Theoretical limits for negative elastic moduli in subacoustic lattice materials

An insightful mechanics-based bottom-up framework is developed for probing the frequency dependence of lattice material microstructures. Under a vibrating condition, effective elastic moduli of such microstructured materials can become negative for certain frequency values, leading to an unusual mechanical behavior with a multitude of potential applications. We have derived the fundamental theoretical limits for the minimum frequency, beyond which the negative effective moduli of the materials could be obtained. An efficient dynamic stiffness matrix based approach is developed to obtain the closed-form limits, which can exactly capture the subwavelength scale dynamics. The limits turn out to be a fundamental property of the lattice materials and depend on certain material and geometric parameters of the lattice in a unique manner. An explicit characterization of the theoretical limits of negative elastic moduli along with adequate physical insights would accelerate the process of its potential exploitation in various engineered materials and structural systems under dynamic regime across the length scales.