On strain-induced degradation of the polymeric skeleton in poro-hyperelastic inflating vessels by a non-equilibrium thermodynamic framework

Abstract

The present work develops the Poro-Hyperelasticity Theory (P-HT) into a fluid-saturated porous polymeric skeleton under Ogden-Hill material model with inhomogeneous properties resulting from bulk degradation. The only source of dissipation in the degradable skeleton is mechanical strain. To capture constitutive and evolution laws, P-HT and the principle of maximum energy dissipation rate are invoked in a non-equilibrium thermodynamic framework. The model is verified by available experimental data and the physical concept of consolidation. The degradation model is applied on a fluid-saturated pressurized polymeric vessel with the porosity-dependent permeability in the plane-strain case. To approximate the non-linear equations of degradable porous vessel, Standard Galerkin Finite Element Method (SGFEM) is implemented through programming in the FlexPDE commercial software. Contrary to the degradable hyperelastic polymers without fluid mechanical effects studied in the literature, the skeleton degradation initially starts with a non-maximum degradation rate. Degradation causes deformation-dependent porosity and permeability in the vessel to increase. The degradation leads to slower evolution of the pore pressure in the vessel. Pore pressure and stress can reach a time-independent flatted region in addition to the final time of coupled process, because of degradable skeleton. Energy dissipation and material softening rates are higher in the inner radius of the inflating vessel.