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An analysis of strong discontinuities in a saturated poro-plastic solid. (English) Zbl 0971.74029
From the summary: We present an analysis of strong discontinuities in fully saturated porous media in the infinitesimal range. In particular, from a local constitutive level we describe the incorporation of the local effects of surfaces of discontinuity in the displacement field, and thus the singular distributions of associated strains, into the large-scale problem characterizing the quasi-static equilibrium of the solid. The characterization of the flow of the fluid through the porous space is accomplished by means of a localized (singular) distribution of the fluid content, that is, involving a regular fluid mass distribution per unit volume and a fluid mass per unit area of the discontinuity surfaces in the small scale of the material. The proposed framework also involves the coupled equation of conservation of fluid mass and seepage through the porous solid via Darcy’s law, and considers a continuous pressure field with discontinuous gradients. Enhanced finite element methods are developed, which accommodate different localized fields at the element level. Numerical simulations are presented illustrating the performance of the numerical methods.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76S05 Flows in porous media; filtration; seepage
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