English
Related papers

Related papers: Shear band patterns by boundary integral equations

200 papers

We study incremental wave propagation for what is seemingly the simplest boundary value problem, namely that constitued by the plane interface of a semi-infinite solid. With a view to model loaded elastomers and soft tissues, we focus on…

Materials Science · Physics 2007-12-04 Michel Destrade

In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…

Optimization and Control · Mathematics 2025-12-05 Yassine El Gantouh , Yang Liu

Concentrated suspensions may shear-thin when the suspended particles form planar sheets that slide over one another with less friction than if the particles are randomly distributed. In a na\"ive model the suspension is described by a mean…

Soft Condensed Matter · Physics 2014-02-25 J. I. Katz

The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…

Numerical Analysis · Mathematics 2023-01-03 Alexander Schlüter , Henning Müller , Sikang Yan , Erik Faust , Ralf Müller

The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities…

Quantum Physics · Physics 2019-08-17 V. I. Man'ko , G. Marmo , F. Zaccaria

A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…

Optics · Physics 2018-05-21 Bin Liu , Lu Li , Boris A. Malomed

Historically, meteorological and climate studies have been prompted by the need for understanding precipitation to have better logistics in food production. Despite all efforts, nonlinearity in atmosphere dynamics is still a source of…

Analysis of PDEs · Mathematics 2020-07-17 Carla Victoria Valencia-Negrete

A finite simple shear deformation of an elastic solid induces unequal normal stresses. This nonlinear phenomenon, known as the Poynting effect, is governed by a universal relation between shear strain and first normal stresses difference,…

Soft Condensed Matter · Physics 2009-11-11 Vincent Labiausse , Reinhard Hohler , Sylvie Cohen-Addad

In the framework of the rate-independent large-strain Cosserat theory of plasticity we calculate analytically explicit solutions of a two-dimensional shear problem. We discuss two cases where the micro-rotations are stationary solutions of…

Mathematical Physics · Physics 2012-08-17 Thomas Blesgen

A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 B. Konopelchenko , L. Martinez Alonso

Various experiments evidence spatial heterogeneities in sheared yield stress fluids. To account for heterogeneities in the velocity gradient direction, we use a simple model corresponding to a non-monotonous local constitutive curve and…

Soft Condensed Matter · Physics 2009-11-07 G. Picard , A. Ajdari , L. Bocquet , F. Lequeux

We present a linear stability analysis to demonstrate that a flat coherent phase boundary formed by the (de)intercalation of solutes into a compound is unstable against perturbations with wavelengths larger than a critical wavelength. This…

Materials Science · Physics 2020-05-05 Youtian Zhang , Ming Tang

We study theoretically the edge fracture instability in sheared complex fluids, by means of linear stability analysis and direct nonlinear simulations. We derive an exact analytical expression for the onset of edge fracture in terms of the…

Soft Condensed Matter · Physics 2017-07-19 Ewan J. Hemingway , Halim Kusumaatmaja , Suzanne M. Fielding

Elastic scattering governed by the Lame system associated with the third-type or fourth-type boundary condition is considered. It was shown in [8] by two of the authors that under suitable geometric conditions on the boundary surface of the…

Analysis of PDEs · Mathematics 2019-05-16 Junjiang Lai , Hongyu Liu , Jingni Xiao , Yifeng Xu

We investigate analytically and numerically the interaction between grain boundaries and second phase precipitates in two-phase coherent solids in the presence of misfit strain. Our numerical study uses amplitude equations that describe the…

Materials Science · Physics 2016-11-02 Yechuan Xu , Pierre-Antoine Geslin , Alain Karma

Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…

Pattern Formation and Solitons · Physics 2013-07-09 Nikolai A. Kudryashov , Dmitry I. Sinelshchikov

An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…

Classical Physics · Physics 2008-12-09 J. G. Murphy , M. Destrade

We study numerically shear banded flow in planar and curved Couette geometries. Our aim is to explain two recent observations in shear banding systems of roll cells stacked in the vorticity direction, associated with an undulation of the…

Soft Condensed Matter · Physics 2015-05-14 Suzanne M. Fielding

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

Motivated by the need for a theoretical study in a planar geometry that can easily be implemented experimentally, we study the pressure driven Poiseuille flow of a shear banding fluid. After discussing the "basic states" predicted by a one…

Soft Condensed Matter · Physics 2009-09-03 Suzanne M. Fielding , Helen J. Wilson