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Computational multiphase micro-periporomechanics for dynamic shear banding and fracturing of unsaturated porous media

Dynamic shearing banding and fracturing in unsaturated porous media is a significant problem in engineering and science. This article proposes a multiphase micro-periporomechanics (uPPM) paradigm for modeling dynamic shear banding and fracturing in unsaturated porous media. Periporomechanics (PPM) is a nonlocal reformulation of classical poromechanics to model continuous and discontinuous deformation/fracture and fluid flow in porous media through a single framework. In PPM, a multiphase porous material is postulated as a collection of a finite number of mixed material points. The length scale in PPM that dictates the nonlocal interaction between material points is a mathematical object that lacks a direct physical meaning. As a novelty, in the coupled uPPM, a microstructure-based material length scale is incorporated by considering micro-rotations of the solid skeleton following the Cosserat continuum theory for solids. As a new contribution, we reformulate the second-order work for detecting material instability and the energy-based crack criterion and J-integral for modeling fracturing in the uPPM paradigm. The stabilized Cosserat PPM correspondence principle that mitigates the multiphase zero-energy mode instability is augmented to include unsaturated fluid flow. We have numerically implemented the novel uPPM paradigm through a dual-way fractional-step algorithm in time and a hybrid Lagrangian-Eulerian meshfree method in space. Numerical examples are presented to demonstrate the robustness and efficacy of the proposed uPPM paradigm for modeling shear banding and fracturing in unsaturated porous media.