Mathematical Sciences: Symmetry Methods and Nonlinear Analysis in Elastomechanics

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The investigator will study differential equations with symmetry and applications to solid mechanics. The applications involve geometrically exact formulations of nonlinearly elastic and viscoelastic solids and structures. The goals of the work are to detect new phenomena and to further develop and exploit the connection between symmetry and nodal properties of solutions of elliptic equations, particularly in the context of global bifurcation and continuation problems. The way that structures bend can be described mathematically as the solution of equations describing the structure. Often the bending depends on a parameter, for instance the load on the structure, If as the load varies the structure can bend in different ways for the same load, then the solutions are said to bifurcate at that value of the load. Global descriptions of the bifurcations are generally hard to get, but are very valuable. When the structure is symmetric, those symmetries can be used to get a better grip on the global behavior. Applications arise not only in analysing structures but also in studying the behavior of materials themselves.