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Solid-solid phase transition modelling: relaxation procedures, configurational energies and thermomechanical behaviours

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INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE 1999年第14期37卷 1821-1840页

作者： Pagano, S Alart, P Univ Montpellier 2 Mech & Civil Engn Lab F-34095 Montpellier 5 France

The behaviour of materials involving Solid-solid phase transitions may be modelled by more or less smooth laws. The corresponding physical basis and microscopic mechanisms are still in most cases controversial and out of our purpose. In a previous paper, we studied (from mathematical and numerical point of view) relaxation procedures of non-convex bulk potentials issued from the Fremond modelling. For example, the quasiconvexification is obtained by considering specific microstructures. By accepting local minima of the total energy as possible equilibrium state, we can find, numerically, hysteretic behaviours and fronts of phase transition. However, some thermomechanical modellings of solid-solid phase transitions involve interaction energies between the phases which account at the macroscopic scale for the incompatibilities between deformations at the microscopic scale. We define a class of models which contains the Fremond model as the simplest one. An interaction term is introduced and is discussed in the context of the generalized standard materials. This term may lead, according to a parameter noted G, to the instability of the equilibrium. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： shape memory alloys relaxation procedures configurational energies thermomechanical models numerical algorithms

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Teaching module for laminar and turbulent forced convection on a flat plate

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COMPUTER APPLICATIONS IN ENGINEERING EDUCATION 1998年第2期6卷 115-125页

作者： Ribando, RJ Coyne, KA O'Leary, GW Univ Virginia Sch Engn & Appl Sci Dept Mech Aerosp & Nucl Engn Charlottesville VA 22903 USA

This article describes a PC-based teaching module for the classical problem of forced convection over a heated flat plate. The transformed boundary layer equations for an incompressible fluid are solved using a finite-difference numerical procedure on a grid that grows along with the boundary layer. Simple transition and mixing length turbulence models allow the algorithm to be used across a wide range of Reynolds numbers. The program returns a colored contour plot of the thermal boundary layer on the screen and shows the edge of the velocity boundary layer. The effects of the Reynolds number and Prandtl numbers are dramatically demonstrated. The user can use a slider mechanism to take local measurements of the plate temperature and surface temperature gradient, and from these data develop local and overall "virtual" convection correlations. (C) 1998 John Wiley & Sons, Inc.

关键词： heat transfer engineering education forced convection numerical algorithms graphical user interface

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An atomistically informed kinetic Monte Carlo model of grain boundary motion coupled to shear deformation

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 68卷 98-110页

作者： Prieto-Depedro, M. Martin-Bragado, I. Segurado, J. IMDEA Mat Inst Madrid Spain Tech Univ Madrid Madrid Spain

The shear coupled motion of grain boundaries (GBs) is modelled by using two different atomistic simulation techniques: molecular dynamics (MD) and kinetic Monte Carlo (KMC). MD simulations are conducted to identify the elementary mechanisms that take place during the coupled motion of GBs. This process is described on the one hand, in terms of the geometrical approach of the dislocation content in the boundary;and on the other hand, by the thermodynamics of the dislocation passage, shown as a thermal activated process. Relevant MD output is extended into a KMC model that considers the GB migration as a result of a sequence of discrete rare events. The independent motion of each structural unit forming the boundary conforms a single event, having a rate per unit of time to move to the next stable position computed according to the transition state theory. The limited time scale of classical MD is overcome by KMC, that allows to impose realistic deformation velocities up to 10 pm/s. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Grain boundaries Dislocations Stress relaxation numerical algorithms Metallic material

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Computational study of vibrationally relaxing gas past blunt body in hypersonic flows

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2000年第1期14卷 18-26页

作者： Josyula, E USAF Res Lab Air Vehicles Directorate Wright Patterson AFB OH 45433 USA

numerical simulations are presented of a steady-state, hypersonic Row over a two-dimensional cylinder of 1 m radius under conditions where the relaxation of the vibrational modes is significant. A Mach 6.5 nitrogen flow was simulated at freestream pressures of 50, 250, and 500 Pa, with a freestream translational temperature of 300 K. Two different freestream vibrational temperatures, 300 K (causing vibrational heating) and 4000 K (causing vibrational cooling) were considered to study the effects on the flowfield. An upwind-difference numerical scheme was used to solve the inviscid Euler equations coupled to the vibrational kinetic models of diatomic nitrogen, assumed as an anharmonic oscillator of 40 quantum levels using two sets of reaction rates. Comparison with previously reported computations showed a maximum variation of 10% in translational and first-level vibrational temperature along the surface due to differences in numerical schemes and grid densities;variation caused hy the two different reaction rate sets was less than 2%. The vibrational cooling case showed a 10% higher shock-standoff distance than the vibrational heating case. The population distribution for the cooling Ease was non-Boltzmann due to nonresonant energy exchanges in the postshock region, greater in the shoulder region than in the stagnation region. An increase in freestream pressure for the cooling case increased the shock-standoff distance and non-Boltzmann behavior in the postshock region and near the surface. There was, however, a larger equilibrium region in between, in the stagnation region.

关键词： Freestream Conditions Stagnation Region Conservation Equations Hypersonic Flows numerical Simulation Stagnation Streamlines Shock Layers Vibrational Energy numerical algorithms Predictor Corrector Method

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Glide mobility of the 1/2[1101(001) edge dislocation in UO₂ from molecular dynamics simulation

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INTERNATIONAL JOURNAL OF PLASTICITY 2017年 89卷 85-95页

作者： Lunev, A. V. Kuksin, A. Yu. Starikov, S. V. Russian Acad Sci Joint Inst High Temp 13 Bld 2Izhorskaya St Moscow 125412 Russia Moscow Inst Phys & Technol Moscow 141700 Russia

Both the mechanical properties of oxide nuclear fuel and the high burn-up grain restructuring are known to be related to dislocation motion. Previous studies show that at temperatures above 1000 K slip on 001) crystallographic planes in UO2 is dominant, and 1/2(110)(001} dislocations should have the highest mobility. However, no information is available on the temperature and stress dependence of dislocation velocities in UO2. This information is required as input in higher scale simulation techniques, such as dislocation dynamics, to gain an insight into the unusual plastic behaviour of this oxide. In this study we employed molecular dynamics to gather a representative set of data on the 1/2(110) (001) dislocation motion in UO2 at temperatures from 1000 to 2000 K and shear stress from 25 to 1000 MPa. We found that dislocation motion was thermally activated, with two distinct modes of motion. Based on this knowledge, we selected an analytic expression for dislocation velocity and performed fitting to MD data. This expression described the simulation data well, and was also used to make a physically justified prediction for dislocation velocities at typical operating conditions of the oxide nuclear fuel. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Dislocations Ceramic material numerical algorithms Atomistic simulation

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A general methodology for investigating flow instabilities in complex geometries:: application to natural convection in enclosures

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INTERNATIONAL JOURNAL FOR numerical METHODS IN FLUIDS 2001年第2期37卷 175-208页

作者： Gadoin, E Le Quéré, P Daube, O CNRS LIMSI F-91403 Orsay France CEMIF Evry France

This paper presents a general methodology for studying instabilities of natural convection flows enclosed in cavities of complex geometry. Different tools have been developed, consisting of time integration of the unsteady equations, steady state solving, and computation of the most unstable eigenmodes of the Jacobian and its adjoint. The methodology is validated in the classical differentially heated cavity, where the steady solution branch is followed for vary large values of the Rayleigh number and most unstable eigenmodes are computed at selected Rayleigh values. Its effectiveness for complex geometries is illustrated on a configuration consisting of a cavity with internal heated partitions. We finally propose to reduce the Navier-Stokes equations to a differential system by expanding the unsteady solution as the sum of the steady state solution and of a linear combination of the leading eigenmodes. The principle of the method is exposed and preliminary results are presented. Copyright (C) 2001 John Wiley & Sons, Ltd.

关键词： Arnoldi-Krylov method flow instabilities natural convection Newton's method numerical algorithms

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On a finite strain viscoplastic theory based on a new internal dissipation inequality

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INTERNATIONAL JOURNAL OF PLASTICITY 2004年第7期20卷 1281-1311页

作者： Lin, RC Brocks, W GKSS Forschungszentrum Geesthacht GmbH Inst Mat Res D-21502 Geesthacht Germany

This work is focused on the theoretical development and numerical implementation of a viscoplastic law. According to the second law of thermodynamics a dissipation inequality described in the rotated material coordinate system is developed. Based on this dissipation inequality and the principle of maximum dissipation a finite strain viscoplastic model described also in the rotated material coordinate system is formulated. The evolution equations are expressed in terms of the material time derivatives of the rotated elastic logarithmic strain, the accumulated plastic strain and the strain-like tensor conjugate to the rotated back stress. The mathematical structure of this theory is concise and similar to that of the infinitesimal viscoplastic theory. These characteristics make the numerical implementation of this theory easy. The stress integration algorithm and the algorithmic tangent moduli for the infinitesimal theory can be applied to the numerical implementation of the present finite strain theory with a little reformulation. The complicated algorithmic formulations for most of other finite plastic laws can be therefore circumvented. In order to check the effectivity of the present finite strain theory a set of numerical examples under strict deformation conditions are presented. These numerical examples prove the excellent performance of the present viscoplastic material law at describing the finite strain elastoplastic and viscoplastic problems. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： constitutive behaviour elastic-viscoplastic material finite strain finite elements numerical algorithms

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Tour planning for an unmanned air vehicle under wind conditions

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2007年第5期30卷 1299-1306页

作者： McNeely, Rachelle L. Iyer, Ram V. Chandler, Phillip R. Texas Tech Univ Dept Math & Stat Lubbock TX 79409 USA USAF Res Lab Wright Patterson AFB Wright Patterson AFB OH 45433 USA

A very important subproblem in the task assignment problem for unmanned air vehicles is the evaluation of costs for the state transitions of a directed graph. Usually a Dubins vehicle flying in the absence of wind is considered in the computation of costs. However, when a prevailing wind vector field is considered, the costs taken on very different values and the task assignment problem can have very different solutions. In this paper, we consider the problem of constructing minimum-time trajectories for a Dubins vehicle in the presence of a time-varying wind vector field. We present results on the existence and uniqueness of minimum-time solutions for a Dubins vehicle flying in a general time-varying wind vector field under some technical conditions. These results extend the conclusions of the well-known Dubins theorem. We also propose an algorithm for obtaining the minimum-time solution for an unmanned air vehicle and prove its convergence. We also present the results of numerical experiments that show that the importance of considering wind vector fields while planning the tour for an unmanned air vehicle.

关键词： Air Vehicle Micro Air Vehicle numerical Stability Coordinate Transformations Pontryagin's Maximum Principle Air Force Research Laboratory algorithms Convergence Boundary Value Problems numerical algorithms Euler Equations

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Torsion and bending periodic boundary conditions for modeling the intrinsic strength of nanowires

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2008年第11期56卷 3242-3258页

作者： Cai, Wei Fong, William Eisen, Erich Weinberger, Christopher R. Stanford Univ Dept Mech Engn Stanford CA 94305 USA

We present a unified approach for atomistic modeling of torsion and bending of nanowires that is free from artificial end effects. Torsional and bending periodic boundary conditions (t-PBC and b-PBC) are formulated by generalizing the conventional periodic boundary conditions (PBC) to cylindrical coordinates. The approach is simpler than the more general objective molecular dynamics formulation because we focus on the special cases of torsion and bending. A simple implementation of these boundary conditions is presented and correctly conserves linear and angular momenta. We also derive the virial expressions for the average torque and bending moment under these boundary conditions that are analogous to the virial expression for the average stress in PBC. The method is demonstrated by molecular dynamics simulation of Si nanowires under torsion and bending, which exhibit several modes of failure depending on their diameters. (c) 2008 Elsevier Ltd. All rights reserved.

关键词： Elastic properties Microstructure Fracture numerical algorithms

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MIXING CONTROL IN A PLANE SHEAR-LAYER

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AIAA JOURNAL 1989年第12期27卷 1744-1751页

作者： KORCZAK, KZ WESSEL, RA Case Western Reserve University Cleveland Ohio

An investigation of mixing processes in a plane shear layer by a direct numerical simulation with a high-order numerical technique, the isoparametric spectral element method, is presented. The computational domain includes a region with the splitter plate where two laminar (Blasius) boundary layers with different velocities and concentrations merge to form the shear layer and a downstream region where the flow undergoes transition to highly unsteady structures with intensive mixing. The augmentation of mixing as a function of a downstream location and the intensity and type of vortical structures in the layer are investigated by an introduction of disturbance at the high-velocity inflow. The character of the dynamic mixing is displayed along with time-averaged profiles and statistical characteristics. © 1989 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Boundary Layer Thickness Spectral Element Method Direct numerical Simulation Vortex Structure Navier Stokes Equations Velocity Profiles Dynamic Pressure Probability Density Functions numerical algorithms Schmidt Number

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