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Geometric Control of Fracture and Topological Metamaterials

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Geometry is not only a language to explain phenomena of the natural world, but also a tool to organize and trigger specific behaviors in material systems. As Jean le Rond D’Alembert wrote in 1752, “Geometry, which must obey Physics only when it meets with it, sometimes commands it”. In patterned liquid crystals, DNA lattices, colloidal crystals, and classic models of phase transitions, geometric constraints offer a mechanism to drive the order and dynamics of soft matter systems, both in and out of equilibrium. When curvature acts as the driving constraint on a two-dimensional material, that material’s constituents may no longer tile their preferred local arrangement throughout curved space (Fig. 1.1). The material may respond elastically by stretching and compressing to accommodate its new geometry, or by forming defects such as dislocations and disclinations. Might we similarly use curvature to guide the material failure of thin elastic materials conformed to corrugated surfaces?

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Authors and Affiliations

  1. Kavli Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, CA, USA

    Noah Mitchell

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  1. Noah Mitchell
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Mitchell, N. (2020). Introduction. In: Geometric Control of Fracture and Topological Metamaterials. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-36361-1_1

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