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Related papers: A Nonlocal Model for Dislocations with Embedded Di…

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In this paper we derive a new model for visco-elasticity with large deformations where the independent variables are the stretch and the rotation tensors which intervene with second gradients terms accounting for physical properties in the…

Analysis of PDEs · Mathematics 2024-10-21 Abramo Agosti , Pierluigi Colli , Michel Frémond

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Within the PUM global-local enrichment scheme [1, 2] different physical models can exist to…

Computational Engineering, Finance, and Science · Computer Science 2024-05-06 Matthias Birner , Patrick Diehl , Robert Lipton , Marc Alexander Schweitzer

Peridynamics is a nonlocal theory for dynamic fracture analysis consisting in a second order in time partial integro-differential equation. In this paper, we consider a nonlinear model of peridynamics in a two-dimensional spatial domain. We…

Numerical Analysis · Mathematics 2021-02-15 Luciano Lopez , Sabrina Francesca Pellegrino

We consider the nonlocal formulation of continuum mechanics described by peridynamics. We provide a link between peridynamic evolution and brittle fracture evolution for a broad class of peridynamic potentials associated with unstable…

Analysis of PDEs · Mathematics 2013-06-20 Robert Lipton

A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…

Soft Condensed Matter · Physics 2009-11-11 Thomas Ihle , Erkan Tuzel , Daniel M. Kroll

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…

Optimization and Control · Mathematics 2023-06-27 Lucian Nita , Eduardo M. G. Vila , Marta A. Zagorowska , Eric C. Kerrigan , Yuanbo Nie , Ian McInerney , Paola Falugi

We present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear…

Soft Condensed Matter · Physics 2017-05-02 C. Blanch-Mercader , J. Casademunt

This study presents the application of variable-order (VO) fractional calculus to the modeling of nonlocal solids. The reformulation of nonlocal fractional-order continuum mechanic framework, by means of VO kinematics, enables a unique…

Numerical Analysis · Mathematics 2020-09-01 Mehdi Jokar , Sansit Patnaik , Fabio Semperlotti

In this article we present the numerical simulation of a dislocation incorporated into a Cosserat plate. The simulation is based on the mathematical model for bending of Cosserat elastic plates recently developed by the authors. The…

Soft Condensed Matter · Physics 2022-10-06 Lev Steinberg , Roman Kvasov

A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for…

Functional Analysis · Mathematics 2014-02-04 Bacim Alali , Kuo Liu , Max Gunzburger

Using gradient elasticity, we give in this Letter the non-singular fields produced by arbitrary dislocation loops in isotropic media. We present the `modified' Mura, Peach-Koehler and Burgers formulae in the framework of gradient elasticity…

Materials Science · Physics 2014-01-22 Markus Lazar

Recently, a dislocation free deformation mechanism was proposed by Kiritani et al., based on a series of experiments where thin foils of fcc metals were deformed at very high strain rates. In the experimental study, they observed a large…

Materials Science · Physics 2015-06-24 J. Schiøtz , T. Leffers , B. N. Singh

Considering recent results revealing the existence of multi-scale rigid clusters of grains embedded in granular surface flows, i.e. flows down an erodible bed, we describe here the surface flows rheology through a non-local constitutive…

Condensed Matter · Physics 2016-02-26 D. Bonamy , P. Mills

Porous media containing cracks, fractures, or internal discontinuities arise throughout subsurface geomechanics, biomechanics, and materials science. Numerical simulation of the coupled hydromechanical response is inherently challenging…

Computational Engineering, Finance, and Science · Computer Science 2026-04-20 David Michael Riley , Guglielmo Scovazzi , Ioannis Stefanou

We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting…

Analysis of PDEs · Mathematics 2025-02-07 Andrea Aspri , Elena Beretta , Anna L. Mazzucato

A method for simulation of elastoplastic solids in multibody systems with nonsmooth and multidomain dynamics is developed. The solid is discretised into pseudo-particles using the meshfree moving least squares method. The particles carry…

Soft Condensed Matter · Physics 2016-11-14 John Nordberg , Martin Servin

Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances. This review illustrates different…

Quantitative Methods · Quantitative Biology 2025-02-14 Swadesh Pal , Roderick Melnik

High entropy alloys (HEAs) are single phase crystals that consist of random solid solutions of multiple elements in approximately equal proportions. This class of novel materials have exhibited superb mechanical properties, such as high…

Materials Science · Physics 2020-04-21 Tianpeng Jiang , Yang Xiang , Luchan Zhang

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…

Materials Science · Physics 2007-05-23 A. Carpio , L. L. Bonilla

This work rigorously implements a recent model of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete dislocation lines. The model is geometrically and elastically nonlinear,…

Analysis of PDEs · Mathematics 2024-02-27 Filip Rindler