Effects of Structural Viscoelasticity in Non-Divergence free Deformable Porous Media with Incompressible Constituents

Abstract

In this paper, we investigate the importance of structural viscoelasticity in the mechanical response of deformable porous media with incompressible constituents under sudden changes in the external applied quasi-static loads using mathematical analysis. Here, the applied load is characterized by a step pulse or a trapezoidal pulse. Mathematical models of non-divergence free deformable porous media are often used to characterize the behaviour of biological tissues such as cartilages, engineered tissue scaffolds, and bones which are viscoelastic and incompressible in nature, and viscoelasticity may change with age, disease or by design. The problem is formulated as a mixed boundary value problem of the theory of poroviscoelasticity, in which an explicit solution is obtained in one-dimension. Further, dimensional analysis is utilized to identify dimensionless parameters that can aid the design of structural properties so as to ensure that the fluid velocity past the porous medium remains bounded below a given threshold to prevent potential damage. Our investigation shows that the fluid dynamics within the medium could abruptly be altered if the applied load encounters a sudden change in time and structural viscoelasticity is too small. This explains the confined compression experiment clarifying the cause of micro-structural damages in biological tissues associated with loss of tissue viscoelastic property, which leads to the cause of diseases like Glaucoma. AMS subject classification: