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A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure…

Materials Science · Physics 2020-10-20 Nathan Perchikov , Jacob Aboudi

A generalized notion of a nonlocal tensor order parameter is introduced within the framework of the phenomenological approach. This parameter has the form of a traceless tensor correlation function or a tensor integral operator. Based on…

Soft Condensed Matter · Physics 2017-07-14 Alexey N. Kudryavtsev , Petr A. Purtov , Sergey I. Trashkeev

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of…

Machine Learning · Computer Science 2019-01-28 Yunzhe Tao , Qi Sun , Qiang Du , Wei Liu

The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…

Analysis of PDEs · Mathematics 2021-06-29 Mikil Foss , Petronela Radu , Yue Yu

An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…

Analysis of PDEs · Mathematics 2017-04-20 G. Buttazzo , G. Cardone , S. A. Nazarov

We present a new mechanistic, phase field-based formulation for predicting hydrogen embrittlement. The multi-physics model developed incorporates, for the first time, a Taylor-based dislocation model to resolve the mechanics of crack tip…

Materials Science · Physics 2021-08-03 M. Isfandbod , E. Martínez-Pañeda

A phase proper orthogonal decomposition (Phase POD) method is demonstrated, utilizing phase averaging for the decomposition of spatio-temporal behaviour of statistically non-stationary turbulent flows in an optimized manner. The proposed…

Fluid Dynamics · Physics 2024-03-01 Yisheng Zhang , Azur Hodzic , Fabien Evrard , Berend Van Wachem , Clara M. Velte

We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…

Analysis of PDEs · Mathematics 2020-12-30 David Melching , Michael Neunteufel , Joachim Schöberl , Ulisse Stefanelli

In this paper, the modelling strategy of a Cosserat rod element (CRE) is addressed systematically for 3-dimensional dynamical analysis of slender structures. We employ the exact nonlinear kinematic relationships in the sense of Cosserat…

Functional Analysis · Mathematics 2007-05-23 D. Q. Cao , Dongsheng Liu , Charles H. -T. Wang

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

This study presents the analytical formulation and the finite element solution of fractional order nonlocal plates under both Mindlin and Kirchoff formulations. By employing consistent definitions for fractional-order kinematic relations,…

Computational Engineering, Finance, and Science · Computer Science 2021-02-03 Sansit Patnaik , Sai Sidhardh , Fabio Semperlotti

We investigate a new class of non-local random deposition models, initially introduced by physicists to study the field of mechanical constraints (stress) applied along a line or on a given area located in a seismic zone. The non-local…

Probability · Mathematics 2025-11-17 Philippe Carmona , François Pétrélis , Nicolas Pétrélis

In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…

Materials Science · Physics 2019-06-26 Nothando Mhlongo , B Daya Reddy

We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density…

Soft Condensed Matter · Physics 2022-06-02 Ivan Kriuchevksyi , Tim Sirk , Alessio Zaccone

Using a model of spinless fermions in a lattice with nearest neighbor and next-nearest neighbor interaction we show that the entropy of the reduced two site density matrix (the bond entropy) can be used as an extremely accurate and easy to…

Strongly Correlated Electrons · Physics 2009-11-13 Rafael A. Molina , Peter Schmitteckert

For a class of systems of nonlinear and nonlocal balance laws in several space dimensions, we prove the local in time existence of solutions and their continuous dependence on the initial datum. The choice of this class is motivated by a…

Analysis of PDEs · Mathematics 2015-04-02 Rinaldo M. Colombo , Francesca Marcellini

A rigorous unified perspective of cohesive zone models is presented, including and comparing potential-based and non potential-based formulations, and encompassing known examples studied in literature. The main novelty of the work consists…

Analysis of PDEs · Mathematics 2025-03-05 Francesco Freddi , Filippo Riva

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this…

Classical Physics · Physics 2019-09-12 Roger A. Sauer , Reza Ghaffari , Anurag Gupta

A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…

Numerical Analysis · Mathematics 2018-01-17 Fei Zhang , Weizhang Huang , Xianping Li , Shicheng Zhang

In this paper, a strain-gradient plasticity model is derived from a mesoscopic model for straight parallel edge dislocations in an infinite cylindrical crystal. The main difference to existing work is that in this work the well-separateness…

Analysis of PDEs · Mathematics 2019-05-01 Janusz Ginster