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Analysis of partly wrinkled membranes by the method of dynamic relaxation

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Abstract

A version of the method of dynamic relaxation is developed to analyze equilibrium configurations of partly wrinkled membranes. In this method equilibria are regarded as long time limits of a damped dynamical problem. The membrane theory considered is based on the concept of a relaxed strain energy function that automatically incorporates the effects of wrinkling. For neo-Hookean materials, existence theorems of nonlinear elasticity are used to show that the relaxed potential energy possesses minimizers in a certain function space. Moreover, solutions of the equilibrium equations furnish global minima of the energy, for certain classes of boundary data. Such deformations are automatically stable according to the minimum-energy criterion. This result motivates the search for solutions of the equilibrium equations, although the existence theory does not guarantee that energy minimizers possess the degree of regularity required by these equations. Several examples of two-and three-dimensional deformations are presented.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Alberta, T6G 2G8, Edmonton, Alberta, Canada

    E. M. Haseganu & D. J. Steigmann

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  1. E. M. Haseganu
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  2. D. J. Steigmann
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Communicated by S. N. Atluri, 20 March 1994

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Haseganu, E.M., Steigmann, D.J. Analysis of partly wrinkled membranes by the method of dynamic relaxation. Computational Mechanics 14, 596–614 (1994). https://doi.org/10.1007/BF00350839

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