Optimal lattice spring models derived from triangular and tetrahedral meshes

Lattice Spring Models (LSMs) are fast and stable simulation methods based on networks of discrete deformable elements, well-suited for large deformations or topological changes in real-time applications. Considering that the identification of spring network topologies and elastic constants lacks standardization, defining a robust design workflow for LSMs would promote their wider adoption, enabling efficient and green simulations. In this work, the essential requirements to obtain optimal spring distributions for physically consistent LSM were outlined. Intrinsic rigidity, homogeneity, isotropy, and boundary conformity were identified as fundamental conditions for achieving realistic behaviors of deformable lattices. To generate optimal spring networks, the possibilities offered by high-quality unstructured triangular and tetrahedral meshes were explored, since they satisfy all the outlined design requirements. Several topological metrics were defined and applied to clusters of spring network samples, with the aim of comparing different lattice topologies. By discussing the obtained results, a series of useful considerations were pointed out, and many best practices to generate optimal mesh-derived lattice configurations were clearly identified. The optimal LSMs were validated on several case studies, including comparisons to dual FEM models, analyses on anisotropic spring networks, and fracture simulations, thus giving highly encouraging results. The proposed approach based on high-quality unstructured triangular and tetrahedral meshes resulted in a valuable strategy to design physically consistent LSMs.