Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, March 27, 2015
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Finite strain gradient elasticity and its application to modeling material defects and solid-solid phase transformations

Abstract:   Classical theory of (hyper-) elasticity assumes the elastic free energy density to be a frame-invariant function of the deformation gradient. However, higher order gradients of the deformation map become prominent in applications involving martensitic like phase transformations, materials defects, dislocations, cracks, etc. In such cases the elastic free energy density must be extended to include strain gradients and the resulting formulation is a gradient theory of elasticity whose foundations were laid down in the 1960's. However, significant numerical challenges have rendered this problem computationally intractable until recently. We present the first complete three-dimensional numerical solutions to a broad range of boundary value problems for a general theory of finite strain gradient elasticity, and discuss the role of higher-order boundary conditions, length scale effects and the relevance of the framework to problems with solid-solid phase transformations and material defects. This is joint work with Krishna Garikipati and Anton Van der Ven (UCSB).

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Speaker:  Shiva Rudraraju
Institution:  University of Michigan (Mech. Eng.)

Event Organizer:   Peter Miller    millerpd@umich.edu

 

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