The increasing popularity of multiphase-field methods is due to their ability to handle challenges and issues that arise in the modeling of complex multicomponent and multiphase problems. With the use of a multiphase-field method and through the introduction of diffuse interface layers, the prediction of microstructure evolution is efficient without the need for numerically expensive tracking of evolving interfaces such as grain and phase boundaries. This benchmark study contributes to the ongoing refinement of multiphase-field methods, facilitating their broader utilization in simulating complex material behaviors with chemo-elastic coupling [5]. Within this work, a series of chemo-elastic equilibrium stages for Fe-C binary alloys is discussed validating chemical, capillary, and mechanical driving forces separately as well as their combination. Based on the grand potential density [1,3] and the jump condition approach [4] chemical and mechanical driving forces are formulated, respectively. Parabolic functions that incorporate parameters from a Calphad-database are used to approximate the phase-specific Gibbs free energy. The recovered sharp interface solutions in the limit of vanishing diffuse interface thickness provide thermodynamic and mechanical equilibrium conditions. A condition for interfacial equilibrium is given by the Gibbs-Thomson equation [2]. By subjecting the chemo-elastic multiphase-field model to analytical solutions benchmarks are defined and discussed.

REFERENCES
[1] A. Choudhury and B. Nestler, Phys Rev E, Vol. 85 (2), 021602, 2012.
[2] W.C. Johnson and J.I.D. Alexander, J Appl Phys, Vol. 59 (8), 2735–2746, 1986.
[3] M. Plapp, Phys Rev E, Vol. 84 (3), 031601, 2011.
[4] D. Schneider, F. Schwab. E. Schoof, A. Reiter, C. Herrmann, M. Selzer, T. Böhlke and B. Nestler, Comput Mech, Vol. 60 (2), 203–217, 2017.
[5] B. Svendsen, P. Shanthraj and D. Raabe, J Mech and Phys Solids, Vol. 112, 619–636, 2018.