Bending dominated response of layered mechanical metamaterials alternating pentamode lattices and confinement plates

Abstract

A numerical study on the elastic response of single-and multi-layer systems formed by alternating pentamode lattices and stiffening plates is presented. Finite element simulations are conducted to analyze the dependence of the effective elastic moduli of such structures upon suitable aspect ratios, which characterize the geometry of the generic pentamode layer at the micro-and macro-scale, and the lamination scheme of the layered structure. The given numerical results highlight that the examined structures exhibit bending-dominated response, and are able to achieve low values of the effective shear modulus and, contemporarily, high values of the effective compression modulus. We are lead to conclude that confined pentamode lattices can be regarded as novel metamaterials that are well suited for seismic isolation and impact protection purposes. Their elastic response can be finely tuned by playing with several geometrical and mechanical design variables.

On the Computational Design of Innovative Seismic Isolation Devices Based on Lattice Materials

“…At the same time, such systems exhibit low (or theoretically zero) stiffness against shear and torsion loads. This kind of response is similar to that exhibited by elastomeric bearings commonly employed as structural supports of buildings and bridge structures [16], and suggests the use of layered pentamode structures as novel seismic isolation devices [10], [13].…”

“…In both such systems, high values of the effective compression modulus can be achieved due to the confinement of the deformation of the soft (pentamode/rubber) layers that is offered by the stiffening plates. The compression modulus of a sfcc PMB is inversely proportional to the lattice thickness [13], and one easily recognizes that the role played by the thickness of the rubber pads in rubber bearings is replaced by the area of the cross-sections of the lattice rods in a PMB (cf. Sect.…”

“…The bending dominated regime of PMBs equipped with rigid connections has been studied in a series of studies, which have examined the experimental response of additively manufactured reduced-scale samples made of a titanium alloy [26], and the simulated response of numerical models of PMBs for varying aspect rations and lamination schemes [11] [12]. The PMBs examined hereafter have the geometry illustrated in Figure 2 and are composed of rods featuring a tapered, bi-conical shape with large diameter D at the mid-span and small diameter d at the extremities [26], [30].…”

“…For critical structures, like power plants, solutions of devices with isolation capabilities in both horizontal and vertical directions are still under development. The literature results reviewed by the present study highlight that PMBs can be designed to behave as tension-capable and performance-based isolation devices, whose properties mainly depend on the geometry of the members forming the unit cell of the lattice, the nature of the connections joining the strut one another, and the struts and the stiffening plates, as well as the mechanical properties and sizes of the component materials [9], [10], [12], [13]. The response of such devices can be easily adjusted to that of the structure to be protected, and their fabrication does not necessarily require heavy industry, and expensive materials, being possible with ordinary 3-D printers.…”

“…A novel feature of layered structures formed by pentamode lattices and stiffening plates, hereafter referred to as "pentamode bearings" (PMBs), has been recently recognized in the literature, through the discovery that such systems exhibit a three-mode response characterized by stiff response against vertical compression and bending modes, and soft response in shear and torsion [9], [10], [11], [12], [13], [14]. It is known that unconfined pentamode lattices exhibit (theoretically) zero stiffness against compression loads in the stretch-dominated limit [2], [3].…”