Propagation of elastic waves in fibrous composite with general anisotropy from two families of obliquely inclined fibers

An isotropic elastic solid reinforced with two families of aligned fibres behaves anisotropic to any deformation. For arbitrary orientation of fibres in either family, one set of fibres may be inclined obliquely to the aligned fibres in other family. A plane that contains the two families of aligned...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik 2024-08, Vol.104 (8), p.n/a
Main Author: Sharma, M. D.
Format: Article
Language:English
Subjects:
Angular velocity
Anisotropy
Composite materials
Constitutive relationships
Coordinates
Elastic anisotropy
Elastic deformation
Elastic waves
Fibers
Group velocity
Horizontal orientation
Isotropic material
Mathematical analysis
Phase velocity
Propagation
Strain
Stress propagation
Surface waves
Symmetry
Tensors
Wave propagation
Wave velocity
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Summary:An isotropic elastic solid reinforced with two families of aligned fibres behaves anisotropic to any deformation. For arbitrary orientation of fibres in either family, one set of fibres may be inclined obliquely to the aligned fibres in other family. A plane that contains the two families of aligned fibres becomes the plane of symmetry for composite material to exhibit monoclinic anisotropy. For this fibrous anisotropy, a fourth‐order elastic tensor is derived to define the constitutive relations between stress tensor and strain tensor. Components of this elastic tensor involve two Lame's moduli, eight fibroelastic coefficients and the angular deviation between two obliquely inclined fibre‐families. The velocities of bulk waves are calculated for propagation along general direction in this anisotropic composite. Propagation of surface wave is considered along the stress‐free plane boundary of anisotropic elastic half‐space. In a coordinate system with coordinate planes deviating from the plane boundary of the medium and/or plane of anisotropic symmetry, the fibrous composite is treated as triclinic for mathematical convenience. Mathematical model is derived to calculate the phase velocity of the surface wave, which varies with direction on the plane boundary. Horizontal energy flux at the boundary is calculated to determine the group velocity and ray direction of the surface wave. Effects of fibre‐orientations are analysed, numerically, on the wave velocities and ray direction of surface wave.
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.202400053