Tailorable thermoelasticity of cubic lattice-based cellular and granular materials by prestress

Abstract

When a cubic lattice packaged by a boundary layer is subjected to a mechanical and temperature load, the force and length change of the bonds are equivalently evaluated by the average stress and strain of the unit cell. Provided a displacement gradient variation at a certain stress state, the variation of stress related to the strain variation provides the effective stiffness of the material at the corresponding configuration. It is discovered that the effective elasticity and thermal expansion coefficient can be tailored by the prestress through the boundary layer, which generates a configurational stress. Because the bonds of a cubic lattice depend on the material types, we consider the harmonic potential of springs for cellular lattices and Hertz's contact potential of balls for granular lattices, respectively. The cubic symmetry of effective elasticity is demonstrated for the three types of cubic lattices. By taking the orientational average, isotropic elastic constants can be obtained for randomly oriented lattices. As the bond length changes with the prestress of the boundary layer and controls the thermoelastic behavior, a novel design method of lattice-based materials confined in a spherical shell is demonstrated to achieve zero thermal expansion and a positive temperature derivative of elasticity.