Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2311.00253

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

Hossein Pashazad·Xiaoyu Song
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hossein Pashazad, Xiaoyu Song. 2023-11-01. Computational multiphase micro-periporomechanics for dynamic shear banding and fracturing of unsaturated porous media. https://arxiv.org/abs/2311.00253

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗