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Magic angles in the mechanics of fibrous soft materials

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Abstract

We discuss a ubiquitous intriguing issue that arises in the mechanics of fibrous soft materials, namely the occurrence of a “magic angle” associated with the fiber direction which gives rise to special features of the mechanical response. Classically, the magic angle concept arose in connection with hydrostatic skeletons or muscular hydrostats such as the common worm, octopus arm, or elephant trunk. It also arises in the field of soft robotics in connection with artificial muscles as well as in nuclear magnetic resonance. Such angles also occur in analysis of the mechanical behavior of fiber-reinforced incompressible elastic soft solids. In this context, the magic angle concept occurs most commonly in structural elements composed of circular cylindrical tubes or solid cylinders reinforced by helically wound fibers. An everyday example of the former is the common garden hose. The fibers can be inextensible as in reinforced rubber or extensible such as collagen fibers in soft tissue. Fibers orientated at the magic angle result in quasi-isotropic mechanical response and can lead to material instability.

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Authors and Affiliations

  1. School of Engineering and Applied Science, University of Virginia, Charlottesville, VA, 22904, USA

    C. O. Horgan

  2. Department of Mechanical Engineering, Dublin City University, Glasnevin, Dublin 9, Ireland

    J. G. Murphy

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  1. C. O. Horgan
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  2. J. G. Murphy
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Correspondence to C. O. Horgan.

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Horgan, C.O., Murphy, J.G. Magic angles in the mechanics of fibrous soft materials. Mech Soft Mater 1, 2 (2019). https://doi.org/10.1007/s42558-018-0001-x

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  • DOI: https://doi.org/10.1007/s42558-018-0001-x

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