Project abstract for group fosdickr

Singularities and Constraints in Elastostatics

The nonlinear theory of elasticity is more appropriate for the investigation of coexistent phase phenomena and singular behavior in the mechanics of materials than its linear counterpart. In the nonlinear theory, the governing system of equations can support the possibility of changes of type for certain applications that are not possible in the linear theory. Often, this is associated with the phenomena of instability and bifurcation, which leads to highly localized large deformations. For solids, there are contemporary computational developments, iteration procedures, adaptive methods, and continuation techniques that are already being used successfully in the computation of regular boundary value problems that arise from such nonlinear theories. These researchers are using some of these ideas in their investigations, but the emphasis of this program is on the role of singularities in problems where solutions are not regular. The injectivity of the deformation map is of great concern here. 

A bibliography of this group’s publications acknowledging MSI is attached.