Pantographic metamaterials: an example of mathematically driven design and of its technological challenges Abstract In this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investiga-tions. The problem to be solved was stated as follows: determine the material (micro)structure governed by those equations that specify a desired behavior. Addressing this problem has led to the synthesis of second gradient materials. In the second stage, it has been necessary to develop numerical integration schemes andDipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma "La Sapienza.", Via Eudossiana 18, 00184 Rome, Italy E-mail: barchiesiemilio@gmail.com the corresponding codes for solving, in physically relevant cases, the chosen equations. Finally, it has been necessary to physically construct the theoretically synthesized microstructures. This has been possible by means of the recent developments in rapid prototyping technologies, which allow for the fabrication of some complex (micro)structures considered, up to now, to be simply some mathematical dreams. We show here a panorama of the results of our efforts (1) in designing pantographic metamaterials, (2) technology of rapid prototyping, and (3) in the mechanical testing of many real prototypes. Among the key findings that have been obtained, there are the following ones: pantographic metamaterials (1) undergo very large deformations while remaining in the elastic regime, (2) are very tough in resisting to damage phenomena, (3) exhibit robust macroscopic mechanical behavior with respect to minor changes in their microstructure and micromechanical properties, (4) have superior strength to weight ratio, (5) have predictable damage behavior, and (6) possess physical properties that are critically dictated by their geometry at the microlevel.

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 dell’Isola et al. (Zeitschrift für Angewandte Math und Physik 66(6):3473–3498, 2015, Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016), the concept of pantographic sheet is proposed. The aim is to design a metamaterial showing: (i) a large range of elastic response; (ii) an extreme toughness in extensional deformation; (iii) a convenient ratio between toughness and weight. However, these required properties must coexist with non-detrimental mechanical characteristics in the presence of other kinds of imposed displacements. The aim of this paper is to prove via numerical simulations that pantographic sheets may effectively resist to coupled bending and extensional deformations. The four-parameter model introduced shows its versatility as it is able to encompass all the considered types of (large) deformations. The numerical integration scheme which we use is based on the same concepts exploited in Turco et al. (Zeitschrift für Angewandte Math und Physik 67(4):1–28, 2016): They prove that the Hencky-type discretization is very efficient also in nonlinear large deformations and large displacements regimes. In Part II of this paper, we will show that the used models are very effective to describe experimental evidence

No abstract

The confined explosion of an annular layered charge composed of a phlegmatized RDX (RDXph) core and an external layer consisting of aluminum powder (Al) or a mixture of ammonium perchlorate (AP) and Al was studied. Experiments were carried out in fully and partially closed structures, i.e., in the explosion chamber of 150 dm3 in volume and in the 40 m3 volume bunker with four small holes and a doorway. Two types of aluminum powder were used in the mixtures. Signals of overpressure from two piezoelectric gauges located at the chamber wall were recorded and the influence of aluminum contents and particle size on a quasi‐static pressure (QSP) was studied. Moreover, the solid residues from the chamber were analyzed by using SEM, TG/DTA and XRD techniques to determine their structure and composition. Pressure and light histories recorded in the bunker enable us to determine the blast wave characteristics and time‐duration of light output. The effect of the charge mass and aluminum particle size on blast wave parameters were investigated. For comparison, the test for RDXph and TNT charges were also carried out.