Micromechanics based 3D framework with second-order damage tensors

Rodrigue Desmorat (1) , Boris Desmorat (2, 3) , Marc Olive (1) , Boris Kolev (4)

1 LMT - Laboratoire de Mécanique et Technologie
2 DALEMBERT - Institut Jean Le Rond d'Alembert
3 UP11 - Université Paris-Sud - Paris 11
4 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: crack density; damage tensor; harmonic decomposition

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Rodrigue Desmorat, Boris Desmorat, Marc Olive, Boris Kolev. Micromechanics based 3D framework with second-order damage tensors. 2017. ⟨hal-01529452v1⟩