An Algebraic Reparametrization of Phase-Specific Strains in Phase-Field Models for Microstructure Evolution

In a recently published continuum thermodynamic approach to the phase-field method, the order parameter is considered an internal state variable, and the phase-field method is interpreted as an approximation of the corresponding sharp-interface theory. The approach involves phase-specific strains and stresses within the diffuse interface region. In the present contribution, the interpolation relation for the effective strain within the diffuse interface is used to obtain an algebraic reparametrization in which the phase-specific strains and their rates are expressed by the effective strain, the effective strain rate, and the corresponding strain jump and its rate. The reparametrization defines a bijective mapping from the two phase-specific strains to the effective strain and the strain jump and therefore preserves the dimension of the mechanical state space. It modifies the thermodynamic forces conjugate to the selected rates and, consequently, the order-parameter and mechanical contributions to the diffuse-interface dissipation, while the total dissipation remains unchanged. At the same time, the heat conduction equation obtained in the original formulation remains unchanged since the corresponding derivation already uses the phase-specific stresses and strain rates in the mechanical power contribution. The algebraic reparametrization is generalized to the multiphase-field method based on internal state variables.