A D V A N C E D M A T E R I A L S & P R O C E S S E S | M A R C H 2 0 2 3 3 9 1 3 Fig. 4 — Sharp vs. diffuse interface formulations. Shown are schematic representations, each depicting a three-dimensional, dual-phase continuum body, with sub-scale sketches attached to a representative material point at the respective interface. Left: physical interface Γ with local oscillations; middle: idealized sharp interface Γ–; and right: diffuse interface Γ˜, described by the order parameter (phase) field η(X). In each case, a single interface splitting the body into two parts was chosen for visualization simplicity. In general, a network of interfaces with complex topology will have to be considered. Interested in advertising with the ASM International Organization on Shape Memory and Superelastic Technologies? Contact Kelly “KJ” Johanns at kelly.johanns@asminternational.org. establishes a generalization of conventional homogenization, the following question arises: Could any effective property interpolation within the diffuse interface fit into the proposed framework by choosing appropriate weighting functions, and if so, under which microscopic constraints? To this end, the concepts of macroscopic links and domain relations are introduced and applied for conventional homogenization schemes in phase field modeling. Important, yet often subtle, implications of such theoretical considerations on the prediction of microstructure formation and evolution by means of phase field modeling are the focus of discussion in this contribution (Fig. 4). (Γ) (Γ¯) (Γ˜) SMJ HIGHLIGHTS
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