Abstract
A nonlinear theory of elastic solids based on the notion oforiented continua is presented with a view to studyingnonlinear dynamics such as thepropagation of solitons. The problem is connected with the nonlinear behavior in some additional degrees-of-freedom which account for the microstructure of the considered media (e.g., internal rotational motions in molecular crystals). A special description of the deformation of the microstructure is developed in terms ofone director. In this part a complete set of coupled dynamical equations is constructed for anisotropic solids in which the macroscopic elastic behavior remains linear while the director exhibits a strongly nonlinear behavior in spite of a simple choice for the free energy of the medium. The continuum model thus constructed contains all the necessary ingredients to allow for the propagation of solitary waves. It is also an abstract model for several types of crystals exhibiting phase-transition phenomena and competitive interaction effects. The propagation of solitary waves in such systems is examined in the second part.
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Pouget, J., Maugin, G.A. Nonlinear dynamics of oriented elastic solids. J Elasticity 22, 135–155 (1989). https://doi.org/10.1007/BF00041108
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DOI: https://doi.org/10.1007/BF00041108