Thermodynamic‐based model for coupling temperature‐dependent viscoelastic, viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Based on the continuum damage mechanics, a general and comprehensive thermodynamic‐based framework for coupling the temperature‐dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery‐type nonlinear viscoelasticity, Perzyna‐type viscoplasticity, and a viscodamage model analogous to the Perzyna‐type viscoplasticity. The resulting constitutive equations are implemented in the well‐known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep‐recovery, creep, uniaxial constant strain rate, and repeated creep‐recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  J. H. Hollomon,et al.  Effect of Strain Rate Upon Plastic Flow of Steel , 1944 .

[2]  Maurice A. Biot,et al.  Theory of Stress‐Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena , 1954 .

[3]  D. C. Drucker,et al.  Soil Mechanics and Work-Hardening Theories of Plasticity , 1955 .

[4]  Walter Noll,et al.  The thermodynamics of elastic materials with heat conduction and viscosity , 1963 .

[5]  Piotr Perzyna,et al.  The constitutive equations for rate sensitive plastic materials , 1963 .

[6]  Walter Noll,et al.  The thermodynamics of elastic materials with heat conduction and viscosity , 1963 .

[7]  Richard Schapery,et al.  Application of Thermodynamics to Thermomechanical, Fracture, and Birefringent Phenomena in Viscoelastic Media , 1964 .

[8]  M. Gurtin,et al.  Thermodynamics with Internal State Variables , 1967 .

[9]  F. A. Leckie,et al.  Creep problems in structural members , 1969 .

[10]  Richard Schapery.  On the characterization of nonlinear viscoelastic materials , 1969 .

[11]  P. Perzyna.  Thermodynamic Theory of Viscoplasticity , 1971 .

[12]  Lee Davison,et al.  Thermomechanical constitution of spalling elastic bodies , 1973 .

[13]  Richard Schapery,et al.  A theory of crack initiation and growth in viscoelastic media II. Approximate methods of analysis , 1975, International Journal of Fracture.

[14]  Richard Schapery,et al.  A theory of crack initiation and growth in viscoelastic media , 1975 .

[15]  Richard Schapery,et al.  A theory of crack initiation and growth in viscoelastic media , 1975 .

[16]  M. E. Kipp,et al.  Theory of spall damage accumulation in ductile metals , 1977 .

[17]  F. Cozzarelli,et al.  Non-linear creep damage under one-dimensional variable tensile stress , 1979 .

[18]  R. Wool,et al.  A theory crack healing in polymers , 1981 .

[19]  Matthew Tirrell,et al.  The healing process at polymer–polymer interfaces , 1981 .

[20]  D. Krajcinovic,et al.  Continuum Damage Mechanics of Fiber Reinforced Concrete , 1985 .

[21]  Piotr Perzyna,et al.  Internal state variable description of dynamic fracture of ductile solids , 1986 .

[22]  F. A. Cozzarelli,et al.  One-dimensional strain-dependent creep damage in inhomogeneous materials , 1986 .

[23]  J. C. Simo,et al.  On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects , 1987 .

[24]  Richard Schapery,et al.  Deformation and fracture characterization of inelastic composite materials using potentials , 1987 .

[25]  Y. Weitsman.  A Continuum Damage Model for Viscoelastic Materials , 1988 .

[26]  Masanobu Oda,et al.  Yield Function for Soil with Anisotropic Fabric , 1989 .

[27]  George Z. Voyiadjis,et al.  A coupled theory of damage mechanics and finite strain elasto-plasticity—II. Damage and finite strain plasticity , 1990 .

[28]  Wai-Fah Chen,et al.  Nonlinear analysis in soil mechanics : theory and implementation , 1990 .

[29]  D. Little,et al.  ONE-DIMENSIONAL CONSTITUTIVE MODELING OF ASPHALT CONCRETE , 1990 .

[30]  Zdeněk P. Bažant,et al.  Mechanics of solid materials , 1992 .

[31]  George Z. Voyiadjis,et al.  A plasticity-damage theory for large deformation of solids—I. Theoretical formulation , 1992 .

[32]  G. Gazonas.  A uniaxial nonlinear viscoelastic constitutive model with damage for M30 gun propellant , 1993 .

[33]  N. D. Cristescu,et al.  A procedure to determine nonassociated constitutive equations for geomaterials , 1994 .

[34]  Delia Florea,et al.  Nonassociated elastic/viscoplastic model for bituminous concrete , 1994 .

[35]  D. Krajcinovic,et al.  Some fundamental issues in rate theory of damage-elastoplasticity , 1995 .

[36]  Y. Richard Kim,et al.  A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete , 1996 .

[37]  George Z. Voyiadjis,et al.  Micro and macro anisotropic cyclic damage-plasticity models for MMCS , 1997 .

[38]  Richard Schapery.  Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics , 1997 .

[39]  Y. Kim,et al.  VISCOELASTIC CONTINUUM DAMAGE MODEL OF ASPHALT CONCRETE WITH HEALING , 1998 .

[40]  J. C. Simo,et al.  Numerical analysis and simulation of plasticity , 1998 .

[41]  Y. Lu,et al.  Numerical approach of visco-elastoplastic analysis for asphalt mixtures , 1998 .

[42]  G. Cederbaum,et al.  Postbuckling of non-linear viscoelastic imperfect laminated plates Part I: material considerations , 1998 .

[43]  F. Leckie.  A course on damage mechanics , 1998 .

[44]  P. Perzyna,et al.  Analysis of the influence of various effects on criteria for adiabatic shear band localization in single crystals , 1998 .

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

[46]  Taehyo Park,et al.  Chapter 16 – The Kinematics of Damage for Finite-Strain Elasto-Plastic Solids , 1999 .

[47]  Richard Schapery.  Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage , 1999 .

[48]  Y. Kim,et al.  CONTINUUM DAMAGE MECHANICS-BASED FATIGUE MODEL OF ASPHALT CONCRETE , 2000 .

[49]  Min Zhou,et al.  Dynamic behavior of concrete at high strain rates and pressures: II. numerical simulation , 2001 .

[50]  Jay D. Humphrey,et al.  A mixture theory for heat-induced alterations in hydration and mechanical properties in soft tissues , 2001 .

[51]  L. Bousshine,et al.  Softening in stress-strain curve for Drucker-Prager non-associated plasticity , 2001 .

[52]  D. Perreux,et al.  A meso–macro finite element modelling of laminate structures: Part I: time-independent behaviour , 2002 .

[53]  D. Little,et al.  Characterization of microdamage and healing of asphalt concrete mixtures , 2002 .

[54]  C. Schwartz,et al.  Time-Temperature Superposition for Asphalt Concrete at Large Compressive Strains , 2002 .

[55]  Matthew W Witczak,et al.  Viscoelastic, Viscoplastic, and Damage Modeling of Asphalt Concrete in Unconfined Compression , 2003 .

[56]  G. Voyiadjis,et al.  Thermodynamic based model for the evolution equation of the backstress in cyclic plasticity , 2003 .

[57]  Cor Kasbergen,et al.  Development and Finite Element Implementation of Stress-Dependent Elastoviscoplastic Constitutive Model with Damage for Asphalt , 2003 .

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

[59]  Robert L. Lytton,et al.  Damage evolution in triaxial compression tests of HMA at high temperatures , 2004 .

[60]  Rami Haj-Ali,et al.  Numerical finite element formulation of the Schapery non‐linear viscoelastic material model , 2004 .

[61]  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 .

[62]  Dallas N. Little,et al.  Viscoplastic modeling of asphalt mixes with the effects of anisotropy, damage and aggregate characteristics , 2005 .

[63]  Samer Dessouky,et al.  Multiscale approach for modeling hot mix asphalt , 2005 .

[64]  Jacob Uzan.  Viscoelastic-Viscoplastic Model with Damage for Asphalt Concrete , 2005 .

[65]  G. Voyiadjis,et al.  Theory of creep deformation with kinematic hardening for materials with different properties in tension and compression , 2005 .

[66]  Dallas N. Little,et al.  A microstructure-based viscoplastic model for asphalt concrete , 2005 .

[67]  J. Lemaître,et al.  Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures , 2005 .

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

[69]  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 .

[70]  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 .

[71]  Samuel H Carpenter,et al.  DISSIPATED ENERGY CONCEPTS FOR HMA PERFORMANCE: FATIGUE AND HEALING , 2006 .

[72]  George Z. Voyiadjis,et al.  A thermodynamic based higher-order gradient theory for size dependent plasticity , 2007 .

[73]  Dallas N. Little,et al.  Computational Constitutive Model for Predicting Nonlinear Viscoelastic Damage and Fracture Failure of Asphalt Concrete Mixtures , 2007 .

[74]  Dallas N. Little,et al.  Development of an Elastoviscoplastic Microstructural-Based Continuum Model to Predict Permanent Deformation in Hot Mix Asphalt , 2007 .

[75]  Hussain U Bahia,et al.  Nonlinearly viscoelastic analysis of asphalt mixes subjected to shear loading , 2007 .

[76]  Dallas N. Little,et al.  Exploring Mechanism of H ealing in Asphalt Mixtures and Quantifying its Impact , 2007 .

[77]  D. Little,et al.  Characterization of Asphalt Mix Response under Repeated Loading Using Anisotropic Nonlinear Viscoelastic-Viscoplastic Model , 2007 .

[78]  A. Muliana,et al.  A multi-scale framework for layered composites with thermo-rheologically complex behaviors , 2008 .

[79]  Dallas N. Little,et al.  A Framework to Quantify the Effect of Healing in Bituminous Materials using Material Properties , 2008 .

[80]  Elhem Ghorbel,et al.  A viscoplastic constitutive model for polymeric materials , 2008 .

[81]  R. Sullivan.  Development of a viscoelastic continuum damage model for cyclic loading , 2008 .

[82]  Eyad Masad,et al.  Nonlinear viscoelastic analysis of unaged and aged asphalt binders , 2008 .

[83]  Michael D. Gilchrist,et al.  On the development and parameter identification of Schapery-type constitutive theories , 2008 .

[84]  Lianghao Han,et al.  A modified Drucker-Prager Cap model for die compaction simulation of pharmaceutical powders , 2008 .

[85]  Chien-Wei Huang,et al.  Development and numerical implementation of nonlinear viscoelastic-viscoplastic model for asphalt materials , 2009 .

[86]  Sun-Myung Kim,et al.  Predicting mesh-independent ballistic limits for heterogeneous targets by a nonlocal damage computational framework , 2009 .

[87]  Eyad Masad,et al.  Improving the Sustainability of Asphalt Pavements through Developing a Predictive Model with Fundamental Material Properties , 2009 .

[88]  Dallas N. Little,et al.  A micro-damage healing model that improves prediction of fatigue life in asphalt mixes , 2010 .

[89]  Dallas N. Little,et al.  Use of Molecular Dynamics to Investigate Self-Healing Mechanisms in Asphalt Binders , 2011 .

[90]  Masoud K. Darabi,et al.  A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials , 2011 .