Finite element methods for the analysis of strong discontinuities in coupled poro-plastic media.

*(English)*Zbl 1124.74324Summary: This paper presents the formulation of finite element methods for the numerical resolution of strong discontinuities in poro-plastic solids. Fully coupled infinitesimal conditions are considered. These solutions are characterized by a discontinuous displacement field, with the associated singular strains, and a singular distribution of the fluid content. Here, singular distributions refer to Dirac delta functions. The singular component of the fluid content distribution models the fluid accumulated per unit area of the discontinuity surface, and it is directly related with the dilatancy characterizing singular inelastic strains localized along such a surface. It further accounts for a discontinuous fluid flow vector, given by Darcy’s law in terms of a continuous pore pressure field. All these considerations are incorporated in the proposed finite element methods through a local enhancement of the finite element interpolations as these discontinuities appear. The local character of these interpolations lead after the static condensation of the enhanced fields to a large-scale problem exhibiting the same structure as common finite element models of the global poro-plastic problem, but incorporating now crucially the localized dissipative effects characteristic of the localized failures. Several numerical simulations are presented to evaluate the performance of the proposed methods.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

76S05 | Flows in porous media; filtration; seepage |

##### Keywords:

Porous media; Elastoplasticity; Strain localization; Strong discontinuity; Enhanced finite element methods; Coupled problems
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\textit{C. Callari} and \textit{F. Armero}, Comput. Methods Appl. Mech. Eng. 191, No. 39--40, 4371--4400 (2002; Zbl 1124.74324)

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