Calculus of Variations and Geometric Measure Theory

M. G. Mora - S. Müller

Derivation of a rod theory for multiphase materials

created by mora on 04 May 2005
modified on 14 Oct 2011


Published Paper

Inserted: 4 may 2005
Last Updated: 14 oct 2011

Journal: Calc. Var. Partial Differential Equations
Volume: 28
Number: 2
Pages: 161-178
Year: 2007


A rigorous derivation is given of a rod theory for a multiphase material, starting from three-dimensional nonlinear elasticity. The stored energy density is supposed to be nonnegative and to vanish exactly on a set consisting of two copies of the group of rotations SO(3). The two potential wells correspond to the two crystalline configurations preferred by the material. We find the optimal scaling of the energy in terms of the diameter of the rod and we identify the limit, as the diameter goes to zero, in the sense of Gamma-convergence.

Keywords: Gamma-convergence, dimension reduction, rod theory, martensitic transformation