Gradient-enhanced Coupled Plasticity-anisotropic Damage Model for Concrete Fracture: Computational Aspects and Applications

It is widely studied that classical continuum damage theory for concrete fracture exhibits an extreme sensitivity to the spatial discretization in the finite element simulations. This sensitivity is caused by the fact that the mathematical description becomes ill-posed at a certain level of accumulated damage. A well-posed problem can be recovered by using a gradient-enhanced damage model in which a material length scale is introduced as a localization limiter. In this work, a nonlocal gradient-enhanced fully coupled plastic-damage constitutive model for plain concrete is developed. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. In order to account for different effects under tensile and compressive loadings, nonlocal damage variables that account for the progressive degradation of mechanical properties under stress states of prevailing tension and compression and two internal length scales, one for tension and the other for compression, are introduced as localization limiters. Therefore, two nonlocal damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. In order to solve the time step problem, a decoupled elastic predictor and plastic corrector steps are performed first in the effective configuration where damage is absent, and then a nonlocal damage corrector step is applied in order to update the final stress state. The algorithmic treatment of both tension and compression is presented in a unified way. A simple procedure to calculate the gradient of the tensile/compressive damage variables is described which can be used directly without the need of intensive numerical modifications of an existing finite element code. The effectiveness of the proposed local model has been demonstrated in both uniaxial and biaxial tension and compression problems and compared with experimental data. Numerical results obtained with the proposed nonlocal model are compared with experimental results concerning bending of three-point notched and four-point notched concrete beams. As the mesh is refined, convergence of numerical results is observed both in terms of damage patterns and of the global response.

[1]  George Z. Voyiadjis,et al.  A direct finite element implementation of the gradient‐dependent theory , 2005 .

[2]  C. L. Chow,et al.  An anisotropic theory of elasticity for continuum damage mechanics , 1987 .

[3]  K. C. Valanis,et al.  A Global Damage Theory and the Hyperbolicity of the Wave Problem , 1991 .

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

[5]  Nikolaos Aravas,et al.  Finite element implementation of gradient plasticity models Part I: Gradient-dependent yield functions , 1998 .

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

[7]  George Z. Voyiadjis,et al.  Advances in Damage Mechanics: Metals and Metal Matrix Composites With an Introduction to Fabric Tensors , 1999 .

[8]  J. Pamin,et al.  Gradient-dependent plasticity in numerical simulation of localization phenomena , 1994 .

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

[10]  George Z. Voyiadjis,et al.  A Finite Strain Plastic-damage Model for High Velocity Impacts using Combined Viscosity and Gradient Localization Limiters: Part II - Numerical Aspects and Simulations , 2006 .

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

[12]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

[13]  Dusan Krajcinovic,et al.  Damage tensors and the crack density distribution , 1993 .

[14]  Anthony N. Palazotto,et al.  Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory , 2004 .

[15]  Gilles Pijaudier-Cabot,et al.  Coupled damage and plasticity modelling in transient dynamic analysis of concrete , 2002 .

[16]  Rashid K. Abu Al-Rub,et al.  A Finite Strain Plastic-damage Model for High Velocity Impact using Combined Viscosity and Gradient Localization Limiters: Part I - Theoretical Formulation , 2006 .

[17]  George Z. Voyiadjis,et al.  Plasticity model for concrete using the bounding surface concept , 1994 .

[18]  Josko Ozbolt,et al.  Plastic-damage model for concrete in principal directions , 2007 .

[19]  Hans Muhlhaus,et al.  A variational principle for gradient plasticity , 1991 .

[20]  Peter Gudmundson,et al.  A unified treatment of strain gradient plasticity , 2004 .

[21]  Zenon Mróz,et al.  A continuum model for plastic-brittle behaviour of rock and concrete , 1979 .

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

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

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

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

[26]  Ioannis Vardoulakis,et al.  A finite element displacement formulation for gradient elastoplasticity , 2001, Bifurcation and Localisation Theory in Geomechanics.

[27]  G. E. Warren,et al.  Fracture energy for three-point-bend tests on single-edge-notched beams , 1988 .

[28]  F. Sidoroff,et al.  Description of Anisotropic Damage Application to Elasticity , 1981 .

[29]  Kenneth Runesson,et al.  An adaptive finite element algorithm for gradient theory of plasticity with coupling to damage , 2000 .

[30]  N.-Q. Pan,et al.  Finite difference computation of the aerodynamic interference of wing—pylon—store combinations at transonic speeds , 1983 .

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

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

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

[34]  René Chambon,et al.  Large strain finite element analysis of a local second gradient model: application to localization , 2002 .

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

[36]  Jerzy Pamin,et al.  Two gradient plasticity theories discretized with the element-free Galerkin method , 2003 .

[37]  Jacky Mazars,et al.  Orthotropic behavior of concrete with directional aspects: modelling and experiments , 1992 .

[38]  Mgd Marc Geers,et al.  On coupled gradient-dependent plasticity and damage theories with a view to localization analysis , 1999 .

[39]  Lars Pilgaard Mikkelsen.  Post-necking behaviour modelled by a gradient dependent plasticity theory , 1997 .

[40]  Dusan Krajcinovic,et al.  CONTINUUM DAMAGE MECHANICS , 1984 .

[41]  S. Ramaswamya,et al.  Finite element implementation of gradient plasticity models Part I : Gradient-dependent yield functions , 2022 .

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

[43]  Dusan Krajcinovic,et al.  The Continuous Damage Theory of Brittle Materials, Part 1: General Theory , 1981 .

[44]  James O. Jirsa,et al.  Behavior of concrete under compressive loadings , 1969 .

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

[46]  B. Nedjar,et al.  Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects , 2001 .

[47]  Eugenio Oñate,et al.  A constitutive model for cracking of concrete based on the incremental theory of plasticity , 1988 .

[48]  George Z. Voyiadjis,et al.  On the coupling of anisotropic damage and plasticity models for ductile materials , 2003 .

[49]  Nikolaos Aravas,et al.  Finite element implementation of gradient plasticity models Part II: Gradient-dependent evolution equations , 1998 .

[50]  Z. Bažant,et al.  Plastic-Fracturing Theory for Concrete , 1979 .

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

[52]  R. Borst,et al.  Phenomenological nonlocal approaches based on implicit gradient-enhanced damage , 2000 .

[53]  Paul Steinmann,et al.  Theory and numerics of geometrically non-linear gradient plasticity , 2003 .

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

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

[56]  Claudia Comi,et al.  A GENERALIZED VARIABLE FORMULATION FOR GRADIENT DEPENDENT SOFTENING PLASTICITY , 1996 .

[57]  Sumio Murakami,et al.  A Continuum Theory of Creep and Creep Damage , 1981 .

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

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

[60]  Stavroula J. Pantazopoulou,et al.  Plasticity Model for Concrete under Triaxial Compression , 2001 .

[61]  Ekkehard Ramm,et al.  An anisotropic gradient damage model for quasi-brittle materials , 2000 .

[62]  Anthony N. Palazotto,et al.  Non-local coupling of viscoplasticity and anisotropic viscodamage for impact problems using the gradient theory , 2003 .

[63]  H. Zbib,et al.  On the gradient-dependent theory of plasticity and shear banding , 1992 .

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

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

[66]  Jian Chen,et al.  A micro‐mechanical damage model based on gradient plasticity: algorithms and applications , 2002 .

[67]  Abu Al-Rub,et al.  Material length scales in gradient-dependent plasticity/damage and size effects: theory and computation , 2004 .

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

[69]  George Z. Voyiadjis,et al.  Multiscale Analysis of Multiple Damage Mechanisms Coupled with Inelastic Behavior of Composite Materials , 2001 .

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

[71]  Jerzy Pamin,et al.  Dispersion analysis and element‐free Galerkin solutions of second‐ and fourth‐order gradient‐enhanced damage models , 2000 .

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

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

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

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

[76]  D. Borst,et al.  Fundamental issues in finite element analyses of localization of deformation , 1993 .

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

[78]  Dusan Krajcinovic,et al.  Continuous Damage Mechanics Revisited: Basic Concepts and Definitions , 1985 .

[79]  Jerzy Pamin,et al.  Some novel developments in finite element procedures for gradient-dependent plasticity , 1996 .

[80]  E. Aifantis.  On the Microstructural Origin of Certain Inelastic Models , 1984 .

[81]  Rui Faria,et al.  An energy release rate-based plastic-damage model for concrete , 2006 .

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

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