MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

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