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arXiv · 2307.03471

Phase-field topology optimization with periodic microstructure

Stefano Almi·Ulisse Stefanelli
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Abstract

Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined design of the macroscopic mechanical piece and its underlying microstructure. In this context, we investigate a topology optimization problem for an elastic medium featuring a periodic microstructure. The optimization problem is variationally formulated as a bilevel minimization of phase-field type. By resorting to Gamma-convergence techniques, we characterize the homogenized problem and investigate the corresponding sharp-interface limit. First-order optimality conditions are derived, both at the homogenized phase-field and at the sharp-interface level.

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Stefano Almi, Ulisse Stefanelli. 2023-07-07. Phase-field topology optimization with periodic microstructure. https://arxiv.org/abs/2307.03471

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