Structural biomaterials (SBs), such as animal bones and shells, are predominantly composed of weak brittle minerals, such as aragonite and opaline silica. However, they display remarkable mechanical properties, such as high strength and toughness. The SBs also possess elaborate mechanical designs that consist of intricate spatial variations of elastic properties and arrangement of weak interfaces at the micro-scale, as well as interesting geometric shapes at the macro scale. It is argued that the SBs’ remarkable properties arise as a consequence of their micro- and macro-scale structure. However, in most cases a clear quantitative understanding of the mechanics and the mechanisms that connect the SBs’ properties to their structures is missing. Such quantitative understanding, when discovered, will constitute valuable new knowledge to the field of mechanics of materials. Additionally, with the advent of digital manufacturing technologies such as 3D printing, there is a possibility that when combined with synthetic materials and chemistries, the new structure-property connections from SBs will lead to the next generation of designer materials.
In the present talk we will discuss a new structure-property connection that we are investigating in the skeletal elements of the marine sponge Tethya aurantia. The skeletal elements are 1-2 mm long glass fibers known as spicules. These spicules are about 50 micrometers thick in the middle and have a characteristic tapered shape. We presume that the spicules are primarily loaded in compression inside the sponge body, and that their primary failure mode involves the spicule first undergoing a lateral buckling instability in response to the compressive loads. Through a synergistic combination of experiments, computations, and theory we will argue that the spicules’ tapered shape is very close to the shape that is optimal for withstanding the mechanical loads inside the sponge without failing. The experiments involve small-scale mechanical tests on the spicules and the theory relates to the calculus of variations problem of maximizing the lowest eigenvalue of a Sturm-Liouville operator.
Dr. Kesari is currently an Assistant Professor of Engineering at Brown University. He started at Brown in 2013, where he is affiliated with the Solid Mechanics group. He is interested in theoretical and experimental solid mechanics problems. These problems are related to the phenomena of adhesion, fracture, and micro-mechanics in solids and involve the use of homogenization and variational methods. His research has appeared in prestigious journals, such as PNAS and was covered by news media such as Scientific American, Science Daily, and Physics World among others. Previously, he obtained his Ph.D. and M.S. degrees from Stanford University in 2011 and 2007, respectively, and his B.S. degree from Indian Institute of Technology, all in Mechanical Engineering. At Stanford, he was awarded the prestigious Juan Simo Outstanding Thesis award and the Herbert Kunzel Fellowship. Recently he was awarded the Haythornthwaite fellowship by the American Society of Mechanical Engineers.