Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
3
2
2005
Preface to Special Issue on Multiscale Modeling Scheme
vii
Jinghong
Fan
Alfred University, Alfred, New York, USA; Research Center for Materials Mechanics, Chongqing University, Chongqing, China
Modeling of Mechanical Behavior of Geomaterials on the Mesoscale
135-148
Pavel V.
Makarov
Institute of Strength Physics and Materials Science, Siberian Branch Russian Academy of Sciences, pr. Academicheskii 2/1, Tomsk 634021, Russia
Yurii P.
Stefanov
Institute of Strength Physics and Materials Science, Siberian Branch Russian Academy of Sciences, pr. Academicheskii 2/1, Tomsk 634021, Russia
Igor Yu.
Smolin
Institute of Strength Physics and Materials Science, Siberian Branch Russian Academy of Sciences, pr. Academicheskii 2/1, Tomsk 634021, Russia
Oleg I.
Cherepanov
Institute of Strength Physics and Materials Science, Siberian Branch Russian Academy of Sciences, pr. Academicheskii 2/1, Tomsk 634021, Russia
To analyze deformation of geomaterials with space and time, two modeling methods are described: a dynamic method where fracture is taken into account explicitly with special emphasis on crack system formation, their coalescence, etc.; a quasi-static method where specific consideration is given to the influence of temperature at quasi-static loading. The constitutive equations used take into account the dilatancy effects, damage accumulation, and degradation of mechanical properties. Consideration is given to calculation examples of deformation and damage localization observed at various scales, namely, from small laboratory samples up to huge crustal elements. In the framework of the dynamic approach, the formations of bands of localized deformation in the vicinity of a failed inclusion and within a medium layer in shear are obtained. Features of strain localization for several geological models of the lithosphere are presented. In the framework of the quasi-static approach, the formation of ring-like structures under cooling of a heterogeneous media is discussed. These problems are considered as the problems of mesoscale since essential meso-constituents are taken into account.
Computational Characterization of Micro- to Macroscopic Deformation Behavior of Amorphous, Crystalline, and Semicrystalline Polyethylene
149-160
Yoshihiro
Tomita
Graduate School of Science and Technology, Kobe University, Nada Kobe, 657-8501 Japan
Makoto
Uchida
Graduate School of Science and Technology, Kobe University, Nada Kobe, 657-8501 Japan
High-density polyethylene (HDPE) is a widely used polymer that contains amorphous and crystalline phases. First, the micro- to macroscopic deformation behavior of an amorphous phase with a heterogeneous distribution of molecular chains, in other words, the distribution of the initial shear strength and single crystalline phase, is investigated by means of computational simulation with the nonaffine molecular chain network model and crystalline theory with a prescribed chain directional extendibility. The results clarify the onset of microscopic shear bands emanating from the slightly weak points and their evolution, interaction, and percolation in the amorphous polymer. Very different deformation behaviors that depend on the applied stress are clarified in terms of the rotation of the chain slip direction in the crystalline phase. Then, the characteristic feature of the deformation and evolution of the interface undulation of composite blocks comprised of amorphous and crystalline phases under uniform tension and compression is clarified. The effects of heterogeneity of the initial shear strength on the interfacial deformation and the deformation of the crystalline phase, and their interactions, which will provide detailed information on the semicrystalline polymer, are given.
Effect of Interlamellar Spacing on the Constitutive Behavior of Pearlitic Steels Via Damage and Multiscale Analysis
161-176
Xiao-Feng
Peng
Laboratory of Phase Change and Interfacial Transport Phenomena, Department of Thermal Engineering, Tsinghua University, Beijing 100084
J.
Fan
Department of Engineering Mechanics, Chongqing University Chongqing, 400044, China
W.
Pi
Department of Engineering Mechanics, Chongqing University Chongqing, 400044, China
The effect of interlamellar spacing on the constitutive behavior of pearlitic steels is investigated through the analysis of the damage in each phase of the materials and using a multiscale approach. A pearlitic material is composed of numerous colonies with randomly distributed orientations, each of which is further composed of numerous fine lamellas of ferrite and cementite. Between each pair of ferrite and cementite lamellas, a thin transient interfacial lamella is assumed. Each of the three phases is considered as an elastoplastic medium with some pattern of microdefect. Based on the concept of energy-release-rate and continuum damage mechanics as well as the geometric characteristics of microdefects in different phases, a unified damage evolution law is obtained. It explicitly contains the interlamellar spacing, accounting for the better mechanical properties of pearlitic materials with smaller interlamellar spacing. The constitutive description for a single pearlitic colony is derived using the obtained damage and its evolution, and taking into account its lamellar microstructure. The description for pearlitic steels is obtained with the Hill's self-consistent scheme. The response of BS11 subjected to asymmetric stress cycling is analyzed. The satisfactory agreement between the computed and experimental results demonstrates the validity of the proposed model.
Thermomechanical Continuum Interpretation of Atomistic Deformation
177-197
Min
Zhou
Georgia Institute of Technology
This paper describes a framework for obtaining thermomechanical continuum interpretations of the results of molecular dynamics calculations. This theory is a further advancement from a pure mechanical equivalent continuum theory developed recently. The analysis is based on the decomposition of atomic particle velocity into a structural deformation part and a thermal oscillation part. On one hand, balance of momentum at the structural level yields fields of stress, body force, traction, mass density, and deformation as they appear to a macroscopic observer. The full dynamic equivalence between the discrete system and continuum system includes (i) preservation of linear and angular momenta; (ii) conservation of internal, external, and inertial work rates; and (iii) conservation of mass. On the other hand, balance of momentum for the thermal motions as it appears to an observer moving at the structural velocity yields the fields of heat flux and temperature. These quantities can be cast in a manner as to conform to the continuum phenomenological equation for heat conduction and generation, yielding scale-sensitive characterizations of specific heat, thermal conductivity, and thermal relaxation time. The coupling between the structural deformation and the thermal conduction processes results from the fact that the equations for structural deformation and for heat conduction are two different forms of the same balance of momentum equation at the fully time-resolved atomic level. This coupling occurs through an inertial force term in each of the two equations, induced by the other process. For the structural deformation equation, the inertial force term induced by thermal oscillations of atoms gives rise to the phenomenological dependence of deformation on temperature. For the heat equation, the inertial force term induced by structural deformation takes the phenomenological form of a heat source.
Multiscale Modeling Of Polymer Composite Properties
199-225
Yuri G.
Yanovsky
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky
Ave., Moscow, 125040, Russia
Polymer composites are heterogeneous viscoelastic media. The ascertainment of the quantitative relations between the microstructure and macromechanical properties of these materials is a very important scientific problem. Some distinctive computer technologies, which lead to multiscale computational experiments and investigations of peculiarities of micromechanical behavior of heterogeneous composite media taking into consideration atomic-molecular formations, have been discussed. These approximations are important elements in the nanotechnological problem of construction of new perspective materials. We consider the results of calculation by the Monte Carlo approach as a perspective method for the description of the important features of atomic and molecular texture and energetics of heterogeneous polymer media, namely, different flexible-chain molecules and nanoclusters of technical carbon chemically terminated with different substances. The representative element of this structure keeps up to 1.5 × 106 atoms. The parallel technologies of calculations and supercomputers have been used. Estimation of structural peculiarities and energies of interaction of systems consisted of polymeric macromolecules and nanoparticles of fillers, variation of superficial chemical properties of fillers, and evaluation of water presence inside the media, all of which are ideated as highly useful for the understanding of the macromechanics of composites. The quantum-mechanical approach is discussed as the method for solution of the foremost problems of micromechanics of reinforced polymer (rubber) composites, namely, (i) an investigation of the interaction of soot model particles with nonterminated and H-terminated surfaces, with segments of polymer chain with different chemical structures, and consideration of the impact of a chemical nature of the polymer and chemical nature of surface soot modification on the enthalpy of binding and the force of micromolecular shifting (friction); (ii) an investigation of the interaction of soot particles without an interface layer between them, and evaluation of the influence of chemical modification of the soot surface on the binding enthalpy and the shifting force of these particles (nonterminated and terminated by H, OH, and COO surface groups); and (iii) an investigation of the interaction of soot particles with an interparticle layer of polymer and water between soot particles, and evaluation of the chemical nature of the particles that are adsorbed at the interface of soot particles on their binding enthalpy and force of microscopic friction (nonterminated and terminated by H soot surfaces). Calculations were done in a parallel mode using supercomputer MVC-1000M (Moscow). Optimization of the viscoelastic behavior of composite media such as rubbers leads to the procedure of identification. Validity of the effect of reinforcement on the basis of the analysis of relaxation properties of materials seems very promising.
Multiscale Analysis and Numerical Modeling of the Portevin-Le Chatelier Effect
227-237
Zhongjia
Chen
CAS Key Laboratory of Mechanical Behavior and Design of Materials,University of Science and Technology of China, Hefei 230027; Department of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, China
Qingchuan
Zhang
CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230027, China
Xiaoping
Wu
CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230027, China
The Portevin-Le Chatelier (PLC) effect refers to one type of plastic instability, which often manifests itself as discontinuous yielding and localized deformation in some metallic alloys deformed under certain conditions. A phenomenological model based on a multiscale analysis is developed to investigate the PLC effect. In this model, a new component of stress is introduced, which takes account of the collective interactions between mobile dislocations and solute atoms, to describe the influence of dynamic strain aging (DSA) on the flow stress. The effects of microscopic pinning and unpinning of dislocations on the macroscopic deformation behavior are considered in an integrative and competitive manner. Due to the competition of these two effects during deformation, the alloys may exhibit the negative strain rate sensitivity of flow stress, which is a necessary condition for the occurrence of the PLC effect. A nonuniform spatial distribution of some material parameters was used in the model to reflect the heterogeneous nature of the deformed material, including a linear change of the initial cross-sectional area and a random perturbation of the initial internal stress. Numerical simulations based on this heterogeneous model were carried out for tensile testing of aluminum alloy 2017, by which the serrated yielding and localized deformation behavior were successfully reproduced. The results also indicate the relation between the macroscopic jerky flow and the pinning/unpinning of dislocations at the micro level.
Mixed KMC-Continuum Models for the Evolution of Rough Surfaces
239-256
Simon P.A.
Gill
Department of Engineering, University of Leicester, University Road Leicester, LE1 7RH, United Kingdom
Paul E.
Spencer
Department of Engineering, University of Leicester, University Road Leicester, LE1 7RH, United Kingdom
Alan C. E.
Cocks
Department of Engineering, University of Leicester, University Road Leicester, LE1 7RH, United Kingdom
An atomistic solid-on-solid (SOS) kinetic Monte Carlo (KMC) model for surface diffusion is found to exhibit curvature-driven decay. An equivalent continuum Mullins-Herring equation is derived and the two systems are shown to be compatible. A mixed KMC-continuum model is proposed that allows discrete atomistic simulations to be embedded within a smooth continuum. A blending region is introduced between the two model descriptions, which allow mass to be transferred between them in a consistent manner. The implementation of this multiscale modeling approach is illustrated with simulations of the decay of a sinusoid and a Gaussian peak.