Numerical simulations based on phase-field methods are indispensable in order to investigate certain interesting and important phenomena in the evolution of microstructures. Microscopic solid state phase transitions are highly affected by mechanical driving forces and therefore the accurate calculation of the stresses in the transition region is essential. We present methods for stress calculations within the phase-field framework for finite deformations, which satisfy the mechanical jump conditions corresponding to sharp interfaces, although the sharp interface is represented as a volumetric region.
The model allows to calculate phase-inherent stresses and deformations even in regions where many phases coexist. Since the phase-inherent variables are known, appropriate methods including dislocation based approaches can be used for the calculation of the internal variables in the bulk as well as in transition regions. We demonstrate that the model reflects the mechanical configurational forces for phase transitions and present applications to stress-induced martensitic phase transformation processes.