Topology design of 2D and 3D elastic material microarchitectures with crystal symmetries displaying isotropic properties close to their theoretical limits

Inverse homogenization using the topological derivative

“…where T D C h is defined in (7). Preliminary result of this class of functional together with the topological derivative (20) was presented in , and for a further and detailed analysis and applications of the technique can be found in [Méndez et al, 2017, Podestá et al, 2019, R.Yera et al, 2020, Rossi et al, 2021.…”

Numerical technique for the 3D microarchitecture design of elastic composites inspired by crystal symmetries

“…For a composite with periodic microstructure, the nexus between the symmetry of its microarchitecture material configuration and the symmetry displayed by its effective physical property is given by the Neumann's principle, broadly applied in crystallography, see Nye [13]. Following this principle, Yera et al [2] suggest the adoption of a crystal symmetry assuring the fulfillment of the target effective elastic symmetry. Recalling that the target problem in this work aims at attaining the isotropic symmetry, then, in 2D topologies, the hexagonal crystal system guarantees the attainment of this property.…”

“…6 Microarchitecture design problems to attain composites with isotropic elastic properties close to the theoretical estimated bounds are next solved. Main results of this task have been presented by the authors elsewhere, see Yera et al [2], where the influence of imposing crystal symmetries to attain the desired objective has been evaluated by testing four space groups of the cubic crystal systems for 3D problems. Additional results of similar problems have been reported by Andreassen and Lazarov [26].…”

“…Closely related to this topic, the authors of this paper, see Yera et al [2], have developed a topology design technique for the microarchitecture synthesis of composites where the resulting material configurations at the microscale copy the symmetry of crystals. The design goal is to attain two-phase, stiff and void, composites with periodic microstructures and isotropic effective elastic properties close to the theoretical bounds.…”

“…The authors have analyzed in Yera et al [2] the use of several space groups of the cubic system to attain two-phase microstructures, one of them is void. In those cases, similar to the present work, the target has been the design of isotropic elastic composites whose effective properties are close to the theoretical bounds of Hashin-Shtrikmann.…”