In this paper, we give a review of the state of the art in the study of mechanical metamaterials. The very attractive property of having a microstructure capable of determining exotic and specifically tailored macroscopic behaviour makes the study of metamaterials a field that is actually in expansion, from both a theoretical and a technological point of view. This work is divided into two sections, describing the phenomenological and theoretical aspects of metamaterials. We first give an overview of some existing metamaterials, such as pentamode materials, auxetic materials, materials with negative mechanical constitutive coefficients and materials with enhanced mechanical properties. We also focus on some emerging areas, such as origami. Then, we present some theoretical studies in the field of mechanical metamaterials, such as those related to first- and second-gradient theories.

In this paper we present a model in which the motions of two families of beams constituting a pantographic sheet, when described with two independent placement fields, allows to correctly simulate the points of fracture onset in axial tension test. The deformation energy is postulated in function of these independent displacements as involving an additive quadratic term of deformation energy depending on the squared norm of their difference. The first performed numerical simulations establish that the most strained pivots are exactly the ones where one observes the first rupture

In the present work, we obtain a dispersion relation for Rayleigh–Lamb wave propagation in a plate of thermoelastic material. For this aim, we consider the theory of generalized thermoelasticity with one relaxation time. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be isothermal and free from stresses. We obtain the analytical solution for the temperature, displacement components, and stresses using an eigenvalue approach. Finally, we derive a dispersion relation for the plate in closed form taking into account isothermal boundary conditions for wave mode propagation. To obtain the phase velocity and attenuation coefficients of propagating wave mode, we use the function iteration numerical scheme to solve the complex dispersion relation. The phase velocity and attenuation coefficients for the first five modes of waves are represented graphically for Lord–Shulman and classical coupled dynamical theories.