Plausibility of Structural Constitutive Equations for Isotropic Soft Tissues in Finite Static Deformations

Abstract

Soft tissues are binary systems of fibers embedded in a fluid matrix. Their equilibrium response to external loading is the sum of the fibers’ stress and the matrix osmotic pressure. The present study examines the conditions under which the elastic response of isotropic tissues, as modeled by structural constitutive equations, is physically plausible. The analysis shows that plausibility is ensured if the fibers’ stretch force increases monotonically with the stretch and if the matrix osmotic pressure increases convexly with the concentration. Published data shows that both conditions prevail in soft tissues. It is thus concluded that structural modeling is compatible with physically plausible response.