Review of Hierarchical Multiscale Modeling to Describe the Mechanical Behavior of Amorphous Polymers

Modern computational methods have proved invaluable for the design and analysis of structural components using lightweight materials. The challenge of optimizing lightweight materials in the design of industrial components relates to incorporating structure-property relationships within the computational strategy to incur robust designs. One effective methodology of incorporating structure-property relationships within a simulation-based design framework is to employ a hierarchical multiscale modeling strategy. This paper reviews techniques of multiscale modeling to predict the mechanical behavior of amorphous polymers. Hierarchical multiscale methods bridge nanoscale mechanisms to the macroscale/continuum by introducing a set of structure-property relationships. This review discusses the current state of the art and challenges for three distinct scales: quantum, atomistic/coarse graining, and continuum mechanics. For each scale, we review the modeling techniques and tools, as well as discuss important recent contributions. To help focus the review, we have mainly considered research devoted to amorphous polymers.

[1]  이태규.  Theory of Non-Newtonian Flow , 1974 .

[2]  Ulrich W. Suter,et al.  Atomistic modeling of mechanical properties of polymeric glasses , 1986 .

[3]  Erhard Krempl,et al.  Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers , 2003 .

[4]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[5]  P. M. Naghdi,et al.  On continuum thermodynamics , 1972 .

[6]  John W. Wilkins,et al.  Simple bias potential for boosting molecular dynamics with the hyperdynamics scheme , 1998 .

[7]  Mark S. Gordon,et al.  Approximate Self‐Consistent Molecular‐Orbital Theory. VI. INDO Calculated Equilibrium Geometries , 1968 .

[8]  J. Pople,et al.  Approximate Self-Consistent Molecular Orbital Theory. I. Invariant Procedures , 1965 .

[9]  Marc S. Lavine,et al.  Molecular dynamics simulation of orientation and crystallization of polyethylene during uniaxial extension , 2003 .

[10]  B. Montanari,et al.  DENSITY FUNCTIONAL STUDY OF CRYSTALLINE POLYETHYLENE , 1997 .

[11]  W. Schröer,et al.  Conformational analysis of symmetric carbonic acid esters by quantum chemical calculations and dielectric measurements , 1991 .

[12]  David J. Benson,et al.  Strain-rate effects in rheological models of inelastic response , 2003 .

[13]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[14]  U. F. Kocks,et al.  A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable , 1988 .

[15]  Bruce A. Finlayson,et al.  Exit Pressure Experiments for Low Density Polyethylene Melts , 1988 .

[16]  Vincenzo Barone,et al.  Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models , 1998 .

[17]  Geoffrey J. Frank,et al.  A viscoelastic–viscoplastic constitutive model for glassy polymers , 2001 .

[18]  M. Boyce,et al.  A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials , 1993 .

[19]  Emily A. Carter,et al.  Challenges in Modeling Materials Properties Without Experimental Input , 2008, Science.

[20]  Kurt Binder,et al.  The influence of the cooling rate on the glass transition and the glassy state in three-dimensional dense polymer melts: a Monte Carlo study , 1993 .

[21]  J. Shepherd,et al.  Multiscale modeling of the deformation of semi-crystalline polymers , 2006 .

[22]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[23]  Doug McLean,et al.  Chain conformations of polycarbonate from ab initio calculations , 1988 .

[24]  Arnold T. Hagler,et al.  An ab Initio CFF93 All-Atom Force Field for Polycarbonates , 1994 .

[25]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[26]  P. Mark Henrichs,et al.  Ring dynamics in a crystalline analog of bisphenol A polycarbonate , 1988 .

[27]  Yoshihiro Tomita,et al.  Molecular dynamics simulation of deformation behavior in amorphous polymer: nucleation of chain entanglements and network structure under uniaxial tension , 2003 .

[28]  D. McDowell,et al.  High cycle fatigue mechanisms in a cast AM60B magnesium alloy , 2002 .

[29]  P. J. Flory,et al.  Analysis of the random configuration of the polycarbonate of diphenylol‐2,2′‐propane , 1968 .

[30]  Mark F. Horstemeyer,et al.  From Atoms to Autos - A new Design Paradigm Using Microstructure-Property Modeling Part 1: Monotonic Loading Conditions , 2001 .

[31]  R. Parr.  Density-functional theory of atoms and molecules , 1989 .

[32]  S. Nosé.  A unified formulation of the constant temperature molecular dynamics methods , 1984 .

[33]  Kurt Kremer,et al.  The Effect of Bond Length on the Structure of Dense Bead-Spring Polymer Melts , 2001 .

[34]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[35]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .

[36]  Kurt Kremer,et al.  STRUCTURE AND RELAXATION OF END-LINKED POLYMER NETWORKS , 1994 .

[37]  Gregory M. Odegard,et al.  Nonlinear multiscale modeling of polymer materials , 2007 .

[38]  Matthew L. Leininger,et al.  Is Mo/ller–Plesset perturbation theory a convergent ab initio method? , 2000 .

[39]  A. I. Leonov.  Nonequilibrium thermodynamics and rheology of viscoelastic polymer media , 1976 .

[40]  Oscar Lopez-Pamies,et al.  Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures , 2006 .

[41]  A. Argon.  A theory for the low-temperature plastic deformation of glassy polymers , 1973 .

[42]  Serdar Göktepe,et al.  Finite viscoplasticity of amorphous glassy polymers in the logarithmic strain space , 2009 .

[43]  William A. Goddard,et al.  Mechanical properties and force field parameters for polyethylene crystal , 1991 .

[44]  Kurt Kremer,et al.  Structure-property correlation of polymers, a Monte Carlo approach , 1991 .

[45]  J. Koelman,et al.  Dynamic simulations of hard-sphere suspensions under steady shear , 1993 .

[46]  J. Jäckle,et al.  Models of the glass transition , 1986 .

[47]  Kurt Kremer,et al.  Multiscale Problems in Polymer Science: Simulation Approaches , 2001 .

[48]  William A. Curtin,et al.  A coupled atomistic/continuum model of defects in solids , 2002 .

[49]  R. Callen,et al.  Thermodynamics and an Introduction to Thermostatistics, 2nd Edition , 1985 .

[50]  Ozgen U. Colak,et al.  Modeling deformation behavior of polymers with viscoplasticity theory based on overstress , 2005 .

[51]  Mark F. Horstemeyer,et al.  Integration of Basic Materials Research Into the Design of Cast Components by a Multi-Scale Methodology , 2000 .

[52]  Doros N. Theodorou,et al.  Hierarchical modelling of polymeric materials , 2007 .

[53]  Juan J. de Pablo,et al.  Multiscale Modeling in Advanced Materials Research: Challenges, Novel Methods, and Emerging Applications , 2007 .

[54]  G. Maugin.  The Thermomechanics of Plasticity and Fracture , 1992 .

[55]  Gerhard A. Holzapfel,et al.  Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science , 2000 .

[56]  R. Yaris,et al.  Local Mechanism of Phenyl Ring π-Flips in Glassy Polycarbonate , 1997 .

[57]  Wang,et al.  Generalized gradient approximation for the exchange-correlation hole of a many-electron system. , 1996, Physical review. B, Condensed matter.

[58]  Rahmi Ozisik,et al.  Simulation of plastic deformation in glassy polymers: Atomistic and mesoscale approaches , 2005 .

[59]  Doros N. Theodorou,et al.  Understanding and predicting structure–property relations in polymeric materials through molecular simulations , 2004 .

[60]  D. W. Saunders,et al.  Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[61]  Michael J. S. Dewar,et al.  Ground states of molecules. XXV. MINDO/3. Improved version of the MINDO semiempirical SCF-MO method , 1975 .

[62]  Wam Marcel Brekelmans,et al.  A Constitutive Equation for the Elasto-Viscoplastic Deformation of Glassy Polymers , 1997 .

[63]  Jozef Bicerano,et al.  Intrachain rotations in the poly(ester carbonates). 2. Quantum-mechanical calculations on large model molecules fully representing each type of phenyl ring environment , 1988 .

[64]  Leon Le Govaert,et al.  Strain-hardening behavior of polycarbonate in the glassy state , 2000 .

[65]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[66]  L. Anand,et al.  A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part I: Formulation , 2009 .

[67]  Jean-Louis Chaboche,et al.  Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of metals and polymers , 1997 .

[68]  H. Sun,et al.  COMPASS: An ab Initio Force-Field Optimized for Condensed-Phase ApplicationsOverview with Details on Alkane and Benzene Compounds , 1998 .

[69]  G. Thackray,et al.  The use of a mathematical model to describe isothermal stress-strain curves in glassy thermoplastics , 1968, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[70]  K. Binder,et al.  On the construction of coarse‐grained models for linear flexible polymer chains: Distribution functions for groups of consecutive monomers , 1991 .

[71]  Haoyue Zhang,et al.  Finite deformation of a polymer: experiments and modeling , 2001 .

[72]  Mary C. Boyce,et al.  Monte Carlo Modeling of Amorphous Polymer Deformation: Evolution of Stress with Strain , 1999 .

[73]  Peter J. Ludovice,et al.  An atomistic model of the amorphous glassy polycarbonate of 4,4-isopropylidenediphenol , 1991 .

[74]  A. Szabo,et al.  Modern quantum chemistry , 1982 .

[75]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[76]  K. Krausz,et al.  Unified constitutive laws of plastic deformation , 1996 .

[77]  A. Voter.  A method for accelerating the molecular dynamics simulation of infrequent events , 1997 .

[78]  David L. Beveridge,et al.  Approximate molecular orbital theory , 1970 .

[79]  Kurt Binder,et al.  Off‐lattice Monte Carlo simulation of dilute and concentrated polymer solutions under theta conditions , 1993 .

[80]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[81]  Erhard Krempl,et al.  An Overstress Model for Solid Polymer Deformation Behavior Applied to Nylon 66 , 2000 .

[82]  Marvin L. Cohen,et al.  Electronic structure of solids , 1984 .

[83]  Kurt Kremer,et al.  Combined Coarse-Grained and Atomistic Simulation of Liquid Bisphenol A-Polycarbonate: Liquid Packing and Intramolecular Structure , 2003 .

[84]  H. Eyring.  Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates , 1936 .

[85]  J. Shepherd,et al.  Modeling morphology evolution and mechanical behavior during thermo-mechanical processing of semi-crystalline polymers , 2006 .

[86]  Mary C. Boyce,et al.  Mechanics of the rate-dependent elastic¿plastic deformation of glassy polymers from low to high strain rates , 2006 .

[87]  Lallit Anand,et al.  On modeling the micro-indentation response of an amorphous polymer , 2006 .

[88]  P. Knowles,et al.  An efficient second-order MC SCF method for long configuration expansions , 1985 .

[89]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[90]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[91]  Peter Fulde,et al.  Electron correlations in molecules and solids , 1991 .

[92]  William A. Goddard,et al.  The Hessian biased singular value decomposition method for optimization and analysis of force fields , 1996 .

[93]  M. Boyce,et al.  Large inelastic deformation of glassy polymers. part I: rate dependent constitutive model , 1988 .

[94]  M. Boyce,et al.  A constitutive model for the nonlinear viscoelastic viscoplastic behavior of glassy polymers , 1995 .

[95]  David L. McDowell,et al.  A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 1: Development of Appropriate Equations , 1985 .

[96]  Said Ahzi,et al.  Modeling and validation of the large deformation inelastic response of amorphous polymers over a wide range of temperatures and strain rates , 2007 .

[97]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

[98]  Anselm H. C. Horn.  Essentials of Computational Chemistry, Theories and Models By Christopher J. Cramer. Wiley: Chichester, England. 2002. 562 pp. ISBN 0-471-48551-9 (hardcover). $110. ISBN 0-471-48552-7 (paperback). $45. , 2003 .

[99]  Mary C Boyce,et al.  Enhanced mobility accompanies the active deformation of a glassy amorphous polymer. , 2002, Physical review letters.

[100]  T. A. Kavassalis,et al.  A molecular-dynamics study of polyethylene crystallization , 1993 .

[101]  A. V. Duin,et al.  ReaxFF: A Reactive Force Field for Hydrocarbons , 2001 .

[102]  Mark F. Horstemeyer,et al.  Modeling stress state dependent damage evolution in a cast Al–Si–Mg aluminum alloy , 2000 .

[103]  J. Pople,et al.  Approximate Self‐Consistent Molecular Orbital Theory. II. Calculations with Complete Neglect of Differential Overlap , 1965 .

[104]  Kurt Kremer,et al.  Simulation of polymer melts. I. Coarse‐graining procedure for polycarbonates , 1998 .

[105]  J. Pople,et al.  Approximate Self‐Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 Systems , 1966 .

[106]  E. Clementi,et al.  Monte Carlo and Molecular Dynamics Simulations , 1989 .

[107]  Hershel Markovitz,et al.  Theory of viscoelasticity. An introduction, R. M. Christensen, Academic Press, New York, 1971. 245 + xi pp. $13.50. , 1971 .

[108]  H. Callen.  Thermodynamics and an Introduction to Thermostatistics , 1988 .

[109]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

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

[111]  B. Montanari,et al.  Density functional study of molecular crystals: Polyethylene and a crystalline analog of bisphenol-A polycarbonate , 1998 .

[112]  Lallit Anand,et al.  The decomposition F = FeFp, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous , 2005 .

[113]  Walter Thiel,et al.  Ground States of Molecules. 38. The MNDO Method. Approximations and Parameters , 1977 .

[114]  A. Voter,et al.  Temperature-accelerated dynamics for simulation of infrequent events , 2000 .

[115]  Steven J. Plimpton,et al.  LENGTH SCALE AND TIME SCALE EFFECTS ON THE PLASTIC FLOW OF FCC METALS , 2001 .

[116]  R. Bartlett.  Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules , 1981 .

[117]  Kurt Binder,et al.  Polymer translocation through a nanopore induced by adsorption: Monte Carlo simulation of a coarse-grained model. , 2004, The Journal of chemical physics.

[118]  R. E. Robertson,et al.  Theory for the Plasticity of Glassy Polymers , 1966 .

[119]  Kevin Leung,et al.  Designing meaningful density functional theory calculations in materials science—a primer , 2004 .

[120]  R. O. Jones,et al.  The density functional formalism, its applications and prospects , 1989 .

[121]  Erhard Krempl,et al.  THE OVERSTRESS DEPENDENCE OF INELASTIC RATE OF DEFORMATION INFERRED FROM TRANSIENT TESTS , 1995 .

[122]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.

[123]  A. Gent.  A New Constitutive Relation for Rubber , 1996 .

[124]  J. Clarke,et al.  Molecular dynamics simulation of an amorphous polymer under tension. 1. Phenomenology , 1991 .

[125]  X. M. Duan,et al.  Local bias potential in hyper molecular dynamics method , 2003 .

[126]  P. Knowles,et al.  A second order multiconfiguration SCF procedure with optimum convergence , 1985 .

[127]  Serge Pérez,et al.  Crystalline features of 4,4'-isopropylidenediphenylbis(phenyl carbonate) and conformational analysis of the polycarbonate of 2,2-bis(4-hydroxyphenyl)propane , 1987 .

[128]  P. Perzyna.  Fundamental Problems in Viscoplasticity , 1966 .

[129]  C. Bauwens-Crowet,et al.  The compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates , 1973 .

[130]  B. Montanari,et al.  Density Functional Study of Polycarbonate. 2. Crystalline Analogs, Cyclic Oligomers, and Their Fragments , 1999 .

[131]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules J. Am. Chem. Soc. 1995, 117, 5179−5197 , 1996 .

[132]  P. J. Wei,et al.  A viscoelastic constitutive model with nonlinear evolutionary internal variables , 2003 .

[133]  U. Suter,et al.  Detailed molecular structure of a vinyl polymer glass , 1985 .

[134]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[135]  John C. Tully,et al.  Molecular dynamics of infrequent events: Thermal desorption of xenon from a platinum surface , 1981 .

[136]  Michael L. Klein,et al.  Thermodynamic properties for a simple model of solid carbon dioxide: Monte Carlo, cell model, and quasiharmonic calculations , 1974 .

[137]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[138]  Paul K. Weiner,et al.  Ground states of molecules , 1972 .

[139]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[140]  M. Boyce,et al.  On the kinematics of finite strain plasticity , 1989 .

[141]  G. Grest,et al.  Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation , 1990 .

[142]  Volodymyr Turkowski,et al.  Time-dependent density-functional theory for ultrafast interband excitations , 2008 .

[143]  P. T. Cummings,et al.  Brownian dynamics simulation of bead-spring chain models for dilute polymer solutions in elongational flow , 1995 .

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

[145]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[146]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[147]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[148]  B. Montanari,et al.  Density Functional Study of Crystalline Analogs of Polycarbonates , 1998 .

[149]  Mark F. Horstemeyer,et al.  Damage influence on Bauschinger effect of a cast A356 aluminum alloy , 1998 .

[150]  Mary C. Boyce,et al.  Deformation of Elastomeric Networks: Relation between Molecular Level Deformation and Classical Statistical Mechanics Models of Rubber Elasticity , 2001 .

[151]  A. Becke.  Density-functional thermochemistry. , 1996 .

[152]  G. B. Olson,et al.  Systems design of high performance stainless steels I. Conceptual and computational design , 2000 .

[153]  R. O. Jones,et al.  Polycarbonate simulations with a density functional based force field , 1999 .

[154]  O. H. Yeoh,et al.  Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates , 1990 .

[155]  M. Volkenstein,et al.  Statistical mechanics of chain molecules , 1969 .

[156]  Moussa Nait-Abdelaziz,et al.  Elasto-viscoplastic constitutive equations for the description of glassy polymers behavior at constant strain rate , 2007 .

[157]  Natasha Maurits,et al.  The MesoDyn project: software for mesoscale chemical engineering , 1999 .

[158]  P. Español,et al.  FLUID PARTICLE MODEL , 1998 .

[159]  David L. McDowell,et al.  Internal State Variable Theory , 2005 .

[160]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[161]  Kurt Kremer,et al.  The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions , 1988 .

[162]  E. L. Short,et al.  Quantum Chemistry , 1969, Nature.

[163]  Ulrich W. Suter,et al.  Local structure and the mechanism of response to elastic deformation in a glassy polymer , 1986 .

[164]  Heh Han Meijer,et al.  Homogenisation of structured elastoviscoplastic solids at finite strains , 2001 .

[165]  Walter Thiel,et al.  A new gradient-corrected exchange-correlation density functional , 1997 .

[166]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[167]  Kremer,et al.  Crossover from Rouse to reptation dynamics: A molecular-dynamics simulation. , 1988, Physical review letters.

[168]  Millard F. Beatty,et al.  Constitutive equations for amended non-Gaussian network models of rubber elasticity , 2002 .

[169]  Kurt Binder,et al.  Modeling polyethylene with the bond fluctuation model , 1997 .

[170]  P. B. Warren,et al.  DISSIPATIVE PARTICLE DYNAMICS : BRIDGING THE GAP BETWEEN ATOMISTIC AND MESOSCOPIC SIMULATION , 1997 .

[171]  J. Z. Zhu,et al.  The finite element method , 1977 .

[172]  E. Giessen,et al.  On Improved Network Models for Rubber Elasticity and Their Applications to Orientation Hardening in Glassy Polymers , 1993 .

[173]  M. Ortiz,et al.  Quasicontinuum analysis of defects in solids , 1996 .

[174]  R. Dreizler,et al.  Density-Functional Theory , 1990 .

[175]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[176]  Mark F. Horstemeyer,et al.  Multiscale modeling of the plasticity in an aluminum single crystal , 2009 .

[177]  Jozef Bicerano,et al.  Intrachain rotations in poly(ester carbonates). 1. Quantum mechanical calculations on the model molecules 2,2-diphenylpropane, diphenylcarbonate, and phenyl benzoate , 1988 .

[178]  A. Voter.  Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events , 1997 .

[179]  A. Ibrahimbegovic.  Nonlinear Solid Mechanics , 2009 .

[180]  Patrick S. Doyle,et al.  On the coarse-graining of polymers into bead-spring chains , 2004 .

[181]  S. L. Mayo,et al.  DREIDING: A generic force field for molecular simulations , 1990 .

[182]  M. Boyce,et al.  Molecular response of a glassy polymer to active deformation , 2004 .

[183]  K. Binder.  Monte Carlo and molecular dynamics simulations in polymer science , 1995 .

[184]  Elias C. Aifantis,et al.  Multiscale modeling of polymer materials using a statistics-based micromechanics approach , 2009 .

[185]  Henry Eyring,et al.  Theory of Non‐Newtonian Flow. I. Solid Plastic System , 1955 .

[186]  Mary C. Boyce,et al.  An investigation of the yield and postyield behavior and corresponding structure of poly(methyl methacrylate) , 1993 .

[187]  Dirk Reith,et al.  Coarse Graining of Nonbonded Inter-Particle Potentials Using Automatic Simplex Optimization to Fit Structural Properties , 2000 .

[188]  Erhard Krempl,et al.  6 – A Small-Strain Viscoplasticity Theory Based on Overstress , 1996 .

[189]  Alan E. Tonelli.  Conformational Characteristics of Isotactic Polypropylene , 1972 .

[190]  Mark F. Horstemeyer,et al.  Cradle-to-grave simulation-based design incorporating multiscale microstructure-property modeling: Reinvigorating design with science , 2003 .

[191]  John M. Deutch,et al.  Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume , 1975 .

[192]  Kurt Kremer,et al.  Bisphenol A Polycarbonate: Entanglement Analysis from Coarse-Grained MD Simulations , 2005 .

[193]  G. Henkelman,et al.  Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table , 2001 .

[194]  A. C. Hurley.  Electron correlation in small molecules , 1976 .

[195]  Lennart Nilsson,et al.  Empirical energy functions for energy minimization and dynamics of nucleic acids , 1986 .

[196]  Lallit Anand,et al.  A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part II: Applications , 2011 .

[197]  Xingao Gong,et al.  Hyper molecular dynamics with a local bias potential , 1999 .

[198]  B. Cherry,et al.  Comment on “the compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates” , 1976 .

[199]  Wam Marcel Brekelmans,et al.  The Influence of Intrinsic Strain Softening on Strain Localization in Polycarbonate: Modeling and Experimental Validation , 2000 .

[200]  Lallit Anand,et al.  A theory of amorphous solids undergoing large deformations, with application to polymeric glasses , 2003 .

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

[202]  E. Kröner,et al.  Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen , 1959 .

[203]  Arnold T. Hagler,et al.  Ab Initio Calculations on Small Molecule Analogs of Polycarbonates , 1995 .

[204]  David H. Allen,et al.  Damage Dependent Constitutive Behavior and Energy Release Rate for a Cohesive Zone in a Thermoviscoelastic Solid , 1999 .

[205]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[206]  Kurt Kremer,et al.  Simulation of Polymer Melts. II. From Coarse-Grained Models Back to Atomistic Description , 1998 .

[207]  B. W. Cherry,et al.  The role of recovery forces in the deformation of linear polyethylene , 1978 .

[208]  George T. Gray,et al.  Three-dimensional, finite deformation, viscoplastic constitutive models for polymeric materials , 1997 .

[209]  Hubert M. James,et al.  Theory of the Elastic Properties of Rubber , 1943 .

[210]  R. Ogden.  Large Deformation Isotropic Elasticity—On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids , 1973 .

[211]  Henry S. Rzepa,et al.  Ground states of molecules: Part XLII. Vibrational frequencies of isotopically-substituted molecules calculated using MINDO/3 force constants , 1977 .

[212]  Peter H. Verdier,et al.  Monte Carlo Studies of Lattice‐Model Polymer Chains. II. End‐to‐End Length , 1966 .