Microstructure-dependent nonlinear viscoelasticity due to extracellular flow within cellular structures

A constitutive model that highlights a special viscoelastic property of materials with cellular microstructures is developed. We model the microstructure as a regularly arranged system of the same elastic cells that are mutually interconnected by elastic linkages. The space between cells is filled by a fluid that may flow freely within this extracellular space. The macroscopic behavior of the whole structure is studied by means of continuum mechanics using a differential scheme with internal variables. Here, the internal variables are chosen as the distances that separate neighboring cells. The evolution equations are derived from the Clausius–Planck inequality, which considers the internal dissipation to be exclusively due to the extracellular fluid movement. Special attention is paid to incompressible materials in the context of uniaxial load. In this context, the importance of the fluid viscosity on material behavior is related to microstructural parameters like the cells’ dimensions and the relative stiffness between the cells and matrix elastic reinforcement.