Boundary evolution-driven lightweight design of functional core materials

Abstract To address the configuration optimisation and interface representation of lightweight functional core materials under multiaxial loading, this study proposes a threshold-shift boundary evolution (TSBE) method. In this method, material distribution is described by a continuous topological potential field, and the boundary between the material domain and the void domain is updated algebraically through threshold shifting under a prescribed volume constraint. To improve the accuracy of interface representation on low-density meshes, subgrid sampling integration is introduced, whereby the material fraction within each element is mapped to equivalent physical parameters. This enables sub-element-scale representation without increasing the number of finite element degrees of freedom. Combined with an energy homogenisation method, the proposed approach is validated using two- and three-dimensional extremal-performance unit cells and functional sandwich cores. The results show that the optimised configurations are structurally stable and that the functional core examples exhibit clear evolutionary patterns, providing methodological support for the design of lightweight core materials under multiaxial loading.