https://hal-enpc.archives-ouvertes.fr/hal-01157362Salmi, MoncefMoncefSalmiIP - Institut Pascal - UBP - Université Blaise Pascal - Clermont-Ferrand 2 - SIGMA Clermont - SIGMA Clermont - CNRS - Centre National de la Recherche ScientifiqueAuslender, FrançoisFrançoisAuslenderLMS - Laboratoire de mécanique des solides - X - École polytechnique - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueBornert, MichelMichelBornertmulti-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes - navier umr 8205 - Laboratoire Navier - IFSTTAR - Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche ScientifiqueFogli, MichelMichelFogliLAMI - Laboratoire de Mécanique et Ingénieries - IFMA - Institut Français de Mécanique Avancée - UBP - Université Blaise Pascal - Clermont-Ferrand 2Apparent and effective mechanical properties of linear matrix-inclusion random composites: Improved bounds for the effective behaviorHAL CCSD2012[SPI.GCIV] Engineering Sciences [physics]/Civil EngineeringBordignon, Frédérique2019-03-04 14:56:072022-10-22 04:56:432019-03-13 08:48:44enJournal articleshttps://hal-enpc.archives-ouvertes.fr/hal-01157362/document10.1016/j.ijsolstr.2012.01.018application/pdf1This paper is devoted to the derivation of improved bounds for the effective behavior of linear elastic matrix-inclusion composites based on a strategy which is inspired by both the works of Huet (1990) and Danielsson et al. (2007). As shown by the former author, the effective properties of random linear composites can be bounded by ensemble averages of their apparent elastic moduli defined on square (or cubic) volume elements (VEs) and computed with either affine displacement Boundary Conditions (BC) or uniform traction BC. However, in the case of a large contrast of the constituents, the discrepancy between the upper and lower bounds remains significant, even for large values of the VE size. This occurs because the contribution to the total potential (or complementary) energy of the particles (or pores) which intersect the edges of the VE becomes unphysically very large when uniform BC are directly applied to the particles. To avoid such limitations, we considerer non-square (or non-cubic) VEs consisting in simply connex assemblages of cells, each cell being composed of an inclusion surrounded by the matrix, thus forbidding any direct application of BC to the particles. Such VEs are generated by extending the scheme proposed by Danielsson et al. (2007) in the context of periodic random microstructures to fully random microstructures. By applying the classical energy bounding theorems to the non-square VEs, new bounds for the effective behavior are derived. Their application to a two-phase composite composed of an isotropic matrix and aligned identical fibers randomly distributed in the transverse plane leads to sharper bounds which converge quickly with the VE size, even for infinite contrasts. © 2012 Elsevier Ltd. All rights reserved.