Phase Field Method

A phase-field model is based on the phase-transition theory in the fields of mechanics and material sciences. The topology optimization is formulated as a continuous problem with the phase-field as design variables within a fixed reference domain. All regions are described in terms of the phase field which makes no distinction between the solid, void and their interface. The Van der Waals-Cahn-Hilliard theory is applied to define the variational topology optimization as a dynamic process of phase transition. The Gamma-convergence theory is then adapted for an approximate solution to this free-discontinuity problem. As a result, a numerical procedure is developed which treats the whole design domain simultaneously without any explicit tracking of the interface.

Phase Field For Two Material Phases

Phase Field For Three Material Phases

Nonlinear Diffusions

Cahn-Hilliard Model for Optimization of Structure Topology (OST)

We proposed a new Cahn-Hilliard model for the optimization of multi-materials structure topology. The minimization of the elastic energy or mean compliance is regarded as an important external driving force pushing the different phases to its optimal position to make the structure stiffest. At the same time, the minimization of the bulk energy and interface energy acts as an inner mechanics to separate distinct material from original disorder state and to transform materials among different phases. Although disturbing item is added, the generalized Cahn-Hilliard equations are still mass conservative in all time and are energy dissipate. All kinds of Cahn-Hilliard equations are resolved by a powerful Multigrid algorithm.

Quadternary Cahn-Hilliard Equations without Elasticity

Binary C-H Model for OST

Ternary C-H Model for OST

Quadternary C-H Model for OST