The Nineteenth Israeli Mini-Workshop in Applied and Computational Mathematics

Elik Olami (Hebrew University)

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

In this talk we discuss the dynamics of continua on differentiable manifolds. We present a covariant derivation of equations of motion, viewing motion as a curve in the 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; residual stress results 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.

Joint work with Raz Kupferman and Reuven Segev.

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