Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites

J. Guilleminot (1) , Christian Soize (2) , D. Kondo (3) , C. Binetruy (1)

1 TPCIM - Département Technologie des Polymères et Composites & Ingénierie Mécanique
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
3 LML - Laboratoire de Mécanique de Lille - FRE 3723

Many engineering materials exhibit fluctuations and uncertainties on their macroscopic mechanical properties. This randomness results from random fluctuations observed at a lower scale, especially at the meso-scale where microstructural uncertainties generally occur. In the present paper, we first propose a complete theoretical stochastic framework (that is, a relevant probabilistic model as well as a non-intrusive stochastic solver) in which the volume fraction at the microscale is modelled as a random field whose statistical reduction is performed using a Karhunen-Loeve expansion. Then, an experimental procedure dedicated to the identification of the parameters involved in the probabilistic model is presented and relies on a non-destructive ultrasonic method. The combination of the experimental results with a micromechanical analysis provides realizations of the volume fraction random field. in particular, it is shown that the volume fraction can be modelled by a homogeneous random field whose spatial correlation lengths are determined and may provide conditions on the size of the meso-volumes to be considered.

Mots clés: Uncertainty quantification; Composite materials; Experimental identification; Statistical inverse problem; Random fields; Karhunen-Loeve; Micromechanics; Polynomial chaos; Probabilistic model; Stochastic modelling; Volume fraction

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

J. Guilleminot, Christian Soize, D. Kondo, C. Binetruy. Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites. International Journal of Solids and Structures, 2008, 45 (21), pp.5567-5583. ⟨10.1016/j.ijsolstr.2008.06.002⟩. ⟨hal-00684818⟩