Extended “LMPHETS” Finite Element Models for Coupled Mechano-Electro-Chemical Transport in Soft Tissues

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, u_i = x_i − X_i 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, p^f; electrical potential, μ˜^e; and concentration or “molarity”, c^α = dn^α / dV^f. Here an extended version of these models is described and numerical results are presented for representative test problems associated with transport in soft tissues.