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A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…

Optics · Physics 2020-10-07 J. V. Alvarez , Bahram Djafari-Rouhani , Dani Torrent

A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than…

Analysis of PDEs · Mathematics 2016-02-02 Robert Lipton , Stewart Silling , Richard Lehoucq

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

We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with…

Numerical Analysis · Mathematics 2017-02-07 Xingjie Helen Li , Jianfeng Lu

We present an approach for the data-driven modeling of nonlinear viscoelastic materials at small strains which is based on physics-augmented neural networks (NNs) and requires only stress and strain paths for training. The model is built on…

Computational Engineering, Finance, and Science · Computer Science 2024-01-26 Max Rosenkranz , Karl A. Kalina , Jörg Brummund , WaiChing Sun , Markus Kästner

We present an overdamped continuum description of oriented active solids in which interactions respect the symmetries of space but do not obey the principle of action and reaction. Taking position and orientation as kinematic variables, we…

Soft Condensed Matter · Physics 2025-09-16 Balázs Németh , Takuya Kobayashi , Ronojoy Adhikari

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

Elastic wave speeds are fundamental in geomechanics and have historically been described by an analytic formula that assumes linearly elastic solid medium. Empirical relations stemming from this assumption were used to determine nonlinearly…

Classical Physics · Physics 2023-12-05 David M. Riley , Itai Einav , François Guillard

In this paper, we deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal in exam, so that the mathematical formulation…

Mathematical Physics · Physics 2008-08-19 Adriana Garroni , Giovanni Leoni , Marcello Ponsiglione

To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two…

Soft Condensed Matter · Physics 2022-11-24 Aondoyima Ioratim-Uba , Aurore Loisy , Silke Henkes , Tanniemola B. Liverpool

We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law.…

Systems and Control · Electrical Eng. & Systems 2024-01-31 Tobias Thoma , Paul Kotyczka , Herbert Egger

We consider semi-discrete discontinuous Galerkin approximations of a general elastodynamics problem, in both {\it displacement} and {\it displacement-stress} formulations. We present the stability analysis of all the methods in the natural…

Numerical Analysis · Mathematics 2013-10-31 Paola F. Antonietti , Blanca Ayuso de Dios , Ilario Mazzieri , Alfio Quarteroni

As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the…

Numerical Analysis · Mathematics 2021-09-22 Xiao Xu , Marta D'Elia , John T. Foster

Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral operators couple the solution across phase space. Such…

Numerical Analysis · Mathematics 2026-04-16 Haoning Dang , Fei Wang , Yifan Chen , Zhouyu Liu , Dong Liu , Hongchun Wu

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

State-based peridynamic models provide an important extension of bond-based models that allow the description of general linearly elastic materials. Meshfree discretizations of these nonlocal models are attractive due to their ability to…

Numerical Analysis · Mathematics 2019-03-04 Nathaniel Trask , Benjamin Huntington , David Littlewood

The discrete modeling of a large class of mechanical structures can be based on a stick-and-spring concept. We here present a stick-and-spring theory with potential application to the statics and the dynamics of such nanostructures as…

Materials Science · Physics 2013-07-16 Antonino Favata , Andrea Micheletti , Paolo Podio-Guidugli

This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…

Computational Engineering, Finance, and Science · Computer Science 2022-04-06 Bensingh Dhas , Jamun Kumar N , Debasish Roy , J N Reddy

A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…

Numerical Analysis · Mathematics 2020-08-28 Giacomo Capodaglio , Marta D'Elia , Max Gunzburger , Pavel Bochev , Manuel Klar , Christian Vollmann

The action functional for a linear elastic medium with dislocations is given. The equations of motion following from this action reproduce the Peach-K\"{o}hler and Lorentzian forces experienced by dislocations. The explicit expressions for…

Materials Science · Physics 2022-03-11 P. O. Kazinski , V. A. Ryakin , A. A. Sokolov