Causal Heat Conduction Contravening the Fading Memory Paradigm
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
ME 285A: Foundations of the Theory of Continuous Media
University of California, Berkeley Department of Mechanical Engineering ME 285A: Foundations of the Theory of Continuous Media Syllabus 1. Introduction. The nonlinear field theories. Mathematical preliminaries. Tensors. Fréchet derivative and differential. 2. Kinematics of Deformable Continua. Bodies. Deformations. Polar decomposition theorem. Derivatives of stretch and rotation tensors. Velocity and vorticity fields. Pull-back and push- forward operations. Lie derivative. Material transport of fields. Internal constraints. Relative deformation gradient. Rivlin-Ericksen tensors. 3. Balance Laws. Conservation of mass. Balance of linear and angular momenta for continua. Stress tensors. Balance of energy. A remark on the second law of thermodynamics. 4. General Constitutive Relations (Purely Mechanical Theory). Relationship between stress and history of deformation. Invariance requirements. Simple materials. Symmetry considerations. Cauchy-elastic and Green-elastic (or hyperelastic) materials. Internally constrained elastic materials. Viscous fluids. Materials with memory. Viscoelastic fluids and solids. Reiner-Rivlin fluids. Rivlin-Ericksen fluids. Materials with fading memory. Linear viscoelasticity. Pseudo-Rigid materials. 5. Thermoelastic Materials. Ideal gas. Entropy and Helmholtz free energy functions. Clausius- Duhem inequality. Thermoelasticity. Approach of Coleman and Noll. Approach of Rivlin: construction of entropy function. Internally constrained thermoelatic materials. Linear thermoelasticity. 6. Thermoelastic Materials with Viscosity. Construction of the entropy function for thermoelastic materials with viscosity, and subject to internal constraints. 7. Thermodynamics of Materials with Memory. Materials with fading memory. Instantaneous elasticity. Open questions. 8. Selected Topics. Mixture theory, nonlocal continua. ______________________________________________________________________________ Grading scheme: Homework (~40%), Midterm (~20%), Final Project (~40%). . -
Polymer Rheology: Principles, Techniques and Applications
Polymer Rheology: Principles, Techniques and Applications G. C. Berry Carnegie Mellon University Contents Example Problem............................................................................................. i 1. Introduction ..................................................................................................... 1 2. Principles of Rheometry .................................................................................. 3 3. Linear viscoelastic phenomenology.................................................................. 7 4. Approximations used in linear viscoelasticity................................................... 19 5. The viscosity of dilute of polymer solutions and colloidal dispersions.............. 24 6. Linear viscoelastic behavior of concentrated and undiluted polymeric fluids.... 29 7. Nonlinear viscoelastic behavior of concentrated and undiluted polymeric 35 fluids................................................................................................................ 8. Strain-induced birefringence for concentrated and undiluted polymeric fluids.. 43 9. Linear and nonlinear viscoelastic behavior of colloidal dispersions .................. 55 10. References ....................................................................................................... 59 Table 1 Linear Viscoelastic Function..................................................................... 68 Table 2 Functions and Parameters Used................................................................. 69 Table 3 Relations -
Thermomechanics of Solid Materials with Application to the Gurson-Tvergaard Material Model
VTT PUBLICATIONS 312 F19800095 Thermomechanics of solid materials with application to the Gurson-Tvergaard material model Kari Santaoja VlT Manufacturing Technology . TECHNICAL RESEARCH CENTRE OF FINLAND ESP00 1997 312 Kari Santaoja Thermomechanics of solid materials with application to the Gurson-Tvergaard material model TECHNICAL RESEARCH CENTRE OF FINLAND ESP00 1997 ISBN 951-38-5060-9 (soft back ed.) ISSN 123.54621 (soft back ed.) ISBN 95 1-38-5061-7 (URL: http://www.inf.vtt.fi/pdf/) ISSN 14554849 (URL: http://www.inf.vtt.fi/pdf/) Copyright 0 Valtion teknillinen tutkimuskeskus (VTT) 1997 JULKAISIJA - UTGIVARE - PUBLISHER Valtion teknillinen tutkimuskeskus (VTT), Vuorimiehentie 5, PL 2000, 02044 VTT puh. vaihde (09) 4561, faksi (09) 456 4374 Statens tekniska forskningscentral (VTT), Bergsmansvagen 5, PB 2000,02044 VTT tel. vaxel(O9) 4561, fax (09) 456 4374 Technical Research Centre of Finland (VTT), Vuorimiehentie 5, P.O.Box 2000, FIN42044 VTT, Finland phone internat. + 358 9 4561, fax + 358 9 456 4374 VIT Valmistustekniikka, Ydinvoimalaitosten materiaalitekniikka, Kemistintie 3, PL 1704,02044 VTT puh. vaihde (09) 4561, faksi (09) 456 7002 VTT Tillverkningsteknik, Material och strukturell integritet, Kemistvagen 3, PB 1’704,02044 VTT tel. vaxel(O9) 4561, fax (09) 456 7002 VTT Manufacturing Technology, Maaterials and Structural Integrity, Kemistintie 3, P.O.Box 1704, FIN42044 VTT, Finland phone internat. + 358 9 4561, fax + 358 9 456 7002 Technical editing Kerttu Tirronen VTT OFFSETPAINO. ESP00 1997 Santaoja, Kari. Thermornechanics of solid materials with application to the Gurson-Tvergaard material model. Espoo 1997. Technical Research Centre of Finland, UTPublications 312. 162 p. + app. 14 p. UDC 536.7 Keywords thermomechanical analysis, thermodynamics, plasticity, porous medium, Gurson- Tvergaard model ABSTRACT The elastic-plastic material model for porous material proposed by Gurson and Tvergaard is evaluated. -
Numerical Investigation of Second Sound in Liquid Helium
NUMERICAL INVESTIGATION OF SECOND SOUND IN LIQUID HELIUM by Udo Piram A Thesis Submitted to the Faculty of the DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING In the Graduate College THE UNIVERSITY OF ARIZONA In Partial Fulfillment of the Requirements For the Degree of DIPLOMINGENIEUR at the UNIVERSITY STUTTGART 1991 ACKNOWLEDGMENTS I would like to thank Dr. Fran¸cois Cellier for guidance and assistance during my studies at the University of Arizona and the preparation of this paper. I would also like to thank Prof. Dr. Voß at the University Stuttgart, who organized the exchange program, which made it possible for me to attend school at the University of Arizona. I would like to thank the German Academic Exchange Service for the financial support of the exchange program. Finally, I would like to express my gratitude to my parents for their support of my studies in Germany and the USA. Contents Contents ii List of Figures iii 1 Introduction 1 1.1MechanicalandElectricalSystems...................... 1 1.2ThermodynamicalSystems........................... 2 2 Helium II and Second Sound 4 3 Heat Conduction Modeled With Time–Variant R–C–Networks 7 3.1 R–C–Networks . 7 3.2ModelinginTermsofBondGraphs...................... 9 3.3HeliumIIModeledinTermsofBondGraphs................. 10 3.4NumericalValuesfortheThermalParameters................ 12 3.4.1 Model 1: Initial Temperature 1.4K . 13 3.4.2 Model 2: Initial Temperature 2.1728K . 14 3.5SimulationandResults............................. 16 4 Heat Transport and Two Fluid Model 20 4.1TwoFluidModel................................ 20 4.2HydrodynamicalEquations........................... 22 4.3NumericalValuesfortheThermalParameters................ 23 4.4NumericalMethod............................... 24 i CONTENTS ii 4.5 Boundary Conditions . 25 4.6SimulationandResults............................. 26 5 Conclusions 29 5.1Conclusions................................... 29 5.2Zusammenfassung............................... -
FHF02SC Heat Flux Sensor User Manual
Hukseflux Thermal Sensors USER MANUAL FHF02SC Self-calibrating foil heat flux sensor with thermal spreaders and heater Copyright by Hukseflux | manual v1803 | www.hukseflux.com | [email protected] Warning statements Putting more than 24 Volt across the heater wiring can lead to permanent damage to the sensor. Do not use “open circuit detection” when measuring the sensor output. FHF02SC manual v1803 2/41 Contents Warning statements 2 Contents 3 List of symbols 4 Introduction 5 1 Ordering and checking at delivery 8 1.1 Ordering FHF02SC 8 1.2 Included items 8 1.3 Quick instrument check 9 2 Instrument principle and theory 10 2.1 Theory of operation 10 2.2 The self-test 12 2.3 Calibration 12 2.4 Application example: in situ stability check 14 2.5 Application example: non-invasive core temperature measurement 16 3 Specifications of FHF02SC 17 3.1 Specifications of FHF02SC 17 3.2 Dimensions of FHF02SC 20 4 Standards and recommended practices for use 21 4.1 Heat flux measurement in industry 21 5 Installation of FHF02SC 23 5.1 Site selection and installation 23 5.2 Electrical connection 25 5.3 Requirements for data acquisition / amplification 30 6 Maintenance and trouble shooting 31 6.1 Recommended maintenance and quality assurance 31 6.2 Trouble shooting 32 6.3 Calibration and checks in the field 33 7 Appendices 35 7.1 Appendix on wire extension 35 7.2 Appendix on standards for calibration 36 7.3 Appendix on calibration hierarchy 36 7.4 Appendix on correction for temperature dependence 37 7.5 Appendix on measurement range for different temperatures -
Convective Heat Flux Explained.Indd
Convective heat flux explained Theory Thermal convection is one of the three mechanisms of heat transfer, besides conduction and thermal radia- tion. The heat is transferred by a moving fluid (e.g. wind or water), and is usually the dominant form of heat transfer in liquids and gases. Convection can be divided into natural convection and forced convection. Generally, when a hot body is placed in a cold envi- rameters like velocity of the fluid, material proper- ronment, the heat will flow from the hot body to the ties etc. For example, if one blows air over the tea cup, cold surrounding until an equilibrium is reached. the speed of the fluid is increased and thus the heat Close to the surface of the hot body, the surrounding transfer coefficient becomes larger. This means, that air will expand due to the higher temperature. There- the water cools down faster. fore, the hot air is lighter than the cold air and moves upwards. These differences in density create a flow, Application which transports the heat away from the hot surface To demonstrate the phenomenon of convection, the to the cold environment. This process is called natu- heat flux of a tea cup with hot water was measured ral convection. with the gSKIN® heat flux sensor. In one case, air was When the movement of the fluid is enhanced, we talk blown towards the cup by a fan. The profile of the about forced convection: An example is the cooling of a hot body with a fan: The fluid velocity is increased and thus the device is cooled faster, because the heat transfer is higher. -
Models for Shape Memory Alloy Behavior: an Overview of Modeling Approaches
INTERNATIONAL JOURNAL OF STRUCTURAL CHANGES IN SOLIDS – Mechanics and Applications Volume 1, Number 1, December 2009, pp. 111-148 Models for Shape Memory Alloy Behavior: An overview of modeling approaches Ashish Khandelwal and Vidyashankar Buravalla* GM R&D, India Science Lab, Bangalore, India Abstract Shape memory alloys (SMA) have been known for over five decades and modeling of their response has attracted much attention over the last two decades. Recent increase in the range of applications of these materials has lead to an increased focus on modeling their thermomechanical response. Various approaches ranging from macroscopic phenomenology to microscopic lattice based methods are being pursued to model SMA behavior. Models ranging from simple tools as design aids to complex thermodynamic based models to understand the characteristic martensitic transformation responsible for the shape memory and superelastic response exist. In this report, following a brief introduction to the SMA behavior and the underlying martensitic transformation, an overview of models for SMAs is provided. This is aimed at providing an understanding of the state of the art and also to identify possible future directions. In this review, models are classified both on the basis of the approach and the level (scale) of continuum they address. General methodology of each type of approach is presented briefly followed by a review of the models that fall under that category. Certain liberties are taken in classifying these models to facilitate understanding and thus the present classification is by no means either unique or completely rigorous. Also, while an attempt is made to cover most of the approaches, review of all the models that exist in literature is practically impossible. -
Fundamentals of the Mechanics of Continua'' by E. Hellinger
Exegesis of Sect. III.B from ”Fundamentals of the Mechanics of Continua” by E. Hellinger Simon R. Eugster, Francesco Dell’Isola To cite this version: Simon R. Eugster, Francesco Dell’Isola. Exegesis of Sect. III.B from ”Fundamentals of the Mechanics of Continua” by E. Hellinger. 2017. hal-01568552 HAL Id: hal-01568552 https://hal.archives-ouvertes.fr/hal-01568552 Preprint submitted on 25 Jul 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Zeitschrift für Angewandte Mathematik und Mechanik, 19 May 2017 Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Con- tinua”∗ by E. Hellinger Simon R. Eugster1,2∗∗ and Francesco dell’Isola3,2 1 Institute for Nonlinear Mechanics, University of Stuttgart, Stuttgart, Germany 2 International Research Center for the Mathematics and Mechanics of Complex Systems, MEMOCS, Università dell’Aquila, L’Aquila, Italy 3 Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma La Sapienza, Rome, Italy Received XXXX, revised XXXX, accepted XXXX Published online XXXX Key words Ernst Hellinger, elasticity, thermodynamics, electrodynamics, theory of relativity This is our third and last exegetic essay on the fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECH- ANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. -
Heat Flux Measurement Practical Applications for Electronics
Heat Flux Measurement Practical Applications for Electronics Heat flux sensors are practical measurement tools which are component may be known, as well as the resistance of the useful for determining the amount of thermal energy passed board and solder connections; the resistance at the interface through a specific area per unit of time. Heat flux can be of the component and board to the ambient are not easily thought of as the density of transferred power, similar to known and are dependent on the flow characteristics. While current through a wire or water through a pipe. Measuring analytical or CFD methods can at best predict the heat heat flux can be useful, for example, in determining the transfer coefficient at a particular area, often for complex amount of heat passed through a wall or through a human systems with uneven or sparsely populated components body, or the amount of transferred solar or laser radiant these methods are not accurate and may not be useful. For energy to a given area. In a past article [1] we learned how those components which generate power, but may not need heat flux sensors operate and how they can be calibrated. But the use of a separate heatsink, the heat flux gage can be how can heat flux sensors be used for electronics design? experimentally used to determine the heat transfer coefficient This article highlights several practical uses of the heat flux on the component surface or the compact thermal response sensor in the design of electronics systems. See Figure 1 for on the board (e.g. -
A Brief Review of Elasticity and Viscoelasticity
A Brief Review of Elasticity and Viscoelasticity H.T. Banks, Shuhua Hu and Zackary R. Kenz Center for Research in Scientific Computation and Department of Mathematics North Carolina State University Raleigh, NC 27695-8212 May 27, 2010 Abstract There are a number of interesting applications where modeling elastic and/or vis- coelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging. Here we provide an overview of the sub- ject for both elastic and viscoelastic materials in order to understand the behavior of these materials. We begin with a brief introduction of some basic terminology and relationships in continuum mechanics, and a review of equations of motion in a con- tinuum in both Lagrangian and Eulerian forms. To complete the set of equations, we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials. In addition, we discuss some applications for these constitutive equations. Finally, we give a computational example describing the motion of soil ex- periencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion. AMS subject classifications: 93A30,74B05,74B20,74D05,74D10. Key Words: Mathematical modeling, Eulerian and Lagrangian formulations in continuum mechanics, elasticity, viscoelasticity, computational simulations in soil, constitutive relation- ships. 1 1 Introduction Knowledge of the field of continuum mechanics is crucial when attempting to understand and describe the behavior of materials that completely fill the occupied space and thus act like a continuous medium. -
Second Sound and Ballistic Heat Conduction: Naf Experiments Revisited ⇑ R
International Journal of Heat and Mass Transfer 117 (2018) 682–690 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Second sound and ballistic heat conduction: NaF experiments revisited ⇑ R. Kovács , P. Ván Department of Theoretical Physics, Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, Budapest, Hungary Department of Energy Engineering, BME, Budapest, Hungary Montavid Thermodynamic Research Group, Hungary article info abstract Article history: Second sound phenomenon and ballistic heat conduction, the two wave like propagation modes of heat, Received 25 August 2017 are the two most prominent, experimentally observed non-Fourier effects of heat conduction. In this Received in revised form 4 October 2017 paper we compare three related theories by quantitatively analyzing the crucial NaF experiments of Accepted 8 October 2017 Jackson, Walker and McNelly, where these effects were observed together. We conclude that with the Available online 17 October 2017 available information the best comparison and insight is provided by non-equilibrium thermodynamics with internal variables. However, the available data and information is not the best, and further, new Keywords: experiments are necessary. Non-equilibrium thermodynamics Ó 2017 Elsevier Ltd. All rights reserved. Ballistic propagation NaF experiments Kinetic theory 1. Introduction reflected and scattered only on the boundaries. In the framework of non-equilibrium thermodynamics with internal variables [5], Due to the technological development, manufacturing and the ballistic propagation is represented as a coupling between material designing achieved the level where the classical laws of the thermal and mechanical fields and propagates with the elastic physics and the related engineering methodologies do not hold. -
Nonlinear Viscoelastic Behavior of Glassy Polymers and Its Effect on the Onset of Irreversible Deformation of the Matrix Resin in Continuous Fiber Composites
Nonlinear Viscoelastic Behavior of Glassy Polymers and Its Effect on the Onset of Irreversible Deformation of the Matrix Resin in Continuous Fiber Composites J. M. Caruthers and G. A. Medvedev School of Chemical Engineering, Purdue University 480 Stadium Mall Drive, West Lafayette, IN 47907 [email protected] SUMMARY Predictions of a validated nonlinear viscoelastic model for glassy polymer will be presented for multiaxial deformations, where it will be shown that onset of yield can be described by a strain invariant criterion. Subsequently, the onset of irreversible deformation in off-axis tensile tests of unidirectional laminates of an epoxy-carbon fiber composite will be described using a strain invariant criterion. Keywords: glassy polymers, nonlinear viscoelastic, strain invariants INTRODUCTION The off-axis tensile test has been utilized to examine the elastic and ultimate behavior of composite materials subjected to controlled states of multi-axial deformation in fiber-reinforced composite materials for the past forty years [1-2]. As the fiber angle is varied between 0 and π/2, the state of stress and strain within the composite material varies between states that are dominated by distortional and dilatational deformation. Moreover, the onset and ultimate states typically occur simultaneously in the off-axis tensile test. This coincidence enables a direct experimental determination of the onset of irreversible deformation and is in contrast to the general case for ultimate behavior wherein damage propagation must occur before onset can be detected. Consequently, the off-axis tensile test provides an excellent platform for evaluation of irreversible deformation in polymer matrix composites. Conventional failure theories for composite materials focus on stress and strain states within the effective orthotropic medium and thereby ignore the fact that failure must occur in either of the two constituents and/or at the interface, not in an aphysical effective medium.