## Symmetric Hyperbolic Equations of Motion for a Hyperelastic Material |

**David Wagner**

Union College alumnus, Department of Mathematics, University of Houston

May 28, 2009

4:00 pm

Bailey Hall 207

Refreshments will be served at 3:45 in Bailey Hall 204

We offer an alternate derivation for the symmetric-hyperbolic formulation of the equations of motion for a hyperelastic material with polyconvex stored energy. The derivation uses exterior calculus with weak derivatives, and makes it clear that the expanded system is equivalent, for weak solutions, to the original system. We consider motions with variable as well as constant temperature. In addition, we present equivalent Eulerian equations of motion, which are also symmetric-hyperbolic.

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