Micromechanical Analysis of Anisotropic Damage in Brittle Materials

A general three-dimensional micromechanical approach to modeling anisotropic damage of brittle materials such as concrete, rocks, or certain ceramics is presented. Damage is analyzed as a direct consequence of microcracks growth. Following a rigorous scale change methodology, the macroscopic free energy of the microcracked medium is built considering either open and closed microcracks. Moreover, the microcracks opening/closure criterion as well as the moduli recovery conditions (unilateral effects) are addressed in stress-based and strain-based formulations. An alternative derivation of the homogenized properties, based on the well-known Eshelby method, is also presented and extended here to closed cracks. From the micromechanical analysis, an energy-based yield condition is formulated and illustrated in various stress subspaces. Assuming that the normality rule applies, we then present the damage evolution law and the rate form of the constitutive model. The main capabilities and advantages of the micromechanical model are illustrated through various examples in which material microstructure evolutions are presented.

[1]  B. Budiansky,et al.  Elastic moduli of a cracked solid , 1976 .

[2]  Pere C. Prat,et al.  Microplane Model for Brittle-Plastic Material: I. Theory , 1988 .

[3]  M. Basista,et al.  The sliding crack model of brittle deformation: An internal variable approach , 1998 .

[4]  M. Kachanov,et al.  A microcrack model of rock inelasticity part I: Frictional sliding on microcracks , 1982 .

[5]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[6]  Sergio Lagomarsino,et al.  A microcrack damage model for brittle materials , 1993 .

[7]  J. Rice.  Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity , 1971 .

[8]  T. Mura.  Micromechanics of Defects , 1992 .

[9]  J. Chaboche,et al.  Damage Induced Anisotropy: On the Difficulties Associated with the Active/Passive Unilateral Condition , 1992 .

[10]  R. Kranz.  Microcracks in rocks: a review , 1983 .

[11]  Dusan Krajcinovic,et al.  A micromechanical model for concrete in compression , 1988 .

[12]  Michael Ortiz,et al.  A constitutive theory for the inelastic behavior of concrete , 1985 .

[13]  Sia Nemat-Nasser,et al.  Overall moduli of solids with microcracks: Load-induced anisotropy , 1983 .

[14]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[15]  J. Chaboche,et al.  Le Concept de Contrainte Effective Appliqué à l’Élasticité et à la Viscoplasticité en Présence d’un Endommagement Anisotrope , 1982 .

[16]  Zdeněk P. Bažant,et al.  New explicit microplane model for concrete: Theoretical aspects and numerical implementation , 1992 .

[17]  S Andrieux.  UN MODELE DE MATERIAU MICROFISSURE - APPLICATIONS AUX ROCHES ET AUX BETONS , 1983 .

[18]  Zdenek P. Bazant,et al.  Microplane Model for Brittle‐Plastic Material: II. Verification , 1988 .

[19]  J. Ju,et al.  Micromechanical Damage Models for Brittle Solids. Part II: Compressive Loadings , 1991 .

[20]  J. Ju,et al.  On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects , 1989 .

[21]  S. Nemat-Nasser,et al.  Micromechanics: Overall Properties of Heterogeneous Materials , 1993 .

[22]  Dusan Krajcinovic,et al.  A self-consistent model for microcrack-weakened solids , 1987 .

[23]  Sia Nemat-Nasser,et al.  A Microcrack Model of Dilatancy in Brittle Materials , 1988 .

[24]  Sumio Murakami,et al.  Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics , 1997 .

[25]  André Dragon,et al.  A Model of Anisotropic Damage by Mesocrack Growth; Unilateral Effect , 1996 .