Surrogate models of stress for triply periodic minimal surface lattices

This work formulates compact and efficient surrogates of the stress field for sheet-network, triply periodic minimal surface (TPMS) lattices, which have been gaining popularity due to advancements in additive manufacturing methods. The proposed surrogates can be employed to determine, for example, the largest von Mises or principal stresses in a TPMS lattice as a function of the wall thickness, base material properties, and applied tractions. Therefore, they can be used for the multi-scale analysis and design of porous macro structures made of TPMS lattices with regard to stress-driven criteria. The surrogates circumvent the need to mesh the lattice surface and instead allow the mechanical analysis of the macro structure to be performed using solid finite elements. The construction of the stress surrogates exploits the geometric structure of the TPMS, namely the fact that the unit cell consists of geometric transformations of a single fundamental unit. It is proven that it is only necessary to obtain surrogates for one fundamental unit to compute the stress field for the entire unit cell. Surrogates are developed for multiple types of TPMS lattices. A comparison of the stresses obtained using the surrogates with those obtained using a body-fitted mesh of a compression test specimen made of a TPMS and to published values of strength is presented for validation. To demonstrate the usefulness of the proposed surrogates, they are applied to the stress prediction of a cantilever beam made of a uniform-thickness TPMS and a simply supported beam made of a variable-thickness TPMS. An open-source code that implements the surrogates is made publicly available.