Covariant Linearization of elasticity
Mathematical Physics
2018-10-31 v1 math.MP
Abstract
In this paper we derive a general linearized theory for first-order continuum dynamics on manifolds with particular application to incompatible elasticity. We adopt a global approach viewing the equations of motion as a -form on the configuration space which is the Banach manifold of time-dependent embeddings of a body manifold into a space manifold . The linearization is done by differentiating the equations 1-form with respect to an affine connection which we construct and study extensively. We provide detailed coordinate computations for the linearized equations of a large class of problems in continuum dynamics on manifolds.
Cite
@article{arxiv.1810.12360,
title = {Covariant Linearization of elasticity},
author = {Raz Kupferman and Elihu Olami},
journal= {arXiv preprint arXiv:1810.12360},
year = {2018}
}