### Abstract

The 1-D confined-compression stress-relaxation behavior of a charged, hydrated-soft tissue was analyzed using the continuum mixture theory developed for cartilage (Lai et al., 1991) . A pair of coupled nonlinear partial differential 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 ramp-displacement stress-relaxation experiment was solved using a finite-difference method to obtain the complete spatial and temporal distributions of stress, strain, interstitial water pressure (including osmotic pressure) , ion concentrations, diffusion rates and water velocity within the tissue. Using data available in the literature, it was found that : (1) the equilibrium aggregate modulus of the tissue (as commonly used in the biphasic theory) consists of two components : the Donnan osmotic component and the intrinsic matrix component, and that these two components are of similar magnitude. (2) For the rate of compression of 10% in 200 s, during the compression stage, the fluid pressure at the impermeable boundary supports nearly all the load, while near the free-draining boundary, both the matrix stiffness and the fluid pressure support a substantial amount of the load. (3) Equivalent aggregate modulus and equivalent diffusive coefficient 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 effect of the triphasic medium. The internal fluid pressure predicted by the two models are however different because of osmotic effects. (4) Peak stress at the end of the compression stage is higher for a tissue with higher FCD. We have obtained the strain, stress, flow, pressure and ion concentration fields inside the tissue. Some representative results of these fields are presented. These fields 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.

Original language | English (US) |
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Pages (from-to) | 4945-4962 |

Number of pages | 18 |

Journal | International Journal of Solids and Structures |

Volume | 35 |

Issue number | 34-35 |

DOIs | |

State | Published - Dec 1 1998 |

Externally published | Yes |

### ASJC Scopus subject areas

- Modeling and Simulation
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics

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## Cite this

*International Journal of Solids and Structures*,

*35*(34-35), 4945-4962. https://doi.org/10.1016/S0020-7683(98)00103-6