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A generalized field method for multiphase transformations using interface fields
The recently developed multiphase field method, describing the interaction between an arbitrary number of individual phase fields with individual characteristics, is reformulated by the use of interface fields. This reformulation allows for the decomposition of the nonlinear multiphase field interactions into pairwise interaction of interface fields. This removes some difficulties in the treatment of triple points or higher order interactions that occurred in the original model. The interface fields being defined in a (((N) over tilde)(2)) dimensional space, where (N) over tilde is the order of the multiple point, can be interpreted being the generalized coordinates fdr this variational problem. The considered example of a multiphase change problem indicates clearly that a relaxation ansatz for the evolution of the field variables towards the minimum of the free energy is warranted only for generalized coordinates, while a relaxation ansatz using functionally dependent variables and the Lagrange formalism in general mixes time and energy scales. (C) 1999 Elsevier Science B.V. All rights reserved.