Effects Of Fixed Charges On The Stress Relaxation Behavior Of Hydrated Soft Tissues In A Confined Compression Problem

Abstract

The 0!D con_ned!compression stressrelaxation behavior of a charged\ hydrated!soft tissue was analyzed using the continuum mixture theory developed for cartilage "Lai et al[\ 0880#[ A pair of coupled nonlinear partial di}erential equations governing the displacement component u s of the solid matrix and the cation concentration c were derived[ The initial!boundary value problem\ corresponding to a rampdisplacement stressrelaxation experiment was solved using a _nite!di}erence method to obtain the complete spatial and temporal distributions of stress\ strain\ interstitial water pressure "including osmotic pressure#\ ion concentrations\ di}usion rates and water velocity within the tissue[ Using data available in the literature\ it was found that ] "0# the equilibrium aggregate modulus of the tissue "as commonly used in the biphasic theory# consists of two com! ponents ] the Donnan osmotic component and the intrinsic matrix component\ and that these two components are of similar magnitude[ "1# For the rate of compression of 09) in 199 s\ during the compression stage\ the ~uid pressure at the impermeable boundary supports nearly all the load\ while near the free!draining boundary\ both the matrix sti}ness and the ~uid pressure support a substantial amount of the load[ "2# Equivalent aggregate modulus and equivalent di}usive coe.cient used in the biphasic theory can be found\ which predict essentially the same stress relaxation behavior[ These equivalent parameters for the biphasic model embody the FCD e}ect of the triphasic medium[ The internal ~uid pressure predicted by the two models are however di}erent because of osmotic e}ects[ "3# Peak stress at the end of the compression stage is higher for a tissue with higher FCD[We have obtained the strain\ str..