Bounds on the Effective Anisotropic Elastic Constants |
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Authors: | SC Cowin G Yang MM Mehrabadi |
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Institution: | (1) Center for Biomedical Engineering, Department of Mechanical Engineering, The School of Engineering of The City College and The Graduate School of The City University of New York, New York, NY, 10031, U.S.A. E-mail;(2) Department of Mechanical Engineering, The School of Engineering, Tulane University, New Orleans, LA, 70118, U.S.A |
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Abstract: | Hill 12] showed that it was possible to construct bounds on the effective isotropic elastic coefficients of a material with
triclinic or greater symmetry. Hill noted that the triclinic symmetry coefficients appearing in the bounds could be specialized
to those of a greater symmetry, yielding the effective isotropic elastic coefficients for a material with any elastic symmetry.
It is shown here that it is possible to construct bounds on the effective elastic constants of a material with any anisotropic
elastic symmetry in terms of triclinic symmetry elastic coefficients. Similarly, it is then possible to specialize the triclinic
symmetry coefficients appearing in the bounds to those of a greater symmetry. Specific bounds are given for the effective
elastic coefficients of cubic, hexagonal, tetragonal and trigonal symmetries in terms of the elastic coefficients of triclinic
symmetry. These results are obtained by combining the approach of Hill 12] with a representation of the stress-strain relations
due, in principle, to Kelvin 25,26] but recast in the structure of contemporary linear algebra.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | elasticity anisotropy bounds elasticity tensor compliance tensor |
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