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.

We propose a multiscale approach to determine the displacement field by digital image correlation. The displacement field is first estimated on a coarse resolution image and progressively finer details are introduced in the analysis as the displacement is more and more securely and accurately determined. Such a scheme has been developed to increase the robustness, accuracy, and reliability of the image-matching algorithm. The procedure is used on two different types of examples. The first one deals with a representative image that is deformed precisely and purposefully to assess the intrinsic performances. In particular, the maximum measurable strain is determined. The second case deals with a series of pictures taken during compression experiments on mineral-wool samples. The different steps ofthe procedure are analyzed and their respective role is assessed. Both reflection and transmission images are tested.