Introduction to mechanical metamaterials and their effective properties

Metamaterials are rationally designed composites made of building blocks which are composed of one or more constituent materials. Metamaterial properties can go beyond those of the ingredient materials, both qualitatively and quantitatively. In addition, their properties can be mapped on some generalized continuum model. We present the general procedure of designing elastic metamaterials based on masses and springs. We show that using this simple approach we can design any set of effective properties including linear elastic metamaterials,—defined by bulk modulus, shear modulus, mass density—and nonlinear metamaterials,—with instabilities or programmable parts. We present designs and corresponding numerical calculations to illustrate their constitutive behavior. Finally, we discuss the addition of a thermal stimulus to mechanical metamaterials.