MODELING HETEROGENEOUS MARTENSITIC WIRES

Abstract

We give a direct derivation of a theory of martensitic heterogeneous wires in the zero thickness and homogenization limit via a convergence result. We start from three-dimensional nonlinear hyperelasticity theory augmented by a term of interfacial energy of the van der Waals type. The derivation involves no a priori choice of asymptotic expansion or Ansatz. It yields a wire theory with two Cosserat vector fields. A formal derivation is given of higher theories for homogeneous wires, which yields one corrector for the deformation of the central line and two correctors for the Cosserat vector fields. Finally, we present a few numerical results.