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Generalized Euclidean Distances for Elasticity Tensors

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Abstract

The aim of this short paper is to provide, for elasticity tensors, generalized Euclidean distances that preserve the property of invariance by inversion. First, the elasticity law is expressed under a non-dimensional form by means of a gauge, which leads to an expression of elasticity (stiffness or compliance) tensors without units. Based on the difference between functions of the dimensionless tensors, generalized Euclidean distances are then introduced. A subclass of functions is proposed, which permits the retrieval of the classical log-Euclidean distance and the derivation of new distances, namely the arctan-Euclidean and power-Euclidean distances. Finally, these distances are applied to the determination of the closest isotropic tensor to a given elasticity tensor.

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Correspondence to Léo Morin.

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Morin, L., Gilormini, P. & Derrien, K. Generalized Euclidean Distances for Elasticity Tensors. J Elast 138, 221–232 (2020). https://doi.org/10.1007/s10659-019-09741-z

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Mathematics Subject Classification

  • 74B05
  • 74E10
  • 15A69
  • 15B48

Keywords

  • Elasticity tensor
  • Log-Euclidean distance
  • Closest isotropic tensor