Analytical solutions for equivalent elastic compliance of cubic lattice structures subjected to hypergravity conditions

Abstract

In order to comprehensively understand the mechanical behavior of biological entities and aerospace applications subjected to hypergravity environments, we delve into the impact of hypergravity on the equivalent compliance of cubic lattice structures. Capitalizing on the periodic spatial distribution, we employ a unit cell methodology to deduce the homogenized stress-strain relationship for the lattice structures, subsequently obtaining the associated equivalent compliance. The equivalent compliance can be conveniently reduced to instances without hypergravity influence. Furthermore, numerical simulations are executed to validate the derivations and to illustrate that hypergravity indeed affects the mechanical properties of lattice structures. We introduce a non-dimensional hypergravity factor, which quantifies the impact of hypergravity magnitude relative to the Young’s modulus of the base material. Our findings reveal that the hypergravity factor influences perpendicular compliance quadratically and parallel compliance linearly. Simultaneously, the perpendicular shear compliance remains unaffected, whereas the parallel shear compliance experiences an inverse effect. Additionally, the lattice structure transforms into a gradient material oriented in the hypergravity direction, consequently generating a scale effect.