New methodology for calculating damage variables evolution in Plastic Damage Model for RC structures

The behavior of reinforced concrete (RC) structures under severe demands, as strong ground motions, is highly complex; this is mainly due to joint operation of concrete and steel, with several coupled failure modes. Furthermore, given the increasing awareness and concern for the important seismic worldwide risk, new developments have arisen in earthquake engineering. Nonetheless, simplified numerical models are widely used (given their moderate computational cost), and many developments rely mainly on them. The authors have started a long-term research whose final objective is to provide, by using advanced numerical models, solid basis for these developments. Those models are based on continuum mechanics, and consider Plastic Damage Model to simulate concrete behavior. Within this context, this paper presents a new methodology to calculate damage variables evolution; the proposed approach is based in the Lubliner/Lee/Fenves formulation and provides closed-form expressions of the compressive and tensile damage variables in terms of the corresponding strains. This methodology does not require calibration with experimental results and incorporates a strategy to avoid mesh-sensitivity. A particular algorithm, suitable for implementation in Abaqus, is described. Mesh-insensitivity is validated in a simple tension example. Accuracy and reliability are verified by simulating a cyclic experiment on a plain concrete specimen. Two laboratory experiments consisting in pushing until failure two 2-D RC frames are simulated with the proposed approach to investigate its ability to reproduce actual monotonic behavior of RC structures; the obtained results are also compared with the aforementioned simplified models that are commonly employed in earthquake engineering.

[1]  Farhad Aslani,et al.  Stress–strain model for concrete under cyclic loading , 2012 .

[2]  Milan Jirásek,et al.  Embedded crack model: I. Basic formulation , 2001 .

[3]  B. Sinha,et al.  STRESS - STRAIN RELATIONS FOR CONCRETE UNDER CYCLIC LOADING , 1964 .

[4]  Glaucio H. Paulino,et al.  Evolutionary characteristic length method for smeared cracking finite element models , 1997 .

[5]  Z. Bažant,et al.  Nonlocal Continuum Damage, Localization Instability and Convergence , 1988 .

[6]  Antonio Huerta,et al.  An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model , 2006 .

[7]  W. Krätzig,et al.  An elasto-plastic damage model for reinforced concrete with minimum number of material parameters , 2004 .

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

[9]  Ted Belytschko,et al.  Continuum Theory for Strain‐Softening , 1984 .

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

[11]  R. A. Vonk,et al.  Softening of concrete loaded in compression , 1992 .

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

[13]  J. Mazars.  APPLICATION DE LA MECANIQUE DE L'ENDOMMAGEMENT AU COMPORTEMENT NON LINEAIRE ET A LA RUPTURE DU BETON DE STRUCTURE , 1984 .

[14]  Jack P. Moehle,et al.  "BUILDING CODE REQUIREMENTS FOR STRUCTURAL CONCRETE (ACI 318-11) AND COMMENTARY" , 2011 .

[15]  F. Vecchio,et al.  Shear Deformations in Reinforced Concrete Frames , 1993 .

[16]  Gilles Pijaudier-Cabot,et al.  Isotropic and anisotropic descriptions of damage in concrete structures , 1999 .

[17]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[18]  Chanakya Arya,et al.  Buckling resistance of unstiffened webs , 2009 .

[19]  Ziad N. Taqieddin,et al.  Anisotropic damage-plasticity model for concrete , 2008 .

[20]  Sun-Myung Kim,et al.  Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture , 2010 .

[21]  J. Oliver,et al.  A strain-based plastic viscous-damage model for massive concrete structures , 1998 .

[22]  Michael D. Kotsovos,et al.  Effect of testing techniques on the post-ultimate behaviour of concrete in compression , 1983 .

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

[24]  Milan Jirásek,et al.  Damage-plastic model for concrete failure , 2006 .

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

[26]  Sergio Oller,et al.  A numerical model of the structural behavior of buckling-restrained braces , 2012 .

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

[28]  T. Belytschko,et al.  A finite element with embedded localization zones , 1988 .

[29]  A. H. Marchertas,et al.  Concrete model with normality and sequential identification , 1987 .

[30]  Egidio Rizzi,et al.  On the formulation of anisotropic elastic degradation.: II. Generalized pseudo-Rankine model for tensile damage , 2001 .

[31]  Alex H. Barbat,et al.  Plastic‐damage analysis of reinforced concrete frames , 2010 .

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

[33]  Wai-Fah Chen,et al.  CONSTITUTIVE RELATIONS FOR CONCRETE , 1975 .

[34]  J.G.M. van Mier,et al.  Strain-softening of concrete under multiaxial loading conditions , 1984 .

[35]  Tao Yu,et al.  Finite element modeling of confined concrete-II: Plastic-damage model , 2010 .

[36]  R. Borst,et al.  Non-Associated Plasticity for Soils, Concrete and Rock , 1984 .

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

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

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

[40]  J. Mier,et al.  Concrete Fracture: A Multiscale Approach , 2012 .

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

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

[43]  George Z. Voyiadjis,et al.  Gradient-enhanced Coupled Plasticity-anisotropic Damage Model for Concrete Fracture: Computational Aspects and Applications , 2009 .

[44]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1989 .

[45]  Ulrich Häussler-Combe,et al.  Formulation and numerical implementation of a constitutive law for concrete with strain-based damage and plasticity , 2008 .

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

[47]  Gilles Pijaudier-Cabot,et al.  CONTINUUM DAMAGE THEORY - APPLICATION TO CONCRETE , 1989 .

[48]  J. Oliver.  A consistent characteristic length for smeared cracking models , 1989 .

[49]  Filip C. Filippou,et al.  Evaluation of Nonlinear Frame Finite-Element Models , 1997 .

[50]  F. Filippou,et al.  Mixed formulation of nonlinear beam finite element , 1996 .

[51]  Alex H. Barbat,et al.  Viscous damage model for timoshenko beam structures , 1997 .

[52]  D. Oliveira,et al.  Comparison of cyclic response of reinforced concrete infilled frames with experimental results , 2008 .

[53]  Serhan Guner,et al.  Performance Assessment of Shear-critical Reinforced Concrete Plane Frames , 2009 .

[54]  Laurent Daudeville,et al.  Compaction and tensile damage in concrete: constitutive modelling and application to dynamics , 2000 .

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

[56]  Y. J. Kang.  Nonlinear geometric, material and time dependent analysis of reinforced and prestressed concrete frames , 1977 .

[57]  Giang D. Nguyen,et al.  Development of an approach to constitutive modelling of concrete : Isotropic damage coupled with plasticity , 2008 .

[58]  Noël Challamel,et al.  Strain-based anisotropic damage modelling and unilateral effects , 2005 .

[59]  Horia Alejandro Barbat Barbat,et al.  Plastic damage model for nonlinear reinforced concrete frames analysis , 2005 .

[60]  R. Vonk,et al.  Fracture of concrete under multiaxial stress-recent developments , 1991 .

[61]  F. L. Almansa,et al.  Modelización numérica del comportamiento estructural cíclico de barras esbeltas de acero con pandeo restringido , 2014 .

[62]  Sanjay Govindjee,et al.  Anisotropic modelling and numerical simulation of brittle damage in concrete , 1995 .

[63]  Surendra P. Shah,et al.  Effect of Length on Compressive Strain Softening of Concrete , 1997 .

[64]  Rhj Ron Peerlings,et al.  Gradient‐enhanced damage modelling of concrete fracture , 1998 .

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

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

[67]  George Z. Voyiadjis,et al.  A plasticity and anisotropic damage model for plain concrete , 2007 .

[68]  Konstantinos V. Spiliopoulos,et al.  3D Solid Finite-Element Analysis of Cyclically Loaded RC Structures Allowing Embedded Reinforcement Slippage , 2008 .