Isotropic damage model with different tensile–compressive response for brittle materials

Incremental constitutive equations for brittle materials are formulated on the grounds of a frictional microcracked elastic model. The hypothesis of isotropic damage and the description of normal and tangential contact tractions on the crack faces by means of two second-order tensors provide a constitutive model with a reduced number of internal variables. The evolution equations of the latter ones are deduced from frictional and damage limit states and corresponding flow rules, from which the different behaviour to tensile and compressive stress states and dissipation at constant damage are represented. The model response is analysed for different stress states and limit strength domains are derived for monotonically increasing biaxial and triaxial stress states. Comparisons of the theoretical results with experimental data from literature related to concrete and cast-iron corroborate the proposed approach.

[1]  Farhad Ansari,et al.  Mechanics of Damage and Constitutive Relationships for High-Strength Concrete in Triaxial Compression , 1999 .

[2]  Kaspar Willam,et al.  Anisotropic vertex plasticity formulation for concrete in-plane stress , 1997 .

[3]  Wai-Fah Chen.  Plasticity in reinforced concrete , 1982 .

[4]  D. Krajcinovic,et al.  Micromechanically Inspired Phenomenological Damage Model , 1991 .

[5]  Zdeněk P. Bažant,et al.  Tangential stiffness of elastic materials with systems of growing or closing cracks , 1997 .

[6]  George Z. Voyiadjis,et al.  Plasticity-Damage Model for Concrete Under Cyclic Multiaxial Loading , 1993 .

[7]  B. Lawn,et al.  Nonlinear stress-strain curves for solids containing closed cracks with friction , 1998 .

[8]  Jean Lemaitre,et al.  A Course on Damage Mechanics , 1992 .

[9]  Ouyang Chengsheng,et al.  An r-curve approach for fracture of quasi-brittle materials , 1990 .

[10]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[11]  Dusan Krajcinovic,et al.  Damage model for brittle elastic solids with unequal tensile and compressive strengths , 1994 .

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

[13]  L.J.M. Nelissen,et al.  Biaxial Testing of Normal Concrete , 1972 .

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

[15]  K. Gerstle,et al.  Response of Mortar and Concrete to Biaxial Compression , 1977 .

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

[17]  S. Pietruszczak,et al.  An elastoplastic constitutive model for concrete , 1988 .

[18]  E. Oñate,et al.  A plastic-damage model for concrete , 1989 .

[19]  Kaspar Willam,et al.  Fracture Energy Formulation for Inelastic Behavior of Plain Concrete , 1994 .

[20]  F. S. Rostásy,et al.  Strength of concrete subjected to high temperature and biaxial stress: Experiments and modelling , 1995 .

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

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

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

[24]  Jean-Louis Chaboche,et al.  Development of Continuum Damage Mechanics for Elastic Solids Sustaining Anisotropic and Unilateral Damage , 1993 .

[25]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[26]  Edward C. Ting,et al.  An Elastic-Fracture Model for Concrete , 1979 .

[27]  Arthur H. Nilson,et al.  Stress-Strain Response and Fracture of Concrete in Uniaxial and Biaxial Compression , 1972 .

[28]  D. Halm,et al.  An anisotropic model of damage and frictional sliding for brittle materials , 1998 .

[29]  C. Bellamy.  Strength of Concrete Under Combined Stress , 1961 .

[30]  Kurt H. Gerstle,et al.  Behavior of Concrete Under Biaxial Stresses , 1969 .

[31]  H. Schreyer,et al.  An anisotropic damage model with dilatation for concrete , 1988 .

[32]  H. Gachon,et al.  Strain and ultimate strength of concrete under triaxial stress , 1971 .

[33]  H. Schreyer,et al.  Combined Plasticity and Damage Mechanics Model for Plain Concrete , 1990 .

[34]  R. M. Zimmerman,et al.  Compressive Strength of Plain Concrete Under Multiaxial Loading Conditions , 1970 .

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

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

[37]  K. Maekawa,et al.  The Deformational Behavior and Constitutive Equation of concrete Based on the Elasto-Plastic and Fracture Model , 1983 .

[38]  Andrzej Winnicki,et al.  Plastic Model for Concrete in Plane Stress State. I: Theory , 1998 .