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Skin modeling is an ongoing research area that highly benefits from modernparallel algorithms. This article aims at applying shape optimization tocompute cell size and arrangement for elastic energy minimization of a cellularcomposite material model for the upper layer of the human skin. Agradient-penalized shape optimization algorithm is employed and tested on thedistributed-memory cluster Hazel Hen, HLRS, Germany. The performance of thealgorithm is studied in two benchmark tests. First, cell structures areoptimized with respect to purely geometric aspects. The model is then extendedsuch that the composite is optimized to withstand applied deformations. In bothsettings, the algorithm is investigated in terms of weak and strongscalability. The results for the geometric test reflect Kelvin's conjecturethat the optimal space-filling design of cells with minimal surface is given bytetrakaidecahedrons. The PDE-constrained test case is chosen in order todemonstrate the influence of the deformation gradient penalization on fineinter-cellular channels in the composite and its influence on the multigridconvergence. A scaling study is presented for up to 12,288 cores and 3 billionDoFs.

Parallel 3d shape optimization for cellular composites on large distributed-memory clusters