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ABSTRACT In this article, we formulate a computational large‐deformation‐plasticity (LDP) periporomechanics (PPM) paradigm through a multiplicative decomposition of the deformation gradient following the notion of an intermediate stress‐free configuration. PPM is a nonlocal meshless formulation of poromechanics for deformable porous media through integral equations in which a porous material is represented by mixed material points with nonlocal poromechanical interactions. Advanced constitutive models can be readily integrated within the PPM framework. In this paper, we implement a linearly elastoplastic model with Drucker–Prager yield and post‐peak strain softening (loss of cohesion). This is accomplished using the multiplicative decomposition of the nonlocal deformation gradient and the return mapping algorithm for LDP. The paper presents a series of numerical examples that illustrate the capabilities of PPM to simulate the development of shear bands, large plastic deformations, and progressive slope failure mechanisms. We also demonstrate that the PPM results are robust and stable to the material point density (grid spacing). We illustrate the complex retrogressive failure observed in sensitive St. Monique clay that was triggered by toe erosion. The PPM analysis captures the distribution of horst and graben structures that were observed in the failed clay mass. 

Abstract Dynamic crack branching in unsaturated porous media holds significant relevance in various fields, including geotechnical engineering, geosciences, and petroleum engineering. This article presents a numerical investigation into dynamic crack branching in unsaturated porous media using a recently developed coupled micro‐periporomechanics (PPM) paradigm. This paradigm extends the PPM model by incorporating the micro‐rotation of the solid skeleton. Within this framework, each material point is equipped with three degrees of freedom: displacement, micro‐rotation, and fluid pressure. Consistent with the Cosserat continuum theory, a length scale associated with the micro‐rotation of material points is inherently integrated into the model. This study encompasses several key aspects: (1) Validation of the coupled micro‐PPM paradigm for effectively modeling crack branching in deformable porous media, (2) Examination of the transition from a single branch to multiple branches in porous media under drained conditions, (3) Simulation of single crack branching in unsaturated porous media under dynamic loading conditions, and (4) Investigation of multiple crack branching in unsaturated porous media under dynamic loading conditions. The numerical results obtained in this study are systematically analyzed to elucidate the factors that influence crack branching in porous media subjected to dynamic loading. Furthermore, the comprehensive numerical findings underscore the efficacy and robustness of the coupled micro‐PPM paradigm in accurately modeling dynamic crack branching in variably saturated porous media. 

Abstract Dynamic shearing banding and fracturing in unsaturated porous media are significant problems in engineering and science. This article proposes a multiphase micro‐periporomechanics (PPM) 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 PPM, 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 PPM 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 PPM 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 PPM paradigm for modeling shear banding and fracturing in unsaturated porous media. 

Abstract In this article, we investigate the creep mechanism of clay at the nanoscale. We conduct the molecular dynamics (MD) modeling of clay samples consisting of hexagonal particles under compression and shear. The MD simulations include oedometer creep, shear creep, direct shear tests, and stress relaxation. The numerical results show that the nanoscale creep mechanism of clay is related to particle rotation, translation, and stacking under different loading conditions. The clay sample under creep shows two types of particle arrangements, that is, the shifted face‐to‐face configuration and the face‐to‐edge configuration. The orientation angle of clay particles is computed to track the rotation of individual particles due to creep. The fabric variation of the clay under creep is characterized by the dihedral angle between the basal particle plane and the x‐y plane and the order parameter. It is found that the factors affecting the microstructure variation of the clay aggregate include stress levels, loading rates, and particle sizes. In the nanoscale shear creep test, the creep process comprises three stages, that is, primary, secondary, and tertiary. The microstructure change during creep depends on the initial alignment of clay particles. The clay creep under a more significant stress level results in a more considerable order parameter and a more orientated clay structure. 

Abstract The atomic‐scale cracking mechanism in clay is vital in discovering the cracking mechanism of clay at the continuum scale in that clay is a nanomaterial. In this article, we investigate mechanisms of modes I and II crack propagations in pyrophyllite and Ca‐montmorillonite with water adsorption through reactive molecular dynamics (MD) with a bond‐order force field. Clay water adsorption is considered by adding water molecules to the clay surface. During the equilibration stage, water adsorption could cause bending deformation of the predefined edge crack region. The relatively small orientating angle of water molecules indicates the formation of hydrogen bonds in the crack propagation process. The peak number density of adsorbed water decreases with the increasing strains. The atomistic structure evolution of the crack tip under loading is analyzed to interpret the nanoscale crack propagation mechanism. The numerical results show that the crack tip first gets blunted with a significant increase in the radius of the curvature of the crack tip and a slight change in crack length. The crack tip blunting is studied by tracking the crack tip opening distance and O–Si–O angle in the tetrahedral Si–O cell in modes I and II cracks. We compare bond‐breaking behaviors between Al–O and Si–O. It is found that Si–O bond breaking is primarily responsible for crack propagation. The critical stress intensity factor and critical energy release rate are determined from MD simulation results. 

Abstract The engineering problems involving clay under non‐isothermal conditions (e.g., geothermal energy harvest, landfill cover system, and nuclear waste disposal) are multiscale and multiphysics by nature. The nanoscale hydrodynamics of clay at elevated temperature is essential in developing a physics‐based multiscale model for clay under non‐isothermal conditions. The nonequilibrium molecular dynamics (NEMD) is a useful tool to study the nanoscale hydrodyndamics of clay. This article presents an NEMD modeling of hydrodynamics of clay nanopores at elevated temperatures. Water flow confined in pyrophyllite and montmorillonite clay nanopores is investigated. The nonequilibrium state is maintained by uniformly exerting an external force on each water molecule. The NEMD simulations have provided a molecular‐scale perspective of temperature effect on clay‐water density, water flow velocity, shear viscosity, clay‐water slip length, hydraulic conductivity, and clay‐water friction coefficient. The numerical results have shown a strong temperature dependence of fluid flow velocity, shear viscosity, clay‐water slip length, and hydraulic conductivity at the nanoscale. We have validated the applicability of cubic law in determining hydraulic conductivity at the nanopore scale at elevated temperatures. It is found from our numerical results that slip clay‐water boundary condition is an essential factor in properly determining nanoscale fluid flow velocity. By numerical examples, we also study the impact of nanopore size and clay layer thickness on the hydrodynamics of the clay‐water system. 

Abstract In this article we formulate a stable computational nonlocal poromechanics model for dynamic analysis of saturated porous media. As a novelty, the stabilization formulation eliminates zero‐energy modes associated with the original multiphase correspondence constitutive models in the coupled nonlocal poromechanics model. The two‐phase stabilization scheme is formulated based on an energy method that incorporates inhomogeneous solid deformation and fluid flow. In this method, the nonlocal formulations of skeleton strain energy and fluid flow dissipation energy equate to their local formulations. The stable coupled nonlocal poromechanics model is solved for dynamic analysis by an implicit time integration scheme. As a new contribution, we validate the coupled stabilization formulation by comparing numerical results with analytical and finite element solutions for one‐dimensional and two‐dimensional dynamic problems in saturated porous media. Numerical examples of dynamic strain localization in saturated porous media are presented to demonstrate the efficacy of the stable coupled poromechanics framework for localized failure under dynamic loads. 

The mechanical behavior of unsaturated porous media under non-isothermal conditions plays a vital role in geo-hazards and geo-energy engineering (e.g., landslides triggered by fire and geothermal energy harvest and foundations). Temperature increase can trigger localized failure and cracking in unsaturated porous media. This article investigates the shear banding and cracking in unsaturated porous media under non-isothermal conditions through a thermo–hydro–mechanical (THM) periporomechanics (PPM) paradigm. PPM is a nonlocal formulation of classical poromechanics using integral equations, which is robust in simulating continuous and discontinuous deformation in porous media. As a new contribution, we formulate a nonlocal THM constitutive model for unsaturated porous media in the PPM paradigm in this study. The THM meshfree paradigm is implemented through an explicit Lagrangian meshfree algorithm. The return mapping algorithm is used to implement the nonlocal THM constitutive model numerically. Numerical examples are presented to assess the capability of the proposed THM mesh-free paradigm for modeling shear banding and cracking in unsaturated porous media under non-isothermal conditions. The numerical results are examined to study the effect of temperature variations on the formation of shear banding and cracking in unsaturated porous media. 

Strain localization and cracking in porous media are significant issues in engineering and science. Periporomechanmics is a strong nonlocal framework for modeling the mechanics and physics of porous media with evolving discontinuities. In periporomechanics, the horizon that usually lacks a physical meaning serves as a nonlocal parameter. In this article, as a new contribution, we formulate a Cosserat periporomechanics paradigm incorporating a micro-structure related length scale for modeling shear banding and cracking in dry porous media. In this new Cosserat-periporomechanics framework, each material point is endowed with both translational and rotational degrees of freedom following the Cosserat continuum theory. We formulate a stabilized Cosserat constitutive correspondence principle through which classical micro-polar constitutive models for porous media can be used in Cosserat periporomechanics. We have numerically implemented the Cosserat periporomechanics paradigm through an explicit Lagrangian meshfree algorithm. We first present numerical examples to validate the implemented computational Cosserat periporomechanics paradigm for modeling shear bands and cracks. We then present numerical examples to demonstrate the efficacy and robustness of the Cosserat periporomechanics for modeling the shear banding bifurcation and crack branching in dry porous media.