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Micromechanics based 3D framework with second-order damage tensors

Abstract : The harmonic product of tensors—leading to the concept of harmonic factorization—has been defined in a previous work (Olive et al, 2016). In the practical case of 3D crack density measurements on thin walled structures, this mathematical tool allows us to factorize the harmonic (irreducible) part of the fourth-order damage tensor as an harmonic square: an exact harmonic square in 2D, an harmonic square over the set of so-called mechanically accessible directions for measurements in the 3D case. The corresponding micro-mechanics framework based on second—instead of fourth— order damage tensors is derived and an illustrating example is provided.
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Contributor : Rodrigue Desmorat <>
Submitted on : Thursday, June 15, 2017 - 7:16:25 PM
Last modification on : Thursday, January 23, 2020 - 6:22:13 PM
Document(s) archivé(s) le : Wednesday, December 13, 2017 - 12:05:20 PM


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  • HAL Id : hal-01529452, version 2
  • ARXIV : 1706.00845


Rodrigue Desmorat, Boris Desmorat, Marc Olive, Boris Kolev. Micromechanics based 3D framework with second-order damage tensors. 2017. ⟨hal-01529452v2⟩



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