Soft tissues are hydrated fibrous materials that exhibit nonlinear material response and undergo finite straining during in vivo loading. A continuum model of these structures (“LMPHETS” [1,2]) is a porous solid matrix (with charges fixed to the solid fibers) saturated by a mobile fluid (water) and multiple species (e.g., three mobile species designated by α, β = p, m, b where p = +, m = −, and b = ± charge) dissolved in the mobile fluid. A “mixed” LMPHETS theory and finite element models (FEMs) were presented [1] in which the “primary fields” are the displacements, ui = xiXi and the mechano-electro-chemical potentials, ν˜ξ* (ξ, η = f, e, m, b) that are continuous across material interfaces. “Secondary fields” (discontinuous at material boundaries) are mechanical fluid pressure, pf; electrical potential, μ˜e; and concentration or “molarity”, cα = dnα / dVf. Here an extended version of these models is described and numerical results are presented for representative test problems associated with transport in soft tissues.

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