Design, Herstellung und experimentelle Analyse von additiv gefertigten Metamaterialien mit pantographischer Substruktur

Due to the rapid developments in the field of additive manufacturing technologies in the recent past, the cost-effectively manufacturing of complex, small scaled components became possible. These demanding components mostly consist of multiple substructures on the micro- or macroscale. Based on the inner substructure (microscale), a special desired global deformation behavior can be triggered (macroscale). These structures are often referred to as mechanical metamaterials in literature. A very promising example of such a metamaterial is the so-called pantographic structure, which consists of two orthogonal arrays of beams connected by internal cylinders (pivots). In order to manufacture a metamaterial with a pantographic substructure, a parametrized, computer-aided design model was developed and used to produce differently sized specimens made of at least four different materials (Polylactide, Epoxy resin, Polyamide, Aluminum) by means of four different additive manufacturing technologies (Fused Deposition Modeling, Stereolithography, Selective Laser Melting, Direct Metal Laser Sintering). These specimens have been investigated experimentally in quasi-static extension, shearing, and torsion tests, evaluated by digital image correlation. All pantographics show a non-linear, resilient deformation behavior. By means of digital image correlation three-dimensional deformations (such as the buckling in shearing tests) could be captured and determined quantitatively. Based on these measurements, new (higher) material parameters have been determined by means of an inverse analysis and a higher gradient model has been evaluated.Durch den rapiden Entwicklungsfortschritt der letzten Jahre im Bereich der additiven Fertigung ist es möglich geworden, die kompliziertesten Bauteilstrukturen mit kleinsten Geometrien kosteneffizient und in ausreichend guter Qualität herzustellen. Diese höchst anspruchsvoll zu fertigenden Bauteile bestehen meist aus mehreren Substrukturen auf der Mikro- oder Makroskala. Basierend auf der inneren Geometrie (Mikroskala), kann ein speziell gewünschtes, globales Verformungsverhalten eingestellt werden (Makroskala). Diese Strukturen werden in der Literatur meist als mechanische Metamaterialien bezeichnet. Ein vielversprechendes Beispiel eines solchen Metamaterials ist die so genannte pantograpische Struktur, die aus zwei Ebenen mit jeweils senkrecht zueinander periodisch angeordneten Balken besteht, die durch Zylinder miteinander verbunden sind. Um dieses Metamaterial mit pantographischer Substruktur herzustellen, wurde ein parametrisiertes, rechnerunterstütztes Model entwickelt, mit dessen Hilfe in vier unterschiedlichen additiven Fertigungsverfahren (Schmelzschichtung, Stereolithographie, Selektives Laserschmelzen, Direktes Metall-Lasersintern) Proben unterschiedlichster Größe aus mindestens vier verschiedenen Materialien (Polymilchsäure, Epoxid-Harz, Polyamid, Aluminiumlegierung) hergestellt wurden. Diese Proben wurden experimentell in quasi-statischen Zug-, Scher- und Torsionsversuchen untersucht und mittels digitaler Bildkorrelation evaluiert. Alle Pantographen zeigen ein nicht-lineares, widerstandsfähiges Verformungsverhalten. Mit Hilfe der digitalen Bildkorrelation konnten auch drei dimensionale Verformungen (wie beispielsweise das Beulen in Scherversuchen) aufgenommen und quantitativ bestimmt werden. Basierend auf diesen Messungen wurden durch Anwendung einer inversen Analyse neue (höhere) Materialparameter bestimmt und ein höheres Gradientenmodell validiert

SHEARING TESTS APPLIED TO PANTOGRAPHIC STRUCTURES

With the advancements in 3D printing technology, rapid manufacturing of fabric materials with complex geometries became possible. By exploiting this technique, different materials with different structures have been developed in the recent past with the objective of making generalized continuum theories useful for technological applications. So-called pantographic structures are introduced: Inextensible fibers are printed in two arrays orthogonal to each other in parallel planes. These superimposed planes are inter-connected by elastic cylinders. Five differently-sized samples were subjected to shear-like loading while their deformation response was analyzed. Results show that deformation behavior is strong non-linear for all samples. Furthermore, all samples were capable to resist considerable external shear loads without leading to complete failure of the whole structure. This extraordinary behavior makes these structures attractive to serve as an extremely tough metamaterial

Investigation of deformation behavior of PETG-FDM-printed metamaterials with pantographic substructures based on different slicing strategies

Based on the progress and advances of additive manufacturing technologies, design and production of complex structures became cheaper and therefore rather possible in the recent past. A promising example of such complex structure is a so-called pantographic structure, which can be described as a metamaterial consisting of repeated substructure. In this substructure, two planes, which consist of two arrays of beams being orthogonally aligned to each other, are interconnected by cylinders/pivots. Different inner geometries were taken into account and additively manufactured by means of fused deposition modeling technique using polyethylene terephthalate glycol (PETG) as filament material. To further understand the effect of different manufacturing parameters on the mechanical deformation behavior, three types of specimens have been investigated by means of displacement-controlled extension tests. Different slicing approaches were implemented to eliminate process-related problems. Small and large deformations are investigated separately. Furthermore, 2D digital image correlation was used to calculate strains on the outer surface of the metamaterial. Two finite-element simulations based on linear elastic isotropic model and linear elastic transverse isotropic model have been carried out for small deformations. Standardized extension tests have been performed on 3D-printed PETG according to ISO 527-2. Results obtained from finite-element method have been validated by experimental results of small deformations. These results are in good agreement with linear elastic transverse isotropic model (up to about εxx=1.2% of axial elongation), though the response of large deformations indicates a nonlinear inelastic material behavior. Nevertheless, all samples are able to withstand outer loading conditions after the first rupture, resulting in resilience against ultimate failure.DFG, 414044773, Open Access Publizieren 2021 - 2022 / Technische Universität Berli

3D-measurements of 3D-deformations of pantographic structures

Samples of differently sized so-called pantographic structures are subjected to large deformation loading tests up to rupture, while their response to the deformation is recorded by an optical 3D-measurement system. Digital image correlation is used to calculate the deformation that took place perpendicular to the reference plane by the help of a four-camera system. Results show that the deformation behavior is strongly non-linear and that the structures are capable to perform large (elastic) deformations without leading to complete failure

Material characterization and computations of a polymeric metamaterial with a pantographic substructure

The development of additive manufacturing methods, such as 3D printing, allows the design of more complex architectured materials. Indeed, the main structure can be obtained by means of periodically (or quasi-periodically) arranged substructures which are properly conceived to provide unconventional deformation patterns. These kinds of materials which are ‘substructure depending’ are called metamaterials. Detailed simulations of a metamaterial is challenging but accurately possible by means of the elasticity theory. In this study, we present the steps taken for analyzing and simulating a particular type of metamaterial composed of a pantographic substructure which is periodic in space—it is simply a grid. Nevertheless, it shows an unexpected type of deformation under a uniaxial shear test. This particular behavior is investigated in this work with the aid of direct numerical simulations by using the finite element method. In other words, a detailed mesh is generated to properly describe the substructure. The metamaterial is additively manufactured using a common polymer showing nonlinear elastic deformation. Experiments are undertaken, and several hyperelastic material models are examined by using an inverse analysis. Moreover, a direct numerical simulation is repeated for all studied material models. We show that a good agreement between numerical simulations and experimental data can be attained

Characterization and Multiscale Modeling of the Mechanical Properties for FDM-Printed Copper-Reinforced PLA Composites

Additive manufacturing is an emerging technology and provides high design flexibility to customers. Fused deposition modeling (FDM) is an economical and promising additive manufacturing method. Due to its many advantages, FDM received great attention in recent years, and comprehensive studies are being undertaken to investigate the properties of FDM-printed polymers and polymer composites. As a result of the manufacturing technology employed in FDM, inner structures are changed with different process parameters, and thus, anisotropic properties are observed. Moreover, composite filaments such as particle- or fiber-reinforced polymers already have anisotropy before FDM printing. In this study, we investigate the effect of different process parameters, namely layer thickness and raster width on FDM-printed copper-reinforced poly(lactic acid) (PLA). Mechanical characterizations with a high-resolution camera are carried out for analyzing the deformation behaviors. Optical microscopy characterizations are performed to observe the mesostructural changes with various process parameters. Scanning electron microscopy (SEM) and an energy-dispersive X-ray spectroscopy (EDS) analysis are conducted for investigating the microstructure, specifically, copper particles in the PLA matrix. A 2D digital image correlation code with a machine learning algorithm is applied to the optical characterization and SEM-EDS images. In this way, micro- and mesostructural features, as well as the porosity ratios of the specimens are investigated. We prepare the multiscale homogenization by finite element method (FEM) simulations to capture the material’s response, both on a microscale and a mesoscale. We determined that the mesostructure and, thereby, the mechanical properties are significantly changed with the aforementioned process parameters. A lower layer thickness and a greater raster width led to a higher elasticity modulus and ultimate tensile strength (UTS). The optical microscopy analysis verified this statement: Decreasing the layer thickness and increasing the raster width result in larger contact lines between adjacent layers and, hence, lower porosity on the mesoscale. Realistic CAD images were prepared regarding the mesostructural differences and porosity ratios. Ultimately, all these changes are accurately modeled with mesoscale and multiscale simulations. The simulation results are validated by laboratory experiments

Pantographic metamaterials show atypical Poynting effect reversal

In an analysis presented in 1909, Poynting (page 546 of [1]) had shown that for finite elastic deformations, the lines of greatest extension and contraction are inclined to the diagonals of the rhombus into which a square is sheared. The implication of this finding was that when slender structures are twisted, they undergo elongation as experimentally verified by Poynting’s measurements with wires [1]. While many theoretical analyses have shown the possibility of Poynting and reverse (inverse) Poynting effect [2–7], measurements of such effects are rather sparse [8–11]. We present here measurements of a highly nonlinear Poynting effect, including its reversal from positive to negative (elongation to compression) direction during torsion. Such atypical behavior is exhibited by a rather exceptional material system that has a pantographic internal structure. For this material system, the classical Cauchy-type continuum model fails and a 2nd gradient continuum model is necessary to describe many of its deformation behaviors

Pantographic metamaterials: an example of mathematically driven design and of its technological challenges

International audienceIn 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 investigations. 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 and 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) in exploiting the modern 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

Advances in pantographic structures: design, manufacturing, models, experiments and image analyses

In the last decade, the exotic properties of pantographic metamaterials have been investigated and different mathematical models (both discrete or continuous) have been introduced. In a previous publication, a large part of the already existing literature about pantographic metamaterials has been presented. In this paper, we give some details about the next generation of research in this field. We present an organic scheme of the whole process of design, fabrication, experiments, models and image analyses