Using Poincaré half-plane to understand Crystal Elasto-Plasticity

Paolo Biscari
Dipartimento di Fisica, Politecnico di Milano


Symmetry plays a key role in establishing the mechanical response of crystalline materials. These materials exhibit a number of peculiar features, including solid-solid phase transitions in shape memory alloys, dislocation nucleation and evolution, and critical response over several orders of magnitude. In this lecture we review how the information encoded in the lattice symmetry can be transferred to continuum models. We also show how and why the Poincaré half-plane provides a natural framework to study 2D crystal elasto-plasticity.