Finite Deformation and Stress in Ideal Fibre-Reinforced Materials
The constitutive theory for strongly anisotropic materials is treated elsewhere (Chapter I) in this book. These materials are characterised by their physical property of having ‘strong’ directions, for each of which the extensional modulus is much greater than the shear moduli associated with that direction. This property is particularly true of many of the man-made fibre-reinforced composites which are now coming into widespread use; in these a relatively weak, isotropic matrix with certain desirable properties (such as lightness or ductility) is strengthened throughout in one or more particular directions by introducing strong reinforcing fibres in those directions. Macroscopically, these composite materials will exhibit mechanical properties which are transversely isotropic if reinforced by one family of fibres, for example, or orthotropic if reinforced by two families (refer Chapter I). This will be so even if all the constituents are isotropic themselves. Moreover, the response of these composites is not just anisotropic - it is usually highly anisotropic, so that isotropic theory would not provide even a rough approximation to their behaviour under most types of loading conditions.
KeywordsPlane Strain Parallel Fibre Normal Line Finite Deformation Discontinuity Line
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