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.

signing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence.

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We simulate pattern formation in the deformations of a pantographic lattice using a model of elastic surfaces that accounts for the geodesic bending of the constituent fibers. The theory predicts an unusual arrangement of coexistent phases observed in an actual lattice, manufactured by a 3D printing process, in which the fibers undergo part-wise uniform shears separated by internal transition layers controlled by geodesic bending stiffness

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This article presents an analysis of the effectiveness of available numerical techniques in mapping the characteristic behavior of ballistic ceramics under projectile impact conditions. As part of the work, the ballistic tests were performed on the layered ceramic/steel composite armor and tested with the 7.62 × 39 mm, armor-piercing incendiary (API) BZ projectile. The experimental tests were then mapped using computer simulations. In numerical analyses, four different techniques were used to describe cubic ceramic tiles Al2O3 placed on the ARMOX 500T steel backing plate, i.e.,: the Finite Element Method without Erosion (FEM), Finite Element with erosion (FEM + Erosion), Smoothed Particles Hydrodynamics (SPH) and a hybrid method that converts finite elements to SPH particles after exceeding the defined failure criteria (FEM to SPH conversion). The effectiveness of the individual methods was compared in terms of quality (mapping of characteristic phenomena occurring during the penetration process), quantity (bulge height of the backing plate) and time needed to complete the calculations. On the basis of the results of the experiments and numerical simulations, it was noticed that the most accurate reproduction of the phenomenon of ballistic impact of AP projectiles on ceramic/steel composite armor can be obtained by using a hybrid method, incorporating the conversion of finite elements into SPH particles. This method should be used in cases where accuracy of the results is more important than the time required to complete the calculations. In other situations where the purpose of the calculation is not to determine, for example, the exact value of penetration depth but only to observe a certain trend, the FEM method with defined erosion criteria (variant 2), which is more than 10 times faster, can be successfully used.

Purpose – The purpose of this paper is to present the methodology of a design process of new lumbar intervertebral disc implants with specific emphasis on the use of rapid prototyping technologies. The verification of functionality of artificial intervertebral discs is also given. The paper describes the attempt and preliminary research to evaluate the properties of the intervertebral disc implant prototypes manufactured with the use of different rapid prototyping technologies, i.e. FDM – fused deposition modelling, 3DP – 3D printing and SLM – selective laser melting. Design/methodology/approach – Based on the computed tomography (CT) scan data, the anatomical parameters of lumbar spine bone tissue were achieved, which were the bases for the design-manufacture process carried out with the use of computer-aided designing/computer-aided engineering/computer-aided manufacturing systems. In the intervertebral disc implant design process, three RP technologies: FDM, 3DP and SLM were used for solving problems related to the reconstruction of geometry and functionality of the disc. Some preliminary tests such as measurement of roughness and structural analyses of material of prototypes made by different prototyping technologies were performed. Findings – This paper allowed the authors to elaborate and patent two new intervertebral disc implants. Because the implant designs are parametrical ones with relation to lumbar bone tissue properties measured on CT scans, they can be also made for individual patients. We also compared some of the properties of intervertebral implants prototypes made with the use of FDM, 3DP and SLM technologies. Originality/value – The paper presents the new intervertebral disc implants and their manufacturing by rapid prototyping. The methodology of designing intervertebral disc implant is shown. Some features of the methodology make it useful for preoperative planning of intervertebral disc surgery, as well.