分野別セミナー

Wedge disclinations are rotational mismatches at the level of a crystal lattice observed in classes of Shape-Memory Alloys undergoing the austenite-to-martensite transformation and in crystal plasticity. First, I will describe an atomistic-to-continuum modeling approach based on an energy functional defined over a triangular lattice accounting for nearest-neighbor interactions. We design special rotational-type boundary value problems on the lattice so that the minimizers necessarily exhibit non-homogeneous rotations. We are interested in the asymptotics of the energy minima and minimizers, as the lattice spacing vanishes, which we compute exactly with Gamma-convergence. We perform numerical calculations for the discrete model and show that both the shape of the solutions as well as the values of the energies are in agreement with classical results for positive and negative disclinations. In the second part of the talk, I will show some numerical computations based on a crystal (micro-) plasticity model which are examples of complex plastification rich in disclinations.