Modeling a triclinic lattice elastic body based on the linear couple stress theory

Abstract

Triclinic lattice structures with generalized parallelepiped unit cells are crucial targets in understanding the influence of lattice structure on the mechanical behaviors of lattice elastic bodies. This study models a three-dimensional elastic body with a triclinic lattice microstructure comprising three uniform elastic members rigidly joined at a single point. Based on the linear couple stress theory, a specialized case of the Cosserat theory, this study derives elasticity tensors in the constitutive equations of the triclinic lattice elastic body that depend on the crossing angles between the members. To derive the angular-dependent elasticity tensors, coordinate transformations between oblique and orthogonal coordinate systems are effectively employed in formulating the substitution of deformation and force fields in the continuum for the fields in the lattice structure. Evaluating the elasticity tensors reveals the influences of the crossing angles on the anisotropic tensile and torsional properties, the existence of the angle-covariant lattice number manipulation that cancels out the size effect, and several types of geometrical shape dependence. This study could contribute to the theoretical evaluation of elastic behaviors of both artificially engineered and naturally formed materials with lattice microstructures.