Biot-elastic and Direct Models of Shells and Strips

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Thin elastic structures such as shells and strips are found in engineering applications across many scales, including aerospace components, soft robots, flexible microelectronic devices, and programmable matter. Despite nearly a century of research on the mechanics of thin structures, questions remain about simple reduced models commonly employed to describe bending and stretching of these bodies in response to pressure or other applied forces. Superficially similar shell models make qualitatively different predictions, such as whether a bent shell will expand or contract under the same conditions. Existing strip models fail to capture experimentally observed shape changes during manipulations. This work will both explain these issues and develop new simple models that will agree with experiments and be useful in a variety of settings, including the design of new flexible and reconfigurable devices, and origami and kirigami structures for engineering applications. Graduate and undergraduate students will be trained as part of this project. The PI and students will develop related laboratory demonstrations and a module for a summer science program for young women in high school. Public outreach efforts will exploit the connections between thin structure mechanics and the behavior of toys such as snap bracelets. This work has two parts. First, an elastic theory will be developed based on systematic expansions in stretch. When applied to shells, this theory will preserve simple relationships between stress and generalized strain and provide the simplest definitions of bending energies. Second, a uniformly valid theory of elastic curves will be developed that interpolates between rod and inextensible wide strip models. This theory will capture bifurcation phenomena of narrow strips and allow numerical integration of strip deformations that create inflection points. More broadly, the work will relate direct and dimensional reduction approaches to thin structures. The new shell theory will be compared with theoretical and numerical results on soft shells from the literature, and the new strip theory will be validated using prior experimental results on bifurcations from the PI?s prior work and the literature. The issues to be addressed in this work are relevant to research areas such as the incompatible elasticity of soft and other materials, design of programmable elastomeric and structured sheets, and instabilities and bifurcations of flexible components.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.