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 ap-
proach involves phase-specific strains and stresses within the diffuse interface region. In
the present contribution, the interpolation relation for the effective strain within the dif-
fuse 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 map-
ping 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 thermody-
namic 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
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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.