing the mechanical behavior of soft tissues

We present a new constitutive formulation that combines certain desirable features of two previously used approaches (phenomenological and microstructural). Specifically, we assume that certain soft tissues can be idealized as composed of various families of noninteracting fibers and a homogeneous matrix. Both the fibers and the matrix are assumed to follow the gross deformation. Within the usual framework of pseudoelasticity, incompressibility, homogeneity, and the continuum hypothesis, a pseudostrain-energy function (W) is proposed wherein W is expressed in terms of matrix and fibrous contributions. Unlike phenomenological approaches where a W is usually chosen in an ad hoc manner, the present approach can be used to postulate reasonable forms of W based on limited structural information and multiaxial stress-strain data. Illustrative applications of the theory are discussed for visceral pleura and myocardium. Concise structurally motivated constitutive relations result, wherein load-dependent anisotropy, nonlinear material behavior, finite deformations, and incompressibility are accounted for.