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Related papers: Nonlocal elastodynamics and fracture

200 papers

Non-local elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak non-locality) and the integral non-local models (strong non-locality). This article focuses on the…

Classical Physics · Physics 2014-04-04 Vasily E. Tarasov

Some Mumford-Shah functionals are revisited as perturbed area functionals in connection with brittle damage mechanics. We find minimizers "on paper" for the classical Mumford-Shah functional for some particular two dimensional domains and…

Analysis of PDEs · Mathematics 2007-05-23 Marius Buliga

In this paper we consider and compare special classes of static theories of gradient elasticity, nonlocal elasticity, gradient micropolar elasticity and nonlocal micropolar elasticity with only one gradient coefficient. Equilibrium…

Materials Science · Physics 2009-11-11 M. Lazar , G. A. Maugin , E. C. Aifantis

We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an…

Analysis of PDEs · Mathematics 2024-02-27 Manuel Friedrich , Manuel Seitz , Ulisse Stefanelli

This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state.…

Numerical Analysis · Mathematics 2021-10-04 Fadi Aldakheel , Nima Noii , Thomas Wick , Olivier Allix , Peter Wriggers

In this paper, the bending behaviour of small-scale Bernoulli-Euler beams is investigated by Eringen's two-phase local/nonlocal theory of elasticity. Bending moments are expressed in terms of elastic curvatures by a convex combination of…

Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the…

Analysis of PDEs · Mathematics 2020-05-11 Giacomo Capodaglio , Marta D'Elia , Pavel Bochev , Max Gunzburger

A continuum model of fracture that describes, in principle, the propagation and interaction of arbitrary distributions of cracks and voids with evolving topology without a fracture criterion is developed. It involves a 'law of motion' for…

Materials Science · Physics 2020-04-22 Amit Acharya

In this work, phase-field modeling of hydraulic fractures in porous media is extended towards a global-local approach. Therein, the failure behavior is solely analyzed in a (small) local domain. In the surrounding medium, a simplified and…

Numerical Analysis · Mathematics 2020-01-20 Fadi Aldakheel , Nima Noii , Thomas Wick , Peter Wriggers

Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. We study the asymptotic behavior of the system, when number of particles tends to infinity, and the distances between them and…

Analysis of PDEs · Mathematics 2018-01-30 E. Khruslov , M. Goncharenko

We demonstrate that the elasticity of jammed solids is nonlocal. By forcing frictionless soft sphere packings at varying wavelength, we directly access their transverse and longitudinal compliances without resorting to curve fitting. The…

Statistical Mechanics · Physics 2017-03-08 Karsten Baumgarten , Daniel Vagberg , Brian P. Tighe

We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…

Analysis of PDEs · Mathematics 2025-12-16 Antonin Chodron de Courcel

Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some modeling…

Numerical Analysis · Mathematics 2022-10-12 Nunzio Dimola , Alessandro Coclite , Giuseppe Fanizza , Tiziano Politi

We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution…

Analysis of PDEs · Mathematics 2024-11-21 Manuel Friedrich , Pascal Steinke , Kerrek Stinson

Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model…

Materials Science · Physics 2007-05-23 E. Katzav , M. Adda-Bedia , B. Derrida

This paper aims to investigate the dynamic response of a material body undergoing fracture subjected to high strain rate loading conditions such as impact or explosion. In particular, our focus is limited to softening elastic damage models…

Computational Engineering, Finance, and Science · Computer Science 2026-01-27 Rajasekar Gopalsamy , Nicolas Chevaugeon

In this study, we introduce a novel stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm…

Soft Condensed Matter · Physics 2025-02-06 S. Mohammad Mousavi , Jason Mulderrig , Brandon Talamini , Nikolaos Bouklas

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of…

Computational Engineering, Finance, and Science · Computer Science 2023-02-06 Matthias Birner , Patrick Diehl , Robert Lipton , Marc Alexander Schweitzer

This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral…

Numerical Analysis · Mathematics 2021-11-03 Sansit Patnaik , Sai Sidhardh , Fabio Semperlotti

Crack propagation is studied numerically using a continuum phase-field approach to mode III brittle fracture. The results shed light on the physics that controls the speed of accelerating cracks and the characteristic branching instability…

Materials Science · Physics 2009-11-10 Alain Karma , Alexander E. Lobkovsky