Macro–micro modeling for coupled elasto–creep and thermal analyses under sintering

Macro–micro modeling is proposed as a new method of sintering analysis for quantitative evaluation of geometric changes in green and brown materials together with precise prediction of their microscopic shrinkage in sintering. Variational principles in the elasto creep frame are utilized to make formulations both for macro and micro models and to simulate time history of geometric configuration, creep strains and stresses by time incremental procedure. Another macro–micro modeling for heat transfer problem is formulated for coupling with the elasto–creep model to consider the effect of heat transfer under the sintering process. Several numerical examples are employed to verify the validity and effectiveness of the present method.