The objective of this Early-Concept Grant for Exploratory Research (EAGER) project is to create new methodologies based on the concept of shell mechanics to investigate the complex and strongly nonlinear behavior of a number of inorganic and biological systems. The study will be carried out by developing technical models, detailed numerical simulations and experiments in two different testbeds that are of fundamental importance to the engineering and biological communities: i) stable localized structures in dynamical systems, and ii) patterns in plants and nature. The behavior and function of the systems will be studied by modeling the response of strongly deformed shells. The application of shell mechanics in simulating the behavior of these systems has the potential to provide unique tools for their investigation, while also exploring and highlighting the cross-disciplinary applications of shell mechanics.
Strong efforts are planned to link the research results to educational activities and outreach, by curriculum development reflecting the interdisciplinary philosophy at the university level and by practical training for K-12 students. In this context, an educational website called "Science of Shapes" will be created to translate research into the K-12 and large science community.
In this project, we investigated the complex and strongly nonlinear behavior of a number of inorganic and biological shell structures using analytical models, detailed numerical simulations and experiments. Some of the problems and systems studies are: 1) Response, instability and wrinkling of pressurized elastic shells such as a beach volleyball and living cells: The results were linked to the observed behavior of living, where the results from simple indentation experiments can be used to infer reach information about the materials properties and turgor pressure in cells. In a complementary investigation, we studied a simple but very intricate phenomenon of wrinkling in pressurized shells. We described how one can directly measure the internal pressure of the shell just by counting the number of wrinkles that appear in simple indentation experiment. 2) Buckling and instability of cylindrical shells in the presence of multiple cracks: Different instability modes of cracked shells were studies and symmetric and anti-symmetric modes of buckling were identified that could occur as the first buckling modes. The exchange between these local buckling modes due to variation of crack size and spacing was illustrated. Additional simulations were carried out for cylinders with multiple symmetrically spaced longitudinal cracks to show how the behavior of single and double cracks can give the buckling load and mode shape of cylinders with multiple cracks. 3) Elasto-plastic analysis of functionally graded structure: Unlike uniform rotating disks where yielding starts from the disk center, plasticity in FG disks can originate at any point. The effect of different metal-ceramic grading patterns as well as the relative elastic moduli and densities of the ceramic and metallic constituents on the developed stresses were studied. Reinforcement of a metal disk with ceramic particles, in both elastic and plastic regimes, can significantly influence the mechanical response of the rotating disk such as the distribution of stresses and the critical angular velocities corresponding to the onset of yielding and full plasticity in disk. Disks with increasing ceramic content from inner to outer radius showed a more uniform von Mises stress distribution for a fixed value of total ceramic content. In contrast, disks with decreasing ceramic content from inner to outer radius had the lowest outer edge displacement for a fixed value of total ceramic content. 4) Mechanical behavior of composite sandwich panels: The compressive response and failure of composite sandwich panels with pyramidal truss cores under axial compression were studied. Our investigation complements the previous studies on the response and performance of lightweight sandwich panels with complex core construction and provides insight into the failure mechanisms of composite sandwich panels. The results of the work have been integrated in the Computational Design course taught by the PI. In addition, during summer 2011 1 Young Scholar and 1 Teachers were involved in the research through the YSP and RET program supported by NSF STEM Center.
