Coefficients of Deformation of an Anisotropic Body

by Frans Van Cauwelaert, Dir. of ASBL Viacontrol-Hainaut; Prof. of Road Construction and Soil Mechanics at the Engrg. School, Institut Reine Astrid Mons, Mons, Belgium,

Serial Information: Journal of the Engineering Mechanics Division, 1977, Vol. 103, Issue 5, Pg. 823-835

Document Type: Journal Paper


The five characteristic elastic constants of an axisymmetric anisotropic solid with a plane of isotropy can usually not all be established by laboratory methods. It is shown by a transformation of the stiffness matrix around one of the axes of the plane of isotropy that these constants can be reduced to three: Young's modulus E along the anisotropic axis of symmetry, Poisson's ratio μ in the anisotropic planes and a constant n, called degree of anisotropy which is the ratio between the aforementioned modulus and Young's modulus in the plane of isotropy. The remaining constants, Poisson's ratio ν in the plane of isotropy and shear modulus G in the anisotropic planes are, respectively, equal to ν=μ/n and G=(1+n+2μ)/E. The equations of stresses and displacements are given for a semi-infinite anisotropic body submitted to a uniformly applied circular load. The conclusions of the numerical applications, although more general, are identical to those obtained by applying Frohlich's theories about stress concentrations.

Subject Headings: Anisotropy | Isotropy | Elasticity | Poisson ratio | Shear modulus | Elastic analysis | Axisymmetry

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