Mechanical coupling and tuned anisotropic elasticity: Numerical and experimental material design for shear-normal and shear-shear interactions

Abstract

Mechanical coupling in architectured materials has been traditionally investigated in the context of generalized continuum mechanics and is often assumed to be non-existent in the framework of classical continuum mechanics. In this paper, we challenge this misconception and study an anisotropic architectured material exhibiting shear-shear and shear-normal coupling from the standpoint of classical continuum mechanics. The material is non-regular tetrahedron lattice, a potential candidate for biomedical implants, but the lack of understanding about its anisotropic behavior and mechanical couplings has limited its application. We exploited the unit-cell definition with periodic boundary conditions and performed elastic and elastoplastic homogenizations. Non-zero coupling sub-matrices appeared in the homogenized elasticity matrix, which we further transformed into material’s natural coordinate system using elastic distance function. This allowed for anisotropy identification and determination of all the coupling parameters. Next, compression tests are conducted on laser powder bed fused Al-12Si (mass%) lattice samples with different relative densities and spatial orientations. Employing test data, mechanical anisotropy and shear-normal couplings are experimentally characterized. Both numerical and experimental results confirmed the presence of mechanical couplings and predicted a similar anisotropic tendency in the material. Finally, the role of manufacturing defects in deterioration of as-designed mechanical properties is discussed.