The goal of the phase field method in optimal design is to provide a systematic, robust, and rigorous method for topology optimization problems. It aims at being a generic framework that can be used in a large variety of applications.
It is based on the penalization of the variation of the properties of designs, and its variational approximation (by means of Gamma-convergence). It uses a smooth function, the phase-field, to represent all the materials involved in the device or the system. This approach is similar in spirit to the "diffuse interface" approximations of "sharp interface" models in phases transition (Cahn-Hilliard, Allen-Cahn etc).
In this talk, we will present the generic framework, apply it to the special case of optimal design of pressurized structures, and detail its numerical implementation.
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