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Related papers: On the Kelvin Problem

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In the theory of elasticity, the constraint of compatibility conditions on displacement field is not equivalent to the property of displacement field. The difference may broaden the possibility of solutions to elasticity problems, which…

Classical Physics · Physics 2024-03-05 Peng Shi

Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known…

Materials Science · Physics 2020-12-08 Benjamin Cameron , Cem Tasan

The ``Eshelby problem" refers to the response of a 2-dimensional elastic sheet to cutting away a circle, deforming it into an ellipse, and pushing it back. The resulting response is dominated by the so-called ``Eshelby Kernel" which was…

Materials Science · Physics 2023-09-26 H. George E. Hentschel , Avanish Kumar , Itamar Procaccia , Saikat Roy

Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with…

Analysis of PDEs · Mathematics 2019-04-04 L. Angela Mihai , Alain Goriely

The nonrelativistic limit of a semilinear field equation is considered in a uniform and isotropic space.The scale-function of the space is constructed based on the Einstein equation.The Cauchy problem of the limit-equation is considered,and…

Mathematical Physics · Physics 2020-12-23 Makoto Nakamura

A class of isotropic and scale invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes infinite with time or collapses to zero in finite time,…

Analysis of PDEs · Mathematics 2023-12-12 Thomas C. Sideris

The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general…

General Relativity and Quantum Cosmology · Physics 2009-11-11 S. D. Maharaj , S. Thirukkanesh

We study the inverse electrostatic and elasticity problems associated with Poisson and Navier equations. The uniqueness of solutions of these problems is proved for piecewise constant electric charge and internal stress distributions having…

Analysis of PDEs · Mathematics 2012-11-08 Andrei Artemev , Leonid Parnovski , Iosif Polterovich

In this paper we establish that the time-harmonic elasticity problem in a half-strip with non-homogeneous Dirichlet conditions on its boundary section and traction-free conditions on its upper and lower boundaries, has a unique weak…

Analysis of PDEs · Mathematics 2022-06-27 Jean-Luc Akian

We introduce a pure--stress formulation of the elasticity eigenvalue problem with mixed boundary conditions. We propose an H(div)-based discontinuous Galerkin method that imposes strongly the symmetry of the stress for the discretization of…

Numerical Analysis · Mathematics 2022-05-06 Salim Meddahi

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…

General Relativity and Quantum Cosmology · Physics 2015-06-25 S. Thirukkanesh , S. D. Maharaj

By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are…

Materials Science · Physics 2007-05-23 Markus Lazar

In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the…

Analysis of PDEs · Mathematics 2022-08-05 Matteo Dalla Riva , Gennady Mishuris , Paolo Musolino

The dependence of the elastic tensor on the equilibrium stress is investigated theoretically. Using ideas from finite-elasticity, it is first shown that both the equilibrium stress and elastic tensor are given uniquely in terms of the…

Geophysics · Physics 2020-11-30 Matthew Maitra , David Al-Attar

We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled…

Numerical Analysis · Mathematics 2018-12-11 Paola F. Antonietti , Francesco Bonaldi , Ilario Mazzieri

In the assumption of hexagonal symmetry of an elastic material the axially symmetric displacement problem in a bounded axially symmetric solid with a Lyapunov boundary is reduced to a system of regular (Fredholm) integral equations.

Analysis of PDEs · Mathematics 2018-02-13 Yu. A. Bogan

The aim of this paper is to analyze a mixed discontinuous Galerkin discretization of the time-harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. We show that…

Numerical Analysis · Mathematics 2014-10-07 Antonio Márquez , Salim Meddahi , Thanh Tran

In this paper we introduce and study a new Kelvin-type transform in the anisotropic setting. In particular, we deal with semilinear and quasilinear anisotropic elliptic problems in the entire space.

Analysis of PDEs · Mathematics 2022-10-03 Francesco Esposito , Giuseppe Riey , Berardino Sciunzi , Domenico Vuono

We consider an elliptic polyharmonic problem of any order which takes place in a punctured bounded domain with Navier conditions. We prove that if the domain is convex in one direction and symmetric with respect to the reflections induced…

Analysis of PDEs · Mathematics 2018-10-08 Stefano Biagi , Enrico Valdinoci , Eugenio Vecchi

Isothermal visco-elastodynamics in the Kelvin-Voigt rheology is formulated in the spatial Eulerian coordinates in terms of velocity and deformation gradient. A generally nonconvex (possibly also frame-indifferent) stored energy is admitted.…

Analysis of PDEs · Mathematics 2022-04-13 Tomáš Roubíček