A symmetric over-nonlocal microplane model M4 for fracture in concrete

Abstract This paper analyzes the effectiveness of a nonlocal integral-type formulation of a constitutive law such as microplane model M4 in which the yield limits soften as a function of the total strain for prediction of fracture propagation. For a correct regularization of the mathematical problems caused by the softening behavior, an “over-nonlocal” generalization of the type proposed by Vermeer and Brinkgreve [Vermeer, P.A., Brinkgreve, R.B.J., 1994. A new effective non-local strain measure for softening plasticity. In: Chambon, R., Desrues, J., Vardoulakis, I. (Eds.), Localization and Bifurcation Theory for Soil and Rocks, Balkema, Rotterdam, pp. 89–100.] is adopted. Moreover, the symmetric weight function, proposed by Borino et al. [Borino, G. Failla, B., Parrinello, F., 2003. A symmetric nonlocal damage theory. International Journal of Solids and Structure 40, 3621–3645.] for damage mechanics, is introduced for the calculation of the nonlocal averaging of the total strain upon which the yield limits depend. The capability of the proposed model for reproducing the stress and strain fields in the vicinity of a notch is also investigated. Finally, the symmetric over-nonlocal generalization of microplane model M4 has been applied for the simulation of a mixed-mode fracture test such as the four-point-shear test and the test of axial tension at constant shear force [Nooru-Mohamend, M.B., 1992. Mixed-mode fracture of concrete: an experimental approach. Doctoral Thesis Delft University of Thechnology, Delft, The Netherlands.]

[1]  S. Foster,et al.  Modelling triaxial compression using the Microplane formulation for low confinement , 2002 .

[2]  T. Belytschko,et al.  Localization limiters in transient problems , 1988 .

[3]  Milan Jirásek,et al.  LOCALIZATION ANALYSIS OF NONLOCAL MODEL BASED ON CRACK INTERACTIONS , 1994 .

[4]  Z. Bažant,et al.  Nonlocal microplane model for fracture, damage, and size effect in structures , 1990 .

[5]  Ta-Peng Chang,et al.  Instability of Nonlocal Continuum and Strain Averaging , 1984 .

[6]  Zdenek P. Bazant,et al.  Imbricate continuum and its variational derivation , 1984 .

[7]  Z. Bažant,et al.  Crack band theory for fracture of concrete , 1983 .

[8]  Zdenek P. Bazant,et al.  Nonlocal microplane model with strain-softening yield limits , 2004 .

[9]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[10]  Z. Bažant,et al.  Fracture and Size Effect in Concrete and Other Quasibrittle Materials , 1997 .

[11]  Milan Jirásek,et al.  On mesh bias of local damage models for concrete , 2004 .

[12]  M. B. Nooru-Mohamed.  Mixed-mode fracture of concrete : An experimental approach , 1992 .

[13]  E. Kröner,et al.  Elasticity theory of materials with long range cohesive forces , 1967 .

[14]  R. J. Crawford,et al.  Mechanics of engineering materials , 1986 .

[15]  H.E.J.G. Schlangen,et al.  Experimental and numerical analysis of fracture processes in concrete : proefschrift , 1993 .

[16]  F. Parrinello,et al.  A symmetric nonlocal damage theory , 2003 .

[17]  Ferhun C. Caner,et al.  MICROPLANE MODEL M5 WITH KINEMATIC AND STATIC CONSTRAINTS FOR CONCRETE FRACTURE AND ANELASTICITY. II: COMPUTATION , 2005 .

[18]  Zdeněk P. Bažant,et al.  Spectral analysis of localization in nonlocal and over-nonlocal materials with softening plasticity or damage , 2005 .

[19]  M. Jirásek,et al.  ROTATING CRACK MODEL WITH TRANSITION TO SCALAR DAMAGE , 1998 .

[20]  A. Stroud.  Approximate calculation of multiple integrals , 1973 .

[21]  Zdenek P. Bazant,et al.  MICROPLANE MODEL FOR STRAIN-CONTROLLED INELASTIC BEHAVIOUR. , 1984 .

[22]  Zdenek P. Bazant,et al.  Instability, Ductility, and Size Effect in Strain-Softening Concrete , 1978 .

[23]  A. Cemal Eringen,et al.  A unified theory of thermomechanical materials , 1966 .

[24]  Joško Ožbolt,et al.  Microplane model for concrete with relaxed kinematic constraint , 2001 .

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

[26]  Z. Bažant,et al.  CRACK SHEAR IN CONCRETE: CRACK BAND MICROPLANE MODEL , 1984 .

[27]  L. Cedolin,et al.  Fracturing material models based on micromechanical concepts: recent advances , 2004 .

[28]  Ferhun C. Caner,et al.  MICROPLANE MODEL M4 FOR CONCRETE: II. ALGORITHM AND CALIBRATION , 2000 .

[29]  Ferhun C. Caner,et al.  Microplane Model M4 for Concrete. I: Formulation with Work-Conjugate Deviatoric Stress , 2000 .

[30]  P. Bazant,et al.  Efficient Numerical Integration on the Surface of a Sphere , 1986 .

[31]  Jacky Mazars,et al.  Prediction of the failure and size effect in concrete via a bi-scale damage approach , 1992 .

[32]  Matti Ristinmaa,et al.  FE-formulation of a nonlocal plasticity theory , 1996 .

[33]  Zdeněk P. Bažant,et al.  Stability against localization of softening into ellipsoids and bands: Parameter study , 1989 .

[34]  Zdenek P. Bazant,et al.  Nonlocal Damage Theory Based on Micromechanics of Crack Interactions , 1994 .

[35]  J. M. Reynouard,et al.  Mixed mode fracture in plain and reinforced concrete: some results on benchmark tests , 2000 .

[36]  Z. Bažant,et al.  Nonlocal Smeared Cracking Model for Concrete Fracture , 1988 .

[37]  Pere C. Prat,et al.  Microplane Model for Concrete. I: Stress-Strain Boundaries and Finite Strain , 1996 .

[38]  G. D. Luzio.  Over-nonlocal microplane model M4: Mode I fracture simulations , 2004 .

[39]  Bernard Budiansky,et al.  A Mathematical Theory of Plasticity Based on the Concept of Slip , 1949 .

[40]  Angelo Simone,et al.  Continuous - Discontinuous modelling of failure , 2003 .