Plausibility of Structural Constitutive Equations for Swelling Tissues—Implications of the C-N and S-E Conditions

Abstract

The mechanically important constituents of swelling tissues are fibers embedded in an osmotically active fluid. The tissues’ response to external loading is the sum of contribution of the axial stresses in the fibers and of the fluid pressure. The fluid osmotic properties play a key role in determining its equilibrium response. The present study examines the conditions under which the elastic response of tissues as modeled by structural constitutive equations, is thermodynamically plausible. The analysis shows that plausibility is ensured if the fibers’ axial force increases monotonically with stretch and if the fluid osmotic pressure increases convexly with concentration. Published data shows that both conditions prevail in swelling tissues. Plausibility considerations seem to pose no specific restrictions on the structure of the tissues’ fibrous network. It is thus concluded that in swelling tissues, structural constitutive formulation is compatible with thermodynamically plausible response.