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MiS Preprint

Derivation of a rod theory for multiphase materials

Maria Giovanna Mora and Stefan Müller


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.

May 3, 2005
May 3, 2005
MSC Codes:
49J45, 74N10, 74K10
martensitic transformation, rod theory, gamma-convergence

Related publications

2007 Repository Open Access
Maria Giovanna Mora and Stefan Müller

Derivation of a rod theory for multiphase materials

In: Calculus of variations and partial differential equations, 28 (2007) 2, pp. 161-178