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Fosdick_RL

Research Abstracts Online
January 2009 - March 2010

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University of Minnesota Twin Cities
Institute of Technology
Department of Aerospace Engineering and Mechanics

PI: Roger L. Fosdick, Associate Fellow

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 regularboundary 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.

Group Members

Adair Roberto Aguiar, Department of Structural Engineering, University of Sao Paolo, Sao Paolo, Brazil
Francesco Freddi, Department of Civil Environmental Engineering and Architecture, University of Parma, Parma, Italy
Darren Mason, Department of Mathematics, Albion College, Albion, Michigan
Edmar B. T. Prado, Department of Structural Engineering, University of Sao Paolo, Sao Paolo, Brazilpar
Gianni Royer-Carfagni, Department of Civil Environmental Engineering and Architecture, University of Parma, Parma, Italy