Meta-modeling of Lattice Mechanical Responses via Design of Experiments

In the context of lattice manufacturing, the problem of mechanical and structural characterization of large lattice domains is relevant. Lattice materials are used in engineering (e.g. in energy absorption and heat conduction) and biomedical (e.g. bone implants and artificial tissues) applications. However, the numerical simulation of large lattice domains is limited by its complicated geometry, which hinders the meshing stage and produces intractable finite element meshes. The existing efforts to simulate large lattice domains are based on the generation of simplified homogeneous domains equipped with material properties that approximate the behavior of the lattice domain equipped with the bulk material. Using this approach, one can estimate the displacements field over the lattice domain using a lighter mesh and a cheaper simulation. However, since stresses are influenced by geometrical conditions, the stresses of the simplified domain do not match the stresses of the lattice domain. As a response to this limitation, this article proposes a methodology based on the systematic use of design of experiments to devise meta-models to estimate the mechanical response of lattice domains. The devised meta-models can be integrated with material homogenization to allow the mechanical characterization of large lattice domains. In this paper, we apply the proposed methodology to develop meta-models for the estimation of the von Mises stress in Schwarz Primitive lattice domains. Results show that the proposed methodology is able to generate efficient and accurate meta-models whose inputs are based on the displacements on the boundary of the Schwarz cell. Therefore, numerical simulations with the homogeneous simplified domain can be used to feed the meta-models. Additional work is still required to integrate the developed meta-models with material homogenization to test large Schwarz Primitive lattice domains under working loads.