linear elasticity

In linear elasticity, universal displacements for a given symmetry class are those displacements that can be maintained by only applying boundary tractions (no body forces) and for arbitrary elastic constants in the symmetry class. In a previous work, we showed that  the larger the symmetry group, the larger the space of universal displacements. Here, we generalize these ideas to the case of anelasticity. In linear anelasticity, the total strain is additively decomposed into elastic strain and anelastic strain, often referred to as an eigenstrain.

Universal displacements are those displacements that can be maintained, in the absence of body forces, by applying only boundary tractions  for any material in a given class of materials. Therefore, equilibrium equations must be satisfied for arbitrary elastic moduli for a given anisotropy class. These conditions can be expressed as a set of partial differential equations for the displacement field that we call universality constraints.

In nonlinear elasticity, universal deformations are the deformations that exist for arbitrary strain-energy density functions and suitable tractions at the boundaries. Here, we discuss the equivalent problem for linear elasticity. We characterize the universal displacements of  linear elasticity: those displacement fields that can be maintained by applying boundary tractions in the absence of body forces for any linear elastic solid in a given anisotropy class.

I am a professor in the Department of Mechanical Engineering at the University of Alberta, Edmonton, Alberta, Canada. I am looking for a PhD student to work in the area of applied mathematics, specifically in solid mechanics (linear elasticity, complex variable methods, boundary integral equation methods) with a possible start date of Sept 2012 or jan 2013.

You can find out more details at:

www.mece.ualberta.ca/~schiavone/schiavon.htm

 
(to appear in the Intl. Journal of Engineering Science)

 Robin J. Knops and Amit Acharya

 The relationship between dislocation theory and the difference of linear elastic solutions for two different sets of elastic moduli, derived by Filon in two-dimensions, is generalised to three-dimensions. Essential features are developed and illustrated by the  examples of the edge and screw dislocations. The inhomogeneity  problem is  discussed within the same context and related to Somigliana dislocations, and  in the limit  to the interstitial atom.