Inserted: 4 may 2005
Last Updated: 14 oct 2011
Journal: Calc. Var. Partial Differential Equations
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