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arXiv · 1810.12360

Covariant Linearization of elasticity

Raz Kupferman·Elihu Olami
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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 $1$-form on the configuration space which is the Banach manifold of $C^1$ time-dependent embeddings of a body manifold $\B$ into a space manifold $\S$. 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.

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Raz Kupferman, Elihu Olami. 2018-10-29. Covariant Linearization of elasticity. https://arxiv.org/abs/1810.12360

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