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- W2079089982 abstract "This paper establishes a three-dimensional hyper-elasticity framework for studying the manner in which fibre bending stiffness affects current knowledge regarding the presence of weak discontinuity surfaces in unconstrained fibre-reinforced solid materials. This is achieved by considering and studying the loss of ellipticity of a new set of incremental partial differential equations, which emerges from the second-gradient, hyper-elasticity theory developed in [11] and yields its conventional theory counterpart as a particular case. It is accordingly seen that, besides the conventional acoustic tensor met in relevant symmetric hyper-elasticity studies, where fibres are assumed perfectly flexible, some new, higher-order acoustic tensor is involved and becomes dominant in the present situation. Nevertheless, the manner becomes also clear in which the present analysis reduces to and, hence, connects with loss of ellipticity concepts met in conventional hyper-elasticity. No particular form is assigned to the strain energy density of the material, which is kept general throughout this paper. Considerable elucidation of the outlined new issues and concepts is however achieved by focusing attention on plane deformations of hyper-elastic solids reinforced by a single family of straight fibres. This development concludes with a specific application which relates the present analysis with kink band formation in unidirectional fibrous composites containing fibres resistant in bending." @default.
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- W2079089982 date "2012-03-01" @default.
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- W2079089982 title "On loss of ellipticity in second-gradient hyper-elasticity of fibre-reinforced materials" @default.
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- W2079089982 doi "https://doi.org/10.1016/j.ijnonlinmec.2011.03.012" @default.
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