We present an effective mechanical equilibrium solution algorithm suitable for finite strain consideration within the phase-field method. The proposed algorithm utilizes a Fourier space solution in its core. The performance of the proposed algorithm is demonstrated using the St. Venant–Kirchhoff hyperelastic model, but the algorithm is also applicable to other hyperelastic models. The use of the fast Fourier transformation routines and fast convergence within several iterations for most common simulation scenarios makes the proposed algorithm suitable for phase-field simulations of rapidly evolving microstructures. Additionally, the proposed algorithm allows using different strain measures depending on the requirements of the underlying problem. The algorithm is implemented in the OpenPhase phase-field simulation library. A set of example simulations ranging from simple geometries to complex microstructures is presented. The effect of different externally applied mechanical boundary conditions and internal forces is also demonstrated. The proposed algorithm can be considered a straightforward update to already existing small strain solvers based on Fourier space solutions.

The complex interplay between the rapid martensitic transformation and the plastic relaxation during martensitic transformation in low-carbon steel is investigated using a combined phase-field and phenomenological crystal plasticity approach. The large transformation-induced deformations and local lattice rotations are rigorously described within the finite strain framework. The study reveals that plastic relaxation plays a crucial role in accommodating the transformation-induced deformations of martensite in the parent austenite phase. By systematically varying the plastic slip rate, imposed cooling rate, and carbon content, the simulations provide insights into the interdependence between these factors, contributing to a better understanding of the martensitic transformation process and the resulting microstructures. The phenomenological crystal plasticity model effectively relates the plastic relaxation rate to the rate of martensitic transformation with a significant time scale difference between the two processes. The findings contribute to a deeper understanding of the interplay between the rapid martensitic transformation and the requirement for plastic deformation.

Recent breakthroughs resolving open questions in materials science by phase-field simulations are reported. They relate to solidification structure formation in additive manufacturing, carbon redistribution during bainitic transformation, and the onset of damage during high-temperature creep of superalloys. The first example deals with the balance between epitaxial growth and nucleation in solidification. The second relates to the controversy regarding diffusion control and dominance of massive transformation in bainite transformation. The third relates to directional coarsening (rafting) in superalloys as a diffusion-controlled phase transformation: loss of coherency of precipitates marks the onset of damage associated with rotation of the crystal lattice and topological inversion. Technical details of the phase-field method are reviewed as necessary, and limitations of the approach are discussed. Graphical