A microarchitecture design methodology to achieve extreme isotropic elastic properties of composites based on crystal symmetries

Abstract

The present contribution describes an optimization-based design technique of elastic isotropic periodic microarchitectures with crystal symmetries aiming at the realization of composites with extreme properties. To achieve this goal, three consecutive procedures are followed: i) a series of inverse homogenization problems with symmetry constraints, ii) a correlation analysis between symmetries and effective elastic properties of the attained microarchitectures, and, iii) the pattern resemblance recognition of these topologies and their redesign, by adopting microstructures with two length-scales, through optimized parametric geometries. This paper is devoted to assessing the third procedure because the first two procedures have been evaluated in previous works of the authors, and here they are only summarized.By applying the methodology, two plane group symmetries are assessed to define two families of 2D periodic parameterized microarchitecture. Once the parameters have been optimized, the resulting composites achieve elastic isotropic properties close to the whole range of the theoretically estimated bounds. Particularly, an unprecedented microstructure attaining the theoretical maximum stiffness is reported. Starting from these parameterized topologies, simple, one-length scale and easily manufacturable geometries are defined. One of the so-designed microarchitectures has been manufactured and tested, displaying an effective Poisson's ratio of -0.90 simultaneously with a high shear modulus.

Periodic rhomboidal cells for symmetry-preserving homogenization and isotropic metamaterials

“…On the one hand, obtaining detailed quantitative information on material parameters typically requires employment of sophisticated combinations of analytical and/or computational techniques [11,12,13,14,15]. On the other hand, some qualitative information can be deduced by simple symmetry arguments and this will be the focus of the * Corresponding author present note.…”

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.…”

Elastostatics of star-polygon tile-based architectured planar lattices

“…By combining the merits of adjustable physical properties, low density, and functionality, they have been widely used in many applications spanning from aerospace [4][5][6][7][8] to medicine [9,10]. In recent works, desired macroscale material parameters (e.g., elastic and shear modulus) can be optimally satisfied by performing inverse parameter identification combined with genetic or topology optimization algorithms over lattice unit cell patterns [11][12][13][14][15][16].…”