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Journal of Elasticity

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09-01-2017

Continuum Dynamics on Manifolds: Application to Elasticity of Residually-Stressed Bodies

Authors: Raz Kupferman, Elihu Olami, Reuven Segev

Published in: Journal of Elasticity | Issue 1/2017

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Abstract

This paper is concerned with the dynamics of continua on differentiable manifolds. We present a covariant derivation of the equations of motion, viewing motion as a curve in an infinite-dimensional Banach manifold of embeddings of a body manifold in a space manifold. Our main application is the motion of residually-stressed elastic bodies, where the residual stresses result from a geometric incompatibility between body and space manifolds. We then study a particular example of elastic vibrations of a two-dimensional curved annulus embedded in a sphere.

previous article Homogenization and Materials Design of Anisotropic Multiphase Linear Elastic Materials Using Central Model Functions

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Title: Continuum Dynamics on Manifolds: Application to Elasticity of Residually-Stressed Bodies
Authors: Raz Kupferman
Elihu Olami
Reuven Segev
Publication date: 09-01-2017
Publisher: Springer Netherlands
Published in: Journal of Elasticity / Issue 1/2017
Print ISSN: 0374-3535
Electronic ISSN: 1573-2681
DOI: https://doi.org/10.1007/s10659-016-9617-y

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Other articles of this Issue 1/2017

Homogenization and Materials Design of Anisotropic Multiphase Linear Elastic Materials Using Central Model Functions

Waves in Nonlocal Elastic Solid with Voids

On the Stress Field of a Nonlinear Elastic Solid Torus with a Toroidal Inclusion

On the Nonlinear Theory of Thermoviscoelastic Materials with Voids

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