A Continuum-on-Atomistic Framework with Bi-Stable Elements for the Computation of Minimum Free Energy Paths

The exploration of non-convex energy landscapes, as arising in phase transitions, is an important task in solid state mechanics. An often employed system in the literature for the study of phase transitions in deformable solids denotes the elastic bar with a non-monotone stress-strain curve. This setting is chosen and modelled by a continuum-on-atomistic model (molecular dynamics coupled with the finite element method). The rod’s material denotes a copper single crystal and undergoes a model phase transition. The resulting non-convex energy landscape is explored by the string method in collective variables. The string method allows for the computation of energy barriers between local minima and to identify minimum free energy paths. The novelty of the present work is the combination of a continuum-on-atomistic method with the string method applied to a problem in mechanics. Numerical examples demonstrate the performance of the numerical model.