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Some Open Problems in Elasticity

  • Chapter
Geometry, Mechanics, and Dynamics

Abstract

Some outstanding open problems of nonlinear elasticity are described. The problems range from questions of existence, uniqueness, regularity and stability of solutions in statics and dynamics to issues such as the modelling of fracture and self-contact, the status of elasticity with respect to atomistic models, the understanding of microstructure induced by phase transformations, and the passage from three-dimensional elasticity to models of rods and shells. Refinements are presented of the author’s earlier work Ball [1984a] on showing that local minimizers of the elastic energy satisfy certain weak forms of the equilibrium equations.

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  1. John M. Ball
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Editors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, 90089-1191, USA

    Paul Newton

  2. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089-1191, USA

    Paul Newton

  3. Department of Applied and Computational Mathematics Engineering Quadrangle, Princeton University, Princeton, NJ, 08544-1000, USA

    Philip Holmes

  4. Department of Mathematics, University of California, Berkeley, Berkeley, CA, 94720, USA

    Alan Weinstein

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To Jerry Marsden on the occasion of his 60th birthday

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Ball, J.M. (2002). Some Open Problems in Elasticity. In: Newton, P., Holmes, P., Weinstein, A. (eds) Geometry, Mechanics, and Dynamics. Springer, New York, NY. https://doi.org/10.1007/0-387-21791-6_1

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