He is member of several scientific committees and boards. Fischer is (co-)author of more than 650 papers, published in acknowledged journals, proceedings or as book chapters. He has been cooperating with the Max-Planck-Institute of Colloids and Interfaces/Biomaterials. He was awarded several prizes, as the Erwin Schrödinger-Prize of the ÖAW and Humboldt Research Prize. He was Guest Professor for 3 years at the Austrian Academy of Sciences, Erich Schmid Institute. Micromechanics and Thermodynamics of Materials is the central research field of F. Dieter Fischer was Full Professor and Chair of Institute of Mechanics, Montanuniversität Leoben from 1983 until 2009. He has written about 220 research publications and holds a fellowship of the European Structural Integrity Society.į. His main research interest lies in the deformation and fracture properties of materials and in the concepts of non-linear fracture mechanics. He was a visiting scientist at the Imperial College, London and at the Massachusetts Institute of Technology, Cambridge. He studied Materials Science at the Montanuniversität Leoben and holds there a venia in Mechanics of Materials. Otmar Kolednik is a senior scientist at the Erich-Schmid-Institute of Materials Science of the Austrian Academy of Sciences and professor at the Department Materials Physics of the Montanuniversität Leoben. He also holds an honorary doctorate from Montpellier University and is recipient of the Leibniz Prize from the German Science Foundation. He is honorary professor at Humboldt University Berlin and Potsdam University and member of several Academies of Science in Germany and Austria. He has published about 500 research papers, many of them on biological and bio-inspired materials. He holds an engineering degree from Ecole Polytechnique in Paris, France, and a doctorate in Physics from the University of Vienna, Austria. Peter Fratzl is a director at the Max Planck Institute of Colloids and Interfaces, Potsdam, Germany, heading the department of Biomaterials. Our analysis unites examples ranging from exoskeletal materials (fish scales, arthropod cuticle, turtle shell) to endoskeletal materials (bone, shark cartilage, sponge spicules) to attachment devices (mussel byssal threads), from both invertebrate and vertebrate animals, while spotlighting success and potential for bio-inspired manmade applications. Moreover, the arrangement of soft/flexible and hard/stiff elements into particular geometries can permit surprising functions, such as signal filtering or ‘stretch and catch’ responses, where the constrained flexibility of systems allows a built-in safety mechanism for ensuring that both compressive and tensile loads are managed well. We show that the tessellation of a hard, continuous surface – its atomization into discrete elements connected by a softer phase – can theoretically result in maximization of material toughness, with little expense to stiffness or strength. We start from basic mechanics principles on the effects of material heterogeneities in hypothetical structures, to derive common concepts from a diversity of natural examples of one-, two- and three-dimensional tilings/layerings. In this tutorial review, we highlight the concept of tessellation, a structural motif that involves periodic soft and hard elements arranged in series and that appears in a vast array of invertebrate and vertebrate animal biomaterials. Other: The images below show other collections of plane figures that cover the plane.Faced with a comparatively limited palette of minerals and organic polymers as building materials, evolution has arrived repeatedly on structural solutions that rely on clever geometric arrangements to avoid mechanical trade-offs in stiffness, strength and flexibility. Some mathematicians have discovered tiles from which it is impossible to construct a symmetric tiling!Īll tiles are the same and each tile can be decomposed into a number Semiregular: The tessellation is periodic and all tiles are regular polygons.Īsymmetric/ Aperiodic: The tessellation does not repeat itself. The tessellation is periodic and tiles are congruent regular polygons. Monohedral/Isohedral: All tiles are the same shape. The tessellation is self-symmetric it's made up of a repeating motif Want to use in this class, and what properties of tessellations are weĪ nice collection of tessellation-related definitions can be found Older definitions stipulate that the shapes all be HSED422/MSED456: Tessellations HSED422/MSED456: What is a Tessellation?Īccording to the Wikipedia, a tessellation is aĬollection of plane figures that fills the plane with no gaps orĪt the Math Forum web site requires all the plane figures to have the
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