GPU-Accelerated Reissner--Mindlin Homogenization for Shellular Unit Cells from Implicit Geometry

We present a GPU-accelerated homogenization method for shellular unit cells whose wall thickness is small but mechanically non-negligible. Our method adopts a Reissner-Mindlin shell model formulated with tangential differential calculus and an unfitted TraceFEM discretization, allowing shell mechanics to be evaluated directly on implicit midsurfaces without constructing conforming surface or volumetric meshes. Building on this adopted shell discretization, we formulate periodic cell problems for computing effective elastic tensors of shellular materials and implement the full pipeline on the GPU. We further provide a backward sensitivity pipeline that supports inverse design of shellular structures using the proposed homogenization formulation. Across analytic and SDF-based unit cells, our implementation evaluates homogenized elastic responses in ~ 50 ms per query while achieving less than 7% error relative to volumetric finite-element baselines. These results make Reissner-Mindlin-shell-based homogenization practical for interactive exploration and rapid optimization of shellular metamaterials.