A hierarchical framework for the multiscale modeling of microstructure evolution in heterogeneous materials.

All materials are heterogeneous at various scales of observation. The influence of material heterogeneity on nonuniform response and microstructure evolution can have profound impact on continuum thermomechanical response at macroscopic “engineering” scales. In many cases, it is necessary to treat this behavior as a multiscale process thus integrating the physical understanding of material behavior at various physical (length and time) scales in order to more accurately predict the thermomechanical response of materials as their microstructure evolves. The intent of the dissertation is to provide a formal framework for multiscale hierarchical homogenization to be used in developing constitutive models.

[1]  D. McDowell,et al.  Gradient concepts for evolution of damage , 1999 .

[2]  John W. Hutchinson,et al.  Crack tip fields in strain gradient plasticity , 1996 .

[3]  S. Torquato,et al.  Generating microstructures with specified correlation functions , 2001 .

[4]  S. Ahzi,et al.  Statistical continuum theory for large plastic deformation of polycrystalline materials , 2001 .

[5]  Thomas J. R. Hughes,et al.  A variational multiscale approach to strain localization – formulation for multidimensional problems , 2000 .

[6]  Wing Kam Liu,et al.  Predictive multiscale theory for design of heterogeneous materials , 2008 .

[7]  J. Leblond,et al.  Numerical implementation and assessment of the GLPD micromorphic model of ductile rupture , 2009 .

[8]  Somnath Ghosh,et al.  Concurrent multi-level model for damage evolution in microstructurally debonding composites , 2007 .

[9]  Min Zhou,et al.  Micromechanical Simulation of Dynamic Fracture Using the Cohesive Finite Element Method , 2004 .

[10]  René Chambon,et al.  A strain space gradient plasticity theory for finite strain , 2004 .

[11]  R. Hill.  On constitutive macro-variables for heterogeneous solids at finite strain , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[12]  Xuxin Tu,et al.  Return mapping for nonsmooth and multiscale elastoplasticity , 2009 .

[13]  Alain Molinari,et al.  Micromechanical modelling of porous materials under dynamic loading , 2001 .

[14]  N.,et al.  A PHENOMENOLOGICAL THEORY FOR STRAIN GRADIENT EFFECTS IN PLASTICITY , 2002 .

[15]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[16]  W. Y. Zhou,et al.  On multiscale significance of Rice’s normality structure , 2006 .

[17]  A. Eringen.  Microcontinuum Field Theories , 2020, Advanced Continuum Theories and Finite Element Analyses.

[18]  Joseph Hoshen,et al.  Percolation and cluster distribution. III. Algorithms for the site-bond problem , 1979 .

[19]  Mohan M. Trivedi,et al.  Texture synthesis using gray-level co-occurrence models: algorithms, experimental analysis, and psychophysical support , 2001 .

[20]  J. Kestin.  Internal Variables in the Local-Equilibrium Approximation , 1992 .

[21]  Somnath Ghosh,et al.  A multi-level computational model for multi-scale damage analysis in composite and porous materials , 2001 .

[22]  L. Siad,et al.  Comparison of explicit and implicit finite element simulations of void growth and coalescence in porous ductile materials , 2008 .

[23]  R. Toupin.  ELASTIC MATERIALS WITH COUPLE STRESSES, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS , 1962 .

[24]  S. Torquato,et al.  Reconstructing random media , 1998 .

[25]  V. Kouznetsova,et al.  Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme , 2002 .

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

[27]  Christian Thaulow,et al.  A complete Gurson model approach for ductile fracture , 2000 .

[28]  J. C. Simo,et al.  Non‐smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms , 1988 .

[29]  James G. Berryman,et al.  Measurement of spatial correlation functions using image processing techniques , 1985 .

[30]  David L. McDowell,et al.  Non-local separation constitutive laws for interfaces and their relation to nanoscale simulations , 2004 .

[31]  Salvatore Torquato,et al.  Generating random media from limited microstructural information via stochastic optimization , 1999 .

[32]  M. Utz,et al.  Efficient reconstruction of multiphase morphologies from correlation functions. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  R. D. Mindlin.  Micro-structure in linear elasticity , 1964 .

[34]  Joseph Hoshen,et al.  The application of the enhanced Hoshen-Kopelman algorithm for processing unbounded images , 1999, IEEE Trans. Image Process..

[35]  A. Gokhale,et al.  Constraints on microstructural two-point correlation functions , 2005 .

[36]  A. Needleman,et al.  Void Nucleation Effects in Biaxially Stretched Sheets , 1980 .

[37]  J. Clayton.  Continuum multiscale modeling of finite deformation plasticity and anisotropic damage in polycrystals , 2006 .

[38]  F. Montáns,et al.  Implicit algorithms for multilayer J2-plasticity , 2000 .

[39]  白以龙,et al.  Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media , 2004 .

[40]  Gregory J. Wagner,et al.  Coupling of atomistic and continuum simulations using a bridging scale decomposition , 2003 .

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

[42]  Young W. Kwon,et al.  Multi-scale modeling of mechanical behavior of polycrystalline materials , 2004 .

[43]  Janet A. Blume,et al.  Compatibility conditions for a left Cauchy-Green strain field , 1989 .

[44]  J. Kestin.  Local-equilibrium formalism applied to mechanics of solids , 1992 .

[45]  R. Stevens,et al.  Micromechanics of randomly oriented ellipsoidal inclusion composites. Part II: Elastic moduli , 1996 .

[46]  Lori Graham-Brady,et al.  Stochastic Morphological Modeling of Random Multiphase Materials , 2008 .

[47]  H. Garmestani,et al.  Microstructure design of a two phase composite using two-point correlation functions , 2004 .

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

[49]  G. Lebon,et al.  Polymer solutions and chemical reactions under flow: A thermodynamic description , 1993 .

[50]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[51]  A. Rosakis,et al.  A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals , 2000 .

[52]  N. Aravas,et al.  Mixed finite element formulations of strain-gradient elasticity problems , 2002 .

[53]  Min Zhou,et al.  A new look at the atomic level virial stress: on continuum-molecular system equivalence , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[54]  E. Cerreta,et al.  Modeling the microstructural evolution of metallic polycrystalline materials under localization conditions , 2007 .

[55]  Giancarlo Sangalli,et al.  Variational Multiscale Analysis: the Fine-scale Green's Function, Projection, Optimization, Localization, and Stabilized Methods , 2007, SIAM J. Numer. Anal..

[56]  2D-3D CONVERSION OF OBJECT SIZE DISTRIBUTIONS IN QUANTITATIVE METALLOGRAPHY , 2006 .

[57]  D. Gross,et al.  Constructing microstructures of poly- and nanocrystalline materials for numerical modeling and simulation , 2002 .

[58]  Horacio Dante Espinosa,et al.  Grain level analysis of crack initiation and propagation in brittle materials , 2001 .

[59]  J. Rice.  Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity , 1971 .

[60]  D. Hasselman,et al.  On the Porosity Dependence of the Elastic Moduli of Polycrystalline Refractory Materials , 1962 .

[61]  W. Brekelmans,et al.  Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling , 2000 .

[62]  Chris J. Pearce,et al.  Scale transition and enforcement of RVE boundary conditions in second‐order computational homogenization , 2008 .

[63]  Francisco J. Montáns,et al.  On the consistency of nested surfaces models and their kinematic hardening rules , 2007 .

[64]  Patrick J. Roache,et al.  Verification and Validation in Computational Science and Engineering , 1998 .

[65]  David L. McDowell,et al.  A multiscale multiplicative decomposition for elastoplasticity of polycrystals , 2003 .

[66]  René Chambon,et al.  Plastic continuum with microstructure, Local Second Gradient Theories for Geomaterials : Localization Studies , 2001 .

[67]  Salvatore Torquato,et al.  Microstructure of two‐phase random media. I. The n‐point probability functions , 1982 .

[68]  Jagan M. Padbidri,et al.  Minimal kinematic boundary conditions for simulations of disordered microstructures , 2005 .

[69]  Hiroshi Kadowaki,et al.  Bridging multi-scale method for localization problems , 2004 .

[70]  Stefan Diebels,et al.  A second‐order homogenization procedure for multi‐scale analysis based on micropolar kinematics , 2007 .

[71]  David L. McDowell,et al.  Numerical simulation of shock wave propagation in spatially-resolved particle systems , 2006 .

[72]  Percy Williams Bridgman,et al.  The Nature of Thermodynamics , 1941 .

[73]  O. Zienkiewicz,et al.  The finite element patch test revisited a computer test for convergence, validation and error estimates , 1997 .

[74]  M. Ostoja-Starzewski.  Material spatial randomness: From statistical to representative volume element☆ , 2006 .

[75]  Nikhilesh Chawla,et al.  Three-dimensional (3D) microstructure visualization and finite element modeling of the mechanical behavior of SiC particle reinforced aluminum composites , 2004 .

[76]  Franck J. Vernerey,et al.  A micromorphic model for the multiple scale failure of heterogeneous materials , 2008 .

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

[78]  Wing Kam Liu,et al.  Multiresolution analysis for material design , 2006 .

[79]  V Varvara Kouznetsova,et al.  Computational homogenization for the multi-scale analysis of multi-phase materials , 2002 .

[80]  Norman A. Fleck,et al.  The prediction of a size effect in microindentation , 1998 .

[81]  S. Torquato,et al.  Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .

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

[83]  Jwo Pan,et al.  A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials , 2009 .

[84]  L. J. Sluys,et al.  Numerical determination of representative volumes for granular materials , 2004 .

[85]  David L. McDowell,et al.  Homogenized finite elastoplasticity and damage: theory and computations , 2004 .

[86]  Hans Eckart Exner,et al.  STEREOLOGY AND 3D MICROSCOPY: USEFUL ALTERNATIVES OR COMPETITORS IN THE QUANTITATIVE ANALYSIS OF MICROSTRUCTURES? , 2011 .

[87]  V. Kouznetsova,et al.  Multi-scale second-order computational homogenization of multi-phase materials : a nested finite element solution strategy , 2004 .

[88]  T. Pardoena,et al.  An extended model for void growth and coalescence , 2022 .

[89]  David L. McDowell,et al.  Evaluation of intersection conditions for two-surface plasticity theory , 1989 .

[90]  Yannis F. Dafalias,et al.  Plastic spin: necessity or redundancy? , 1998 .

[91]  Lori Graham-Brady,et al.  A stochastic computational method for evaluation of global and local behavior of random elastic media , 2005 .

[92]  G. P. Tandon,et al.  Elastic moduli for a class of porous materials , 1989 .

[93]  D. McDowell,et al.  Effects of Microstructure Variability on Intrinsic Fatigue Resistance of Nickel-base Superalloys – A Computational Micromechanics Approach , 2006 .

[94]  Claire Y. Barlow,et al.  Strain gradient effects on microscopic strain field in a metal matrix composite , 2000 .

[95]  P. Thomason,et al.  Ductile Fracture of Metals , 1990 .

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

[97]  G. Lebon,et al.  Extended irreversible thermodynamics , 1993 .

[98]  M. Ortiz,et al.  Effective Cohesive Behavior of Layers of Interatomic Planes , 2006 .

[99]  C. Sun,et al.  Modeling micro-inertia in heterogeneous materials under dynamic loading , 2002 .

[100]  K. Une,et al.  Rim structure formation of isothermally irradiated UO2 fuel discs , 2001 .

[101]  P. Corson.  Correlation functions for predicting properties of heterogeneous materials. III. Effective elastic moduli of two‐phase solids , 1974 .

[102]  David L. McDowell,et al.  Finite element analysis of the stress distributions near damaged Si particle clusters in cast Al–Si alloys , 2000 .

[103]  A. Needleman,et al.  Analysis of the cup-cone fracture in a round tensile bar , 1984 .

[104]  Arun M. Gokhale,et al.  Digital image analysis and microstructure modeling tools for microstructure sensitive design of materials , 2004 .

[105]  Alexander M. Puzrin,et al.  Principles of Hyperplasticity: An Approach to Plasticity Theory Based on Thermodynamic Principles , 2010 .

[106]  Harold S. Park,et al.  Bridging Scale Methods for Nanomechanics and Materials , 2006 .

[107]  Norman A. Fleck,et al.  The role of strain gradients in the grain size effect for polycrystals , 1996 .

[108]  Y. Weitsman,et al.  Randomly reinforced composites: properties, failure and aspects of material design , 2006 .

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

[110]  N. Aravas.  Finite-strain anisotropic plasticity and the plastic spin , 1994 .

[111]  E. Cosserat,et al.  Théorie des Corps déformables , 1909, Nature.

[112]  Wing Kam Liu,et al.  Multi-scale constitutive model and computational framework for the design of ultra-high strength, high toughness steels , 2004 .

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

[114]  S. Hazanov,et al.  On overall properties of elastic heterogeneous bodies smaller than the representative volume , 1995 .

[115]  Martin Ostoja-Starzewski,et al.  Random field models of heterogeneous materials , 1998 .

[116]  Morton E. Gurtin,et al.  A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations , 2005 .

[117]  John D. Clayton,et al.  Dynamic plasticity and fracture in high density polycrystals: constitutive modeling and numerical simulation , 2005 .

[118]  Harold S. Park,et al.  A temperature equation for coupled atomistic/continuum simulations , 2004 .

[119]  Harold S. Park,et al.  An introduction to computational nanomechanics and materials , 2004 .

[120]  N. Fleck,et al.  FINITE ELEMENTS FOR MATERIALS WITH STRAIN GRADIENT EFFECTS , 1999 .

[121]  F. Stummel,et al.  The limitations of the patch test , 1980 .

[122]  Salvatore Torquato,et al.  Extraction of morphological quantities from a digitized medium , 1995 .

[123]  F. Gruttmann,et al.  Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation , 2003 .

[124]  Hai-liang Yu,et al.  FE analysis of inclusion deformation and crack generation during cold rolling with a transition layer , 2008 .

[125]  Amir R. Khoei,et al.  On the implementation of a multi-surface kinematic hardening plasticity and its applications , 2005 .

[126]  Hamid Garmestani,et al.  Two-point probability distribution function analysis of Co-polymer nano-composites , 2005 .

[127]  Zvi Hashin,et al.  The Elastic Moduli of Heterogeneous Materials , 1962 .

[128]  Franck J. Vernerey,et al.  An interactive micro-void shear localization mechanism in high strength steels , 2007 .

[129]  J. Luo,et al.  Porosity-dependence of elastic moduli and hardness of 3Y-TZP ceramics , 1999 .

[130]  F. Babalievski.  Cluster Counting: The Hoshen–Kopelman Algorithm Versus Spanning Tree Approaches , 1998 .

[131]  David L. McDowell,et al.  Equivalent continuum for dynamically deforming atomistic particle systems , 2002 .

[132]  S. I. Serdyukov.  Generalization of the evolution criterion in extended irreversible thermodynamics , 2004 .

[133]  B. Svendsen,et al.  Nonlocal Modeling and Simulation of Ductile Damage and Failure in Metal Matrix Composites , 2008 .