Effects of fixed charges on the stress–relaxation behavior of hydrated soft tissues in a confined compression problem

The 0!D con_ned!compression stress relaxation 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 us of the solid matrix and the cation concentration c were derived[ The initial!boundary value problem\ corresponding to a ramp displacement stress relaxation experiment was solved using a _nite!di}erence method to obtain the complete spatial and temporal distributions of stress\ straininterstitial 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 loadwhile 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 theFCDe}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[Wehave obtained the strain\ stress\ ~ow\ pressure and ion concentration _elds inside the tissue[ Some representative results of these _elds are presented[ These _elds are essential for determining the local variations of mechanical\ electrical and chemical environments around cells necessary for the understanding of the mechano!electrochemical signal transduction processes required for the control of biologic functions[ 0887 Elsevier Science Ltd[ All rights reserved