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The closest
isotropic, cubic and transversely isotropic stiffness and
compliance tensor to an arbitrary anisotropic material
Xinyuan Shao, Peter D. Folkow and Morteza Eskandari-Ghadi |
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Vol. 16 (2021), No. 4, 451–470
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Abstract |
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The aim of this paper is to provide, in the framework of Green elasticity, the closest or nearest fourth-order isotropic, cubic and transversely isotropic elasticity tensors with higher symmetries for a general anisotropic elasticity tensor or any other tensors with lower symmetry. Using a gauge parameter, the procedure is done on a dimensionless form based on different generalized Euclidean distances, namely conventional, log-, and power-Euclidean distance functions. In the case of power-Euclidean distance functions, results are presented for powers of 0.5, 1 and 2. Except for the conventional distance function, the different generalized distance functions adopted in this paper preserve the property of invariance by inversion, meaning that the results for the closest stiffness tensor are also valid for the compliance tensor. Explicit formulations are given for determining the closest isotropic and cubic tensors, where the multiplication tables of the bases are diagonal. More involved coupled equations are given for the coefficients of the closest transversely isotropic elasticity tensors, which can be solved numerically. Two different material cases are studied in the numerical examples, which illustrate the material coefficients and error measures based on the present methods, including the influence from the gauge parameter. |
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Keywords
conventional distance, log-distance, power-Euclidean
distance, closest elasticity tensor, linear vector space
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Milestones
Received: 14 August 2020
Revised: 7 May 2021
Accepted: 1 June 2021
Published: 9 November 2021
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Authors |
| Xinyuan Shao | |
| Applied Mechanics Masters
Program Chalmers University of Technology 41296 Gothenburg Sweden |
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| Peter D. Folkow | |
| Department of Mechanics and Maritime
Sciences Chalmers University of Technology 41296 Gothenburg Sweden |
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| Morteza Eskandari-Ghadi | |
| School of Civil Engineering University of Tehran Tehran 1417466191 Iran |
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