Voltage-dependent modulation of elastic moduli in lattice metamaterials: Emergence of a programmable state-transition capability

Abstract

Two-dimensional lattices are ideal candidate for developing artificially engineered materials and structures across different length-scales, leading to unprecedented multi-functional mechanical properties which can not be achieved in naturally occurring materials and systems. Characterization of effective elastic properties of these lattices is essential for their adoption as structural elements of various devices and systems. An enormous amount of research has been conducted on different geometry of lattices to identify and characterize various parameters which affect the elastic properties. However, till date we can not control the elastic properties actively for a lattice microstructure, meaning that the elastic properties of such lattices are not truly programmable. All the parameters that control the effective elastic properties are passive in nature. After manufacturing the lattice structure with a certain set of geometric or material-based parameters, there is no room to modulate the properties further. In this article, we propose a hybrid lattice micro-structure by integrating piezo-electric materials with the members of the lattice for active voltage-dependent modulation of elastic properties. A bottom-up multi-physics based analytical framework leading to closed-form formulae is derived for hexagonal lattices to demonstrate the concept of active lattices. It is noticed that the Young’s moduli are voltage-dependent, while the shear modulus and the Poisson’s ratios are not functions of the applied voltage. Thus, the compound mechanics of deformation induced by external mechanical stresses and electric field lead to an active control over the Young’s moduli as a function of voltage. Interestingly, it turns out that a programmable state-transition of the Young’s moduli from positive to negative values with a wide range can be achieved in such hybrid lattices. The physics-based analytical framework for active modulation of voltage-dependent elastic properties on the basis of operational demands provide the necessary physical insights and confidence for potential practical exploitation of the proposed concept in various futuristic multi-functional structural systems and devices across different length-scales.