Development of an approach to constitutive modelling of concrete : Isotropic damage coupled with plasticity

The paper presents an approach to constitutive modelling of concrete using damage mechanics and plasticity theory. The thermodynamic formulation, and parameter identification of a non-local coupled damage-plasticity model are presented in this study. The particular focus is the calibration of model parameters. It is shown that both the local parameters and the parameters governing the non-local interaction can be determined from experimental data reliably and consistently. A novel procedure is developed for parameter identification, using the separation of total dissipation energy into additive parts corresponding to different dissipation mechanisms. The relationship between the local and non-local parameters is also addressed, helping to obtain model responses consistent with the fracture energy of the material. The application of the model and the calibration procedure proposed in this study to the numerical failure analysis of concrete structures is illustrated through a series of real structural tests, showing both the performance of the model and the consistency of the proposed calibration procedure.

[1]  Jeeho Lee,et al.  Plastic-Damage Model for Cyclic Loading of Concrete Structures , 1998 .

[2]  F. Meftah,et al.  A multilayered mixed beam element in gradient plasticity for the analysis of localized failure modes , 1998 .

[3]  Ignacio Carol,et al.  A two-surface anisotropic damage/plasticity model for plain concrete , 2000 .

[4]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[5]  Sergio Oller,et al.  Coupled plastic-damaged model , 1996 .

[6]  Giang D. Nguyen,et al.  Damage-Plasticity Modelling of Concrete: Calibration of Parameters using Separation of Fracture Energy , 2006 .

[7]  J. Mier,et al.  Crack Interaction in Concrete , 2005 .

[8]  Giang D. Nguyen,et al.  A coupled damage–plasticity model for concrete based on thermodynamic principles: Part I: model formulation and parameter identification , 2008 .

[9]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—II. Computational aspects , 1987 .

[10]  Zdenek P. Bazant,et al.  ANALYSIS OF WORK-OF-FRACTURE METHOD FOR MEASURING FRACTURE ENERGY OF CONCRETE , 1996 .

[11]  Jan Carmeliet,et al.  Optimal estimation of gradient damage parameters from localization phenomena in quasi‐brittle materials , 1999 .

[12]  Jerzy Pamin,et al.  Gradient plasticity in numerical simulation of concrete cracking , 1996 .

[13]  Kaspar Willam,et al.  A coupled elastoplastic damage model for geomaterials , 2004 .

[14]  E. Sacco,et al.  A plastic nonlocal damage model , 2002 .

[15]  J. Rots Computational modeling of concrete fracture , 1988 .

[16]  Jiann-Wen Ju,et al.  ISOTROPIC AND ANISOTROPIC DAMAGE VARIABLES IN CONTINUUM DAMAGE MECHANICS , 1990 .

[17]  Giang D. Nguyen,et al.  Non‐local damage modelling of concrete: a procedure for the determination of model parameters , 2007 .

[18]  Giang D. Nguyen,et al.  A coupled damage–plasticity model for concrete based on thermodynamic principles: Part II: non‐local regularization and numerical implementation , 2008 .

[19]  M. Elices,et al.  The cohesive zone model: advantages, limitations and challenges , 2002 .

[20]  Anthony Duncan Jefferson,et al.  Craft - a plastic-damage-contact model for concrete II. Model implementation with implicit return-mapping algorithm and consistent tangent matrix , 2003 .

[21]  Z. Bažant,et al.  Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories , 1993 .

[22]  D. Beskos,et al.  Static analysis of 3D damaged solids and structures by BEM , 2002 .

[23]  Roman Lackner,et al.  An anisotropic elastoplastic‐damage model for plain concrete , 1998 .

[24]  Jeeho Lee,et al.  A plastic-damage concrete model for earthquake analysis of dams , 1998 .

[25]  Ellen Kuhl,et al.  Parameter identification of gradient enhanced damage models with the finite element method , 1999 .

[26]  P. H. Feenstra,et al.  Constitutive Model for Reinforced Concrete , 1995 .

[27]  Hans W. Reinhardt,et al.  Tensile Tests and Failure Analysis of Concrete , 1986 .

[28]  Milan Jirásek,et al.  Size effect on fracture energy induced by non‐locality , 2004 .

[29]  Jean-François Dubé,et al.  Calibration of nonlocal damage model from size effect tests , 2003 .

[30]  Anthony Duncan Jefferson,et al.  Craft––a plastic-damage-contact model for concrete. I. Model theory and thermodynamic considerations , 2003 .

[31]  Gilles Pijaudier-Cabot,et al.  Measurement of Characteristic Length of Nonlocal Continuum , 1989 .

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

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

[34]  M. Jirásek,et al.  Plastic model with non‐local damage applied to concrete , 2006 .

[35]  Claudia Comi,et al.  A non-local model with tension and compression damage mechanisms , 2001 .

[36]  Gro Markeset,et al.  Softening of concrete in compression — Localization and size effects , 1995 .

[37]  Francis Tin-Loi,et al.  Parameter identification of quasibrittle materials as a mathematical program with equilibrium constraints , 2001 .

[38]  G. Nguyen A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory , 2005 .

[39]  René de Borst,et al.  Gradient-dependent plasticity: formulation and algorithmic aspects , 1992 .

[40]  Howard L. Schreyer,et al.  Modelling surface orientation and stress at failure of concrete and geological materials , 2007 .

[41]  D. Hordijk TENSILE AND TENSILE FATIGUE BEHAVIOUR OF CONCRETE; EXPERIMENTS, MODELLING AND ANALYSES , 1992 .

[42]  Daichao Sheng,et al.  Shear banding analysis of geomaterials by strain gradient enhanced damage model , 2005 .

[43]  I. M. May,et al.  A LOCAL ARC-LENGTH PROCEDURE FOR STRAIN SOFTENING , 1997 .

[44]  Gilles Pijaudier-Cabot,et al.  From damage to fracture mechanics and conversely: A combined approach , 1996 .

[45]  Z. Bažant Concrete fracture models: testing and practice , 2002 .

[46]  Alexander M. Puzrin,et al.  A thermomechanical framework for constitutive models for rate-independent dissipative materials , 2000 .

[47]  Milan Jirásek,et al.  Consistent tangent stiffness for nonlocal damage models , 2002 .

[48]  Philip C. Perdikaris,et al.  Size Effect on Fracture Energy of Concrete and Stability Issues in Three-Point Bending Fracture Toughness Testing , 1995 .

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

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

[51]  D. Hordijk Local approach to fatigue of concrete , 1991 .

[52]  Francis Tin-Loi,et al.  An optimization approach for indirect identification of cohesive crack properties , 2002 .

[53]  P. Petersson Crack growth and development of fracture zones in plain concrete and similar materials , 1981 .

[54]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1987 .

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

[56]  L. Ferrara,et al.  MODE I FRACTURE BEHAVIOR IN CONCRETE: NONLOCAL DAMAGE MODELING , 2001 .

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