Small strain multiphase-field model accounting for configurational forces and mechanical jump conditions

Computational models based on the phase-field method have become an essential tool in material science and physics in order to investigate materials with complex microstructures. The models typically operate on a mesoscopic length scale resolving structural changes of the material and provide valuable information about the evolution of microstructures and mechanical property relations. For many interesting and important phenomena, such as martensitic phase transformation, mechanical driving forces play an important role in the evolution of microstructures. In order to investigate such physical processes, an accurate calculation of the stresses and the strain energy in the transition region is indispensable. We recall a multiphase-field elasticity model based on the force balance and the Hadamard jump condition at the interface. We show the quantitative characteristics of the model by comparing the stresses, strains and configurational forces with theoretical predictions in two-phase cases and with results from sharp interface calculations in a multiphase case. As an application, we choose the martensitic phase transformation process in multigrain systems and demonstrate the influence of the local homogenization scheme within the transition regions on the resulting microstructures.