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Green's function of static anisotropic elasticity as an algebraic expression of 21 elastic constants in terms of expansion by spherical harmonics, with a tool for evaluation and visualization

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Mendeley Data2026-04-18 收录
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https://data.mendeley.com/datasets/mjzvn6f293
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Green's function, or fundamental solution, representing a displacement field caused by a static point load in a medium of general anisotropy described by 21 elastic constants, cannot have a closed-form expression, yet approximate algebraic expressions of any precision can be obtained with the help of computer algebra in terms of the expansion by real spherical harmonics Ylm: Gij(r, θ, φ | Cab) = 1/r * ΣΣ Glm_ij(Cab) * Ylm(θ, φ) , where Gij = Gji is Green's tensor with 6 independent components ij = xx, yy, zz, yz, xz, xy, Cab - 21 stiffness constants in the 6-dimensional Voigt notation (a, b = 1, 2, ..., 6 = ij) , r, θ, φ - spherical coordinates, ΣΣ - 2 summations: over even orbital number l = 0, 2, 4, ... and over m = -1, -l+1, ..., l. Glm_ij - expansion coefficients for given ij, as functions of elastic constants. The expansion taken up to the order l = l_max has thus a number (l_max + 1)*(l_max/2 + 1) of expansion coefficients for given ij for material of general anisotropy. Crystal symmetries significantly reduce this number, although they are not accounted here, but will be exclusively reported in the upcoming article together with an advanced software, while here a simple tool AnisoGreen running in GNU Octave or MATLAB environments is presented: it evaluates the derived expressions for Glm_ij up to l_max = 20 for an input material and visualizes the function r*Gij by the precalculated mesh of Ylm values. Inside the archive with the program, text files with the expressions for expansion orders from 12 to 20 are kept in 7z archives, since after extraction the occupy together over 13 Gb. All further details are provided in "about.txt" file.
创建时间:
2025-12-09
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