Novel porous structures with non-cubic symmetry: Synthesis, elastic anisotropy, and fatigue life behavior

Natural porous structures are often anisotropic in their elastic properties, i.e., they have directional variations that are related to their topology and geometry. This paper presents the synthesis and simulation framework of novel families of non-cubic porous structures based on implicit modeling of cosine surfaces in the three-dimensional Euclidean space. The synthesis was performed using Field-Driven Design (FDD). An in-depth study of the elastic properties and simulated fatigue compression-compression behavior of a selection of five structures from the orthotropic anisotropy family is presented as case studies exposing the stretching-dominated mechanisms. The apparent properties characterized include Young's modulus (E*), Poisson's ratio (nu*), shear modulus (G*), bulk modulus (K*), and relative density ((rho) over bar). A systematic approach to the characterization of average apparent properties was performed according to the schemes of Voigt, Reuss, and Hill. We show the anisotropic variation of the cosine surface-based porous structures using the Universal Elastic Anisotropy Index (A(U)) and compare it with six well-known triply periodic minimal surface (TPMS) structures by analyzing the stiffness tensor to validate and discuss which individual property (stiffness, rigidity, compressibility) has a higher impact on the final anisotropy value. We also provide a formal curvature analysis, based on the notions of mean (H) and Gaussian (K) curvatures to evidence the ridge-shaped surface in the structures. The proposed porous structures showed advantages when compared to cubic TPMS structures. From the data processing of the five analyzed porous structures, two synthesized structures have A(U)= 0.394 and 0.478, which are lower values than the structures based on Neovius and Schwarz's Primitive surfaces with A(U) = 0.529 and 0.604. In addition, simulation results of cyclic compressive fatigue loading indicate that the fatigue resistance properties of the non-cubic porous structures are higher than the TPMS structures.