On a two-scale phasefield model for topology optimization

In this article, we consider a gradient flow stemming from a problem in two-scale topology optimization. We use the phase-field method, where a Ginzburg–Landau term with obstacle potential is added to the cost functional, which contains the usual compliance but also an additional contribution including a local volume constraint in a penalty term. The minimization of such an energy by its gradient-flow is analyzed in this paper. We use an regularization and discretization of the associated state-variable to show the existence of weak solutions to the considered system.