Mathematical Sciences: Analysis of Cavitation

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With this proposal the principal investigator will continue his analysis of mathematical models of certain polymers and metals in order to predict the failure of these materials when external forces are applied. The mathematical models come from the theories of nonlinear elasticity and viscoelasticity, and their analysis involves the study of singular solutions of hyperbolic and elliptic systems and the use of techniques from the calculus of variations. The most common way of testing when a polymer or metal will fail under the influence of an external force is to subject the actual material to loading until it breaks or deforms. This is fine if one is interested only in the gross properties of the material, but if one wants to understand why the material fails at a given load then one must have recourse to mathematical models of the material. In this grant the principal investigator will use advanced mathematics to uncover the mechanisms of failure and fracture in polymers and metals by examining systems of partial differential equations from the theory of viscoelasticity.