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A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant…

Computational Physics · Physics 2015-08-04 S. Roy Chowdhury , Md Masiur Rahaman , Debasish Roy , Narayan Sundaram

In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either…

Analysis of PDEs · Mathematics 2025-09-11 Klaus Boehnlein , Lucas Bouck , Stefan Neukamm , David Padilla-Garza , Kai Richter

We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the…

Numerical Analysis · Mathematics 2021-10-12 Marta D'Elia , David Littlewood , Jeremy Trageser , Mauro Perego , Pavel Bochev

We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…

Numerical Analysis · Mathematics 2018-06-19 Klaus Böhmer , Robert Schaback

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given…

Materials Science · Physics 2022-01-05 Huaiqian You , Yue Yu , Stewart Silling , Marta D'Elia

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

In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device has two…

Analysis of PDEs · Mathematics 2023-12-06 Heiko Gimperlein , Runan He , Andrew A. Lacey

We present a comprehensive rotation-free Kirchhoff-Love (KL) shell formulation for peridynamics (PD) that is capable of modeling large elasto-plastic deformations and fracture in thin-walled structures. To remove the need for a predefined…

Numerical Analysis · Mathematics 2022-01-12 Masoud Behzadinasab , Mert Alaydin , Nathaniel Trask , Yuri Bazilevs

When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in…

Chaotic Dynamics · Physics 2007-05-23 Michael Small

Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices, all of these models assume central-force interactions between…

Soft Condensed Matter · Physics 2016-01-14 M. Schlegel , J. Brujic , E. M. Terentjev , A. Zaccone

We present a comparative analysis of several methods, known as local Lagrangian approximations, which are aimed to the description of the nonlinear evolution of large-scale structure. We have investigated various aspects of these…

Astrophysics · Physics 2009-11-06 Martin Makler , Takeshi Kodama , Mauricio O. Calvao

In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous…

Analysis of PDEs · Mathematics 2021-06-22 Tadele Mengesha , James M. Scott

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

It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term…

Statistical Mechanics · Physics 2009-10-31 R. Soto , M. Mareschal , M. Malek Mansour

We first consider an elastic thin heterogeneous cylinder of radius of order epsilon: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor…

Analysis of PDEs · Mathematics 2015-03-26 Roberto Paroni , Ali Sili

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

The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are…

Statistical Mechanics · Physics 2021-05-12 Salvatore Torquato , Jaeuk Kim , Michael A. Klatt

This study presents a comprehensive framework for constitutive modeling of a frame-invariant fractional-order approach to nonlocal thermoelasticity in solids. For this purpose, thermodynamic and mechanical balance laws are derived for…

Numerical Analysis · Mathematics 2021-02-11 Sai Sidhardh , Sansit Patnaik , Fabio Semperlotti

Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting…

Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…

Soft Condensed Matter · Physics 2022-12-27 Lorenzo Campana , Mireille Bossy , Jeremie Bec