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Homogenization-based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracks. (English) Zbl 1273.74419
Summary: This paper is devoted to micromechanical modeling of induced anisotropic damage in brittle geomaterials. The formulation of the model is based on a proper homogenization procedure by taking into account unilateral effects and interactions between microcracks. The homogenization procedure is developed in the framework of Eshelby’s inclusion solution and P. Ponte-Castaneda and J. R. Willis [J. Mech. Phys. Solids 43, No. 12, 1919–1951 (1995; Zbl 0919.73061)] estimate. The homogenization technique is combined with the thermodynamics framework at microscopic level for the determination of damage evolution law. A rigorous crack opening-closure transition condition is established and an energy-release-rate-based damage criterion is proposed. Computational aspects on the implementation of micromechanical model are also discussed. The proposed model is evaluated by comparing numerical predictions with experimental data for various laboratory tests on concrete. Parametric studies on unilateral effects and influences of microcracks interactions are finally performed and analyzed.

74R05 Brittle damage
74Q05 Homogenization in equilibrium problems of solid mechanics
74M25 Micromechanics of solids
74L10 Soil and rock mechanics
Full Text: DOI
[1] Brace, A note on brittle crack growth in compression, Journal of Geophysical Research-Solid Earth 68 (12) pp 3709– (1963)
[2] Horii, Overall moduli of solids with microcracks: load-induced anisotropy, Journal of the Mechanics and Physics of Solids 31 (2) pp 155– (1983) · Zbl 0506.73097
[3] Horii, Compression-induced microcrack growth in brittle solids: axial splitting and shear failure, Journal of Geophysical Research-Solid Earth 90 (B4) pp 3105– (1985)
[4] Kranz, Microcracks in rocks: a review, Tectonophysics 100 pp 449– (1983)
[5] Steif, Crack extension under compressive loading, Engineering Fracture Mechanics 20 (3) pp 463– (1984)
[6] Van Mier JGM. Strain-softening of concrete under multiaxial loading conditions. Ph.D. Thesis, Technishe Hogeschool Eindhoven, 1984.
[7] Wong, Micromechanics of faulting in Westerly granite, International Journal of Rock Mechanics and Mining Sciences 19 pp 49– (1982)
[8] Chaboche, Damage induced anisotropy: on the difficulties associated with the active/passive unilateral condition, International Journal of Damage Mechanics 2 pp 311– (1992)
[9] Chaboche, Development of continuum damage mechanics for elastic solids sustaining anisotropic and unilateral damage, International Journal of Damage Mechanics 2 pp 311– (1993)
[10] Welemane, Some remarks on the damage unilateral effect modelling for microcracked materials, International Journal of Damage Mechanics 11 pp 65– (2002)
[11] Welemane, An alternative 3D model for damage induced anisotropy and unilateral effect in microcracked materials, Journal de Physique IV 105 pp 329– (2003)
[12] Carol, Spurious energy dissipation/generation in stiffness recovery models for elastic degradation and damage, International Journal of Solids and Structures 33 pp 2939– (1996) · Zbl 0910.73049
[13] Halm, A model of anisotropic damage by mesocrack growth: unilateral effect, International Journal of Damage Mechanics 5 pp 384– (1996) · Zbl 0920.73321
[14] Krajcinovic, Damage Mechanics (1996)
[15] Kachanov, A microcrack model of rock inelasticity-part I: frictional sliding on microcracks; part II: propagation of microcracks, Mechanics of Materials 1 pp 19– (1982)
[16] Andrieux, Un modèle de matériau microfissuré pour les roches et les bétons, Journal de Mécanique Théorique et Appliquée 5 (3) pp 471– (1986)
[17] Mura, Micromechanics of Defects in Solids (1987) · doi:10.1007/978-94-009-3489-4
[18] Fanella, A micromechanical model for concrete in compression, Engineering Fracture Mechanics 29 pp 49– (1988)
[19] Gambarotta, A microcrack damage model for brittle materials, International Journal of Solids and Structures 30 (2) pp 177– (1993) · Zbl 0775.73196
[20] Nemat-Nasser, Micromechanics: Overall Properties of Heterogeneous Materials (1993) · Zbl 0924.73006
[21] Pensée, Micromechanical analysis of anisotropic damage in brittle materials, Journal of Engineering Mechanics 128 (8) pp 889– (2002)
[22] Pensée, Micromechanics of anisotropic brittle damage: comparative analysis between a stress based and a strain based formulation, Mechanics of Materials 35 pp 747– (2003)
[23] Bazant, Microplane model for progressive fracture of concrete and rock, Journal of Engineering Mechanics 11 (4) pp 559– (1985)
[24] Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proceedings of the Royal Society of London A241 pp 375– (1957) · Zbl 0079.39606
[25] Eshelby, Progress in Solid 2 (1961)
[26] Ponte-Castaneda, The effect of spatial distribution on the behavior of composite materials and cracked media, Journal of the Mechanics and Physics of Solids 43 pp 1919– (1995)
[27] Dormieux, A micromechanical analysis of damage propagation in fluid-saturated cracked media, Comptes Rendus Mecanique 334 pp 440– (2006) · Zbl 1177.74356
[28] Zaoui, Continuum micromechanics: survey, Journal of Engineering Mechanics 128 (8) pp 808– (2002)
[29] Dormieux, Microporomechanics (2006)
[30] Zhu, Micromechanical analysis of coupling between anisotropic damage and friction in quasi brittle materials: role of the homogenization scheme, International Journal of Solids and Structures 45 (5) pp 1385– (2008) · Zbl 1169.74542
[31] Mori, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica 21 pp 571– (1973)
[32] Benveniste, On the Mori-Tanaka method in cracked bodies, Mechanics Research Communication 13 (4) pp 193– (1986) · Zbl 0625.73110
[33] Deude, Propriétés élastiques non linéaires d’un milieu mésofissuré, Comptes Rendus Mecanique 330 pp 587– (2002)
[34] Budiansky, Elastic moduli of a cracked solid, International Journal of Solids and Structures 12 pp 81– (1976) · Zbl 0318.73065
[35] Walpole, Elastic behavior of composite materials: theoretical foundations, Advances in Applied Mechanics 21 pp 169– (1981) · Zbl 0508.73053
[36] Marigo, Formulation d’une loi d’endommagement d’un matériau élastique, Comptes Rendus de l’ Academie des Sciences de Paris, Serie II 292 pp 1309– (1981)
[37] Bazant, Efficient numerical integration on the surface of a sphere, Journal of Applied Mathematics and Mechanics 66 pp 37– (1986)
[38] Ghavamian, Discussion over MECA projects results, Modèle de fissuration de béton, Revue française de Génie Civil 7 (5) pp 544– (2003)
[39] Geopalaeratnam, Softening response of plain concrete in direct tension, ACI Journal 85 (3) pp 310– (1985)
[40] Bazant, Measurement of characteristic length of nonlocal continuum, Journal of Engineering Mechanics 115 (4) pp 755– (1989)
[41] Barthelemy, Détermination du comportement macroscopique d’un milieu à fissures frottantes, Comptes Rendus Mécanique 331 pp 77– (2003)
[42] Willam, Proceedings of SEM-RILEM, International Conference on Fracture of Concrete and Rock pp 192– (1987)
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