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Periporomechanmics is a strong nonlocal framework for modeling the mechanics and physics of variably saturated porous media with evolving discontinuities. In periporomechanics, the horizon serves as a mathematical nonlocal parameter that…

Numerical Analysis · Mathematics 2023-07-03 Xiaoyu Song , Hossein Pashazad

We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…

Graphics · Computer Science 2023-03-21 James F. O'Brien , Jessica K. Hodgins

A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and…

Analysis of PDEs · Mathematics 2024-04-02 Robert P. Lipton , Debdeep Bhattacharya

Structural damage detection using non-contact sensing remains a challenging problem in structural health monitoring. This study presents a data-driven framework based on Dynamic Mode Decomposition (DMD) for extracting structural dynamics…

Systems and Control · Electrical Eng. & Systems 2026-05-05 R K B M Rizmi , Shabbir Ahmed

This paper presents a unified framework for bond-associated peridynamic material correspondence models that were proposed to inherently address the issue of material instability or existence of zero-energy modes in the conventional…

Materials Science · Physics 2024-10-03 Xuan Hu , Hailong Chen , Yichi Zhang , Zening Wang

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…

Numerical Analysis · Mathematics 2024-01-10 Hossein Pashazad , Xiaoyu Song

A particular failure mode of highly porous brittle materials consists in the propagation of cracks under uniaxial compressive loads. Such 'anticracks' have been observed in a range of materials, from snow and porous sandstone to brittle…

Soft Condensed Matter · Physics 2025-03-14 Shucheta Shegufta , Michael Zaiser

Modeling important engineering problems related to flow-induced damage (in the context of hydraulic fracturing among others) depends critically on characterizing the interaction of porous media and interstitial fluid flow. This work…

Numerical Analysis · Mathematics 2012-06-27 Daniel Z. Turner

We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations for flow in, and deformation of, fractured materials. We present models both in the context of finite…

Analysis of PDEs · Mathematics 2021-12-10 Wietse M. Boon , Jan M. Nordbotten

Peridynamics is a nonlocal generalization of continuum mechanics theory which adresses discontinuous problems without using partial derivatives and replacing its by an integral operator. As a consequence, it finds applications in the…

Numerical Analysis · Mathematics 2022-09-07 Luciano Lopez , Sabrina Francesca Pellegrino

We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…

Analysis of PDEs · Mathematics 2021-03-17 Phoebus Rosakis , Timothy J. Healey , Ugur Alyanak

The fracture simulation of random particle reinforced composite structures remains a challenge. Current techniques either assumed a homogeneous model, ignoring the microstructure characteristics of composite structures, or considered a…

Numerical Analysis · Mathematics 2022-12-23 Zihao Yang , Shaoqi Zheng , Shangkun Shen , Fei Han

The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…

Materials Science · Physics 2016-03-09 Amit Acharya , Claude Fressenegeas

Bond-based peridynamics is a nonlocal continuum model in Solid Mechanics in which the energy of a deformation is calculated through a double integral involving pairs of points in the reference and deformed configurations. It is known how to…

Analysis of PDEs · Mathematics 2020-01-10 J. C. Bellido , J. Cueto , C. Mora-Corral

A new quantum action-based theory, Dynamic Quantized Fracture Mechanics (DQFM), is presented that modifies continuum-based dynamic fracture mechanics. The crack propagation is assumed as quantized in both space and time. The static limit…

Materials Science · Physics 2007-05-23 N. Pugno , R. Ruoff

We establish the a-priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models. We consider state based peridynamic models where the force at a material point is due to both the strain between…

Numerical Analysis · Mathematics 2019-03-05 Prashant K. Jha , Robert Lipton

We present a fully coupled boundary integral formulation for modeling steadily propagating semi-infinite plane strain fractures in poroelastic media. By combining fundamental solutions of plain strain poroelasticity for instantaneous fluid…

Geophysics · Physics 2026-04-21 Evgenii Kanin , Andreas Möri , Dmitry Garagash , Brice Lecampion

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based…

Numerical Analysis · Mathematics 2021-06-30 Yue Yu , Huaiqian You , Nathaniel Trask

A new gradient-based formulation for predicting fracture in elastic-plastic solids is presented. Damage is captured by means of a phase field model that considers both the elastic and plastic works as driving forces for fracture. Material…

Computational Engineering, Finance, and Science · Computer Science 2021-08-12 S. S. Shishvan , S. Assadpour-asl , E. Martínez-Pañeda

A constitutive model based on the combination of damage mechanics and plasticity is developed to analyse concrete structures subjected to dynamic loading. The aim is to obtain a model, which requires input parameters with clear physical…

Materials Science · Physics 2011-03-09 Peter Grassl , Ulrika Nystrom , Rasmus Rempling , Kent Gylltoft