anisotropic elasticity

For a given class of materials, universal deformations are those that can be maintained in the absence of body forces by applying only boundary tractions.  Universal deformations play a crucial role in nonlinear elasticity. To date, their classification has been accomplished for homogeneous isotropic solids following Ericksen's seminal work, and  homogeneous anisotropic solids and inhomogeneous isotropic solids in our recent works. In this paper we study universal deformations for inhomogeneous anisotropic solids defined as materials whose energy function depends on position.

Universal deformations of an elastic solid are deformations that can be achieved for all possible strain-energy density functions and suitable boundary conditions. They play a central role in nonlinear elasticity and their classification has been mostly accomplished for isotropic solids following Ericksen's seminal work. Here, we address the same problem for transversely isotropic, orthotropic, and monoclinic solids.

In this paper in the Journal of the Mechanics and Physics of Solids (vol. 84, p. 358, 

http://authors.elsevier.com/a/1Rk5057Zjdx-o ) we propose a
new theory for the mechanical properties of fivefold twinned nanowires.

We show that the Frank vector of the central wedge disclination depends on the uniaxial strain,

Jim Barber and I just got accepted this paper in JMPS, and it is also already available on Arxiv.  We found a remarkably simple closed form solution for adhesion on orthotropic materials in the planes of symmetry.  This shows adhesion can increase significantly due to anisotropy, namely the JKR solution continues to hold in the sense of mean elastic modulus, but the prefactor can grow without limit. We expect applications in crystals indentation, but also in locomotion in biological world.

We have read some papers of stroh formalism and the textbook of Tom Ting, and found that the stroh formalism and the hamilton system proposed by prof.zhong wanxie had some relation. We want to know whether the stroh formalism is enough for the analysis of the anisotropic elastic? Thus's to say, for some problems could not  give the satisfied answer which we may try the hamilton framework. I briefly compare the two methods as follows:

Tom Ting and I have recently developed a method of extending Stroh's anisotropic formalism to problems in three dimensions. The unproofed paper can be accessed at http://www-personal.umich.edu/~jbarber/Stroh.pdf .