The aim of this paper is to set up a methodology in order to build a reduced constitutive law in case of a complex material behavior. The reduction is performed in a certain range of loading conditions in order to preserve the state potential describing the original complex model. Two main steps are used. The first one concerns the reduction of the kinematic of the internal variables from which the associated thermodynamical forces are deduced. In order to define the internal variables, a simple thermodynamic potential form is chosen. The second concerns the building of the evolution laws linking the previous variables. The presented methodology has been applied to the mechanical modeling of SiC/SiC ceramic matrix composites.
AubardXCluzelCGuitardL (1998) Modelling of the mechanical behaviour of 4D carbon/carbon composite materials. Composites Science and Technology, 58(5): 701–708.
2.
AubardXLamonJAllixO (1994) Model of the nonlinear mechanical behavior of 2d sic–sic chemical vapor infiltration composites. Journal of the American Ceramic Society, 77(8): 2118–2126.
3.
Baranger E, Cluzel C, Ladevèze P, et al. (2007) Prediction of the lifetime of self-healing ceramic matrix composites: I – Macroscopic modeling of cracking (in French). In: Proceedings of the 15th National Conference on Composite Materials (JNC15) (in French), Marseille, France, 6–8 June 2007.
4.
Bourgeon M (2010) Thermostructural materials in aerospace industry: Applications and standardization. In: Proceedings of the 7th International Conference on High Temperature Ceramic Matrix Composites, Bayreuth, Germany, 20–22 September 2010.
5.
ChabocheJMaireJ (2002) A new micromechanics based CDM model and its application to CMC’s. Aerospace Science and Technology, 6(2): 131–145.
6.
ChinestaFLadevezePCuetoE (2011) A short review on model order reduction based on proper generalized decomposition. Archives of Computational Methods in Engineering, 18, pp. 1–10.
7.
CluzelCBarangerELadevèzeP (2009) Mechanical behaviour and lifetime modelling of self-healing ceramic-matrix composites subjected to thermomechanical loading in air. Composites Part A: Applied Science and Manufacturing, 40(8): 976–984.
8.
DesmoratRGatuingtFRagueneauF (2007) Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials. Engineering Fracture Mechanics, 74(10): 1539–1560.
9.
GasserALadevèzePPossM (1996) Damage mechanisms of a woven SiC/SiC composite: Modelling and identification. Composites Science and Technology, 56, pp. 779–784.
10.
GenetMMarcinLBarangerE (2011) Computational prediction of the lifetime of self-healing CMC structures. Composites Part A: Applied Science and Manufacturing, 43, pp. 294–303.
11.
Ladevèze P (1983) On an anisotropic damage theory (in French). Internal report 34. Cachan, France: LMT-Cachan.
12.
LadevèzeP(2002) An anisotropic damage theory with unilateral effects: Applications to laminate and three- and four-dimensional composites. In: AllixOHildF (eds) Continuum Damage Mechanics of Materials and Structures, Elsevier, 205–233.
13.
LamonJ (2001) A micromechanics-based approach to the mechanical behavior of brittle-matrix composites. Composites Science and Technology, 61(15): 2259–2272.
14.
LemaitreJ (1992) A Course on Damage Mechanics, New York: Springer.
LesnePSaanouniK (1993) Modeling of irreversible damage-induced strains in brittle elastic composites. Recherche Aérospatiale, 2, pp. 23–37.
17.
Letombe S (2005) Modelling of the damage/oxidation coupling in ceramic matrix composites (in French). PhD Thesis, ENS-Cachan, France.
18.
MarcinLMaireJCarrèreN (2010) Development of a macroscopic damage model for woven ceramic matrix composites. International Journal of Damage Mechanics, 20(6): 939–957.
19.
NguyenQGermainPSuquetP (1983) Continuum thermodynamics. Journal of Applied Sciences, 50, pp. 1010–1020.
20.
PenséeVKondoDDormieuxL (2002) Micromechanical analysis of anisotropic damage in brittle materials. Journal of Engineering Mechanics, 128(8): 889–897.
21.
RyckelynckD (2009) Hyper-reduction of mechanical models involving internal variables. International Journal for Numerical Methods in Engineering, 77(1): 75–89.
22.
RyckelynckDChinestaFCuetoE (2006) On the a priori model reduction: Overview and recent developments. Archives of Computational Methods in Engineering, 13(1): 91–128.
23.
VoyiadjisGKattanP (1993) Damage of fiber-reinforced composite-materials with micromechanical characterization. International Journal of Solids and Structures, 30(20): 2757–2778.
