Mesoscale probabilistic models for the elasticity tensor of fiber reinforced composites: Experimental identification and numerical aspects

Johann Guilleminot (1) , Christian Soize (1) , D. Kondo (2)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 LML - Laboratoire de Mécanique de Lille - FRE 3723

This work deals with the computational and experimental identification of two probabilistic models. The first one was recently proposed in the literature and provides a direct stochastic representation of the mesoscopic elasticity tensor random field for anisotropic microstructures. The second one, formulated in this paper, is associated to the volume fraction random field at the mesoscale of reinforced composites. After having defined the probabilistic models, we first address the question of the identification of the experimental trajectories of the random fields. For this purpose, we introduce a new methodology relying on the combination of a non destructive ultrasonic testing with an inverse micromechanical problem. The parameters involved in the probabilistic models are then identified and allows realizations of the random fields to be simulated by using Monte Carlo numerical simulations. A comparison between simulated and experimental results is provided and demonstrates the relevance of the identification strategy for the chaos coefficients involved in the second model. Finally, we illustrate the use of the first probabilistic model by performing a probabilistic parametric analysis of the RVE size of the considered microstructure.

Mots clés: uncertainty quantification; non-gaussian tensor-valued random field; prior stochastic model; micromechanics; micro-macro mechanics; mesoscale; representative volume element; polynomial chaos; information theory; stochastic homogeneization

Domaines: Mécanique [physics.med-ph]; Matériaux; Probabilités [math.PR]; Statistiques [math.ST]

Johann Guilleminot, Christian Soize, D. Kondo. Mesoscale probabilistic models for the elasticity tensor of fiber reinforced composites: Experimental identification and numerical aspects. Mechanics of Materials, 2009, 41 (12), pp.1309-1322. ⟨10.1016/j.mechmat.2009.08.004⟩. ⟨hal-00684330⟩