A Geometrization of the Configurational Problem. Plasticity and Micromechanics of Nonsaturated Porous Media

Resumen

The primary objective of this work is to evaluate configurational forces by leveraging the geometric structure of the material manifold and the projection of the actual deformation onto it. Two classes of problems are addressed: finite-strain elastoplasticity and pseudo-finite-strain micromechanics in non-saturated porous media. General conditions for the strain energy function are established, and a global balance of pseudomomentum is formulated within a fully material manifold described in terms of a K-configuration. A natural frame of reference is introduced, characterised by K-parallelism (in the sense of Cartan), whereby each point of the elastic solid is associated with a unique stress-free reference configuration via the inverse of K. A Hencky-type form of the strain energy in the relaxed configuration is proposed, derived from general energetic and geometrical considerations. The resulting configurational forces are examined for two scenarios: (i) homogeneous elastoplastic solids with an arbitrary K-reference, and (ii) inhomogeneous porous media in the context of Biot-type formulations. A nonlinear expression for the configurational forces is obtained, which exhibits consistent convergence to the classical infinitesimal-strain formulation in the Biot case. The proposed framework provides a unified geometric basis for both elastoplasticity and micromechanics, and can be extended to other inhomogeneity-driven problems This behavior was numerically observed through the implementation of the boundary value problem using the Finite Element Method.