Mechanics of Dynamic Discontinuities

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As flexible objects move, they often develop discontinuities in their shapes. Discontinuities of interest are features such as sharp folds, contacts with obstacles and guides, or tears. This work seeks to understand the mechanics and dynamics of these discontinuities and investigates how they move, and how they affect the motion of the flexible object as a whole. Fundamental engineering science outcomes may eventually be applied to many different technology domains. Thin, flexible structures like strings, cables, sheets, and plates are important components of many engineered systems, including, among other things, energy harvesting technologies, sensors, marine and aerospace structures. Manufacturing technologies such as transfer printing and textile processing also involve the dynamical behavior of thin, flexible structures and their contact discontinuities. Mechanical metamaterials and morphing devices rely on the manipulation and response of thin plates or strips linked by hinges or other sharp features. The project will also provide opportunities for outreach and education on topics in mechanics, through demonstration of exciting phenomena insightful to the general public. The dynamical behavior of discontinuities is a fundamental topic in analytical mechanics. The work will apply a new unifying variational framework for non-material discontinuities in materials and structures, including kinks and folds, moving contacts and impacts, and peeling and tearing fronts. The approach is new in that it treats all of these objects as time-dependent boundaries. The work is organized around three projects, each representing a different class of discontinuity: 1) Pickup, impact, and peeling of cables and tapes, 2) Propagating folds in membranes, plates, and shells, and 3) Cracking, tearing, and cutting of sheets. The work will generate novel theoretical results on momentum and energy balances in these systems, and analytical solutions for motions of discontinuities. Tabletop experiments with chains will provide experimental data on discontinuous dynamic contacts.