Rate-independent phase transitions in elastic materials: A Young-measure approach

Magnetic color symmetry of lattice rotations in a diamagnetic material.

Oxygen octahedral rotations are the most common phase transitions in perovskite crystal structures. Here we show that the color symmetry of such pure elastic distortions is isomorphic to magnetic point groups, which allows their probing through distinguishing polar versus magnetic symmetry. We demonstrate this isomorphism using nonlinear optical probing of the octahedral rotational transition i...

Phase Field Modeling of Fracture and Composite Materials

The phase field method is a very powerful numerical method to solve moving boundary problems. Here we demonstrate how it can be applied to various processes involving sound propagation and fracture. This approach is related to a new theory of fracture which describes in particular the fast growth of cracks. We study the propagation of elastic waves, the determination of stress intensity factors...

Peierls-Nabarro landscape for martensitic phase transitions

We propose a simple one-dimensional model which can be used to reconstruct the Peierls-Nabarro energy landscape and compute the limits of lattice trapping for martensitic phase transitions. The model represents a nontrivial analog of the discrete Frenkel-Kontorova model. We find the explicit expression for the critical driving force which sets phase boundaries in motion and delimits the width o...

Dynamics of Phase Transitions and Hysteresis in a Viscoelastic Ericksen’s Bar on an Elastic Foundation

This work is a follow-up on the study [32] of interface dynamics and hysteresis in materials undergoing solid-solid phase transitions. We consider the dynamics of a viscoelastic bar with a nonmonotone stress-strain relation and viscous stress linearly proportional to the strain rate. The bar is placed on an elastic foundation with stiffness β mimicking the interaction of phases in higher dimens...

Phase transitions of elastic solid materials