Rheology of Soft Materials Rheology
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10-1 CHAPTER 10 DEFORMATION 10.1 Stress-Strain Diagrams And
EN380 Naval Materials Science and Engineering Course Notes, U.S. Naval Academy CHAPTER 10 DEFORMATION 10.1 Stress-Strain Diagrams and Material Behavior 10.2 Material Characteristics 10.3 Elastic-Plastic Response of Metals 10.4 True stress and strain measures 10.5 Yielding of a Ductile Metal under a General Stress State - Mises Yield Condition. 10.6 Maximum shear stress condition 10.7 Creep Consider the bar in figure 1 subjected to a simple tension loading F. Figure 1: Bar in Tension Engineering Stress () is the quotient of load (F) and area (A). The units of stress are normally pounds per square inch (psi). = F A where: is the stress (psi) F is the force that is loading the object (lb) A is the cross sectional area of the object (in2) When stress is applied to a material, the material will deform. Elongation is defined as the difference between loaded and unloaded length ∆푙 = L - Lo where: ∆푙 is the elongation (ft) L is the loaded length of the cable (ft) Lo is the unloaded (original) length of the cable (ft) 10-1 EN380 Naval Materials Science and Engineering Course Notes, U.S. Naval Academy Strain is the concept used to compare the elongation of a material to its original, undeformed length. Strain () is the quotient of elongation (e) and original length (L0). Engineering Strain has no units but is often given the units of in/in or ft/ft. ∆푙 휀 = 퐿 where: is the strain in the cable (ft/ft) ∆푙 is the elongation (ft) Lo is the unloaded (original) length of the cable (ft) Example Find the strain in a 75 foot cable experiencing an elongation of one inch. -
Glossary: Definitions
Appendix B Glossary: Definitions The definitions given here apply to the terminology used throughout this book. Some of the terms may be defined differently by other authors; when this is the case, alternative terminology is noted. When two or more terms with identical or similar meaning are in general acceptance, they are given in the order of preference of the current writers. Allowable stress (working stress): If a member is so designed that the maximum stress as calculated for the expected conditions of service is less than some limiting value, the member will have a proper margin of security against damage or failure. This limiting value is the allowable stress subject to the material and condition of service in question. The allowable stress is made less than the damaging stress because of uncertainty as to the conditions of service, nonuniformity of material, and inaccuracy of the stress analysis (see Ref. 1). The margin between the allowable stress and the damaging stress may be reduced in proportion to the certainty with which the conditions of the service are known, the intrinsic reliability of the material, the accuracy with which the stress produced by the loading can be calculated, and the degree to which failure is unattended by danger or loss. (Compare with Damaging stress; Factor of safety; Factor of utilization; Margin of safety. See Refs. l–3.) Apparent elastic limit (useful limit point): The stress at which the rate of change of strain with respect to stress is 50% greater than at zero stress. It is more definitely determinable from the stress–strain diagram than is the proportional limit, and is useful for comparing materials of the same general class. -
Lecture 13: Earth Materials
Earth Materials Lecture 13 Earth Materials GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Hooke’s law of elasticity Force Extension = E × Area Length Hooke’s law σn = E εn where E is material constant, the Young’s Modulus Units are force/area – N/m2 or Pa Robert Hooke (1635-1703) was a virtuoso scientist contributing to geology, σ = C ε palaeontology, biology as well as mechanics ij ijkl kl ß Constitutive equations These are relationships between forces and deformation in a continuum, which define the material behaviour. GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Shear modulus and bulk modulus Young’s or stiffness modulus: σ n = Eε n Shear or rigidity modulus: σ S = Gε S = µε s Bulk modulus (1/compressibility): Mt Shasta andesite − P = Kεv Can write the bulk modulus in terms of the Lamé parameters λ, µ: K = λ + 2µ/3 and write Hooke’s law as: σ = (λ +2µ) ε GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Young’s Modulus or stiffness modulus Young’s Modulus or stiffness modulus: σ n = Eε n Interatomic force Interatomic distance GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Shear Modulus or rigidity modulus Shear modulus or stiffness modulus: σ s = Gε s Interatomic force Interatomic distance GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Hooke’s Law σij and εkl are second-rank tensors so Cijkl is a fourth-rank tensor. For a general, anisotropic material there are 21 independent elastic moduli. In the isotropic case this tensor reduces to just two independent elastic constants, λ and µ. -
Frictional Peeling and Adhesive Shells Suomi Ponce Heredia
Adhesion of thin structures : frictional peeling and adhesive shells Suomi Ponce Heredia To cite this version: Suomi Ponce Heredia. Adhesion of thin structures : frictional peeling and adhesive shells. Physics [physics]. Université Pierre et Marie Curie - Paris VI, 2015. English. NNT : 2015PA066550. tel- 01327267 HAL Id: tel-01327267 https://tel.archives-ouvertes.fr/tel-01327267 Submitted on 6 Jun 2016 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. THÈSE DE DOCTORAT DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Spécialité : Physique École doctorale : «Physique en Île-de-France » réalisée Au Laboratoire de Physique et Mécanique des Milieux Hétérogènes présentée par Suomi PONCE HEREDIA pour obtenir le grade de : DOCTEUR DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Sujet de la thèse : Adhesion of thin structures Frictional peeling and adhesive shells soutenue le 30 Novembre, 2015 devant le jury composé de : M. Etienne Barthel Examinateur M. José Bico Directeur de thèse M. Axel Buguin Examinateur Mme. Liliane Léger Rapporteure M. Benoît Roman Invité M. Loïc Vanel Rapporteur 1 Suomi PONCE HEREDIA 30 Novembre, 2015 Sujet : Adhesion of thin structures Frictional peeling and adhesive shells Résumé : Dans cette thèse, nous nous intéressons à l’adhésion d’élastomères sur des substrats rigides (interactions de van der Waals). -
On Nonlinear Strain Theory for a Viscoelastic Material Model and Its Implications for Calving of Ice Shelves
Journal of Glaciology (2019), 65(250) 212–224 doi: 10.1017/jog.2018.107 © The Author(s) 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re- use or in order to create a derivative work. On nonlinear strain theory for a viscoelastic material model and its implications for calving of ice shelves JULIA CHRISTMANN,1,2 RALF MÜLLER,2 ANGELIKA HUMBERT1,3 1Division of Geosciences/Glaciology, Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany 2Institute of Applied Mechanics, University of Kaiserslautern, Kaiserslautern, Germany 3Division of Geosciences, University of Bremen, Bremen, Germany Correspondence: Julia Christmann <[email protected]> ABSTRACT. In the current ice-sheet models calving of ice shelves is based on phenomenological approaches. To obtain physics-based calving criteria, a viscoelastic Maxwell model is required account- ing for short-term elastic and long-term viscous deformation. On timescales of months to years between calving events, as well as on long timescales with several subsequent iceberg break-offs, deformations are no longer small and linearized strain measures cannot be used. We present a finite deformation framework of viscoelasticity and extend this model by a nonlinear Glen-type viscosity. A finite element implementation is used to compute stress and strain states in the vicinity of the ice-shelf calving front. -
1 Fluid Flow Outline Fundamentals of Rheology
Fluid Flow Outline • Fundamentals and applications of rheology • Shear stress and shear rate • Viscosity and types of viscometers • Rheological classification of fluids • Apparent viscosity • Effect of temperature on viscosity • Reynolds number and types of flow • Flow in a pipe • Volumetric and mass flow rate • Friction factor (in straight pipe), friction coefficient (for fittings, expansion, contraction), pressure drop, energy loss • Pumping requirements (overcoming friction, potential energy, kinetic energy, pressure energy differences) 2 Fundamentals of Rheology • Rheology is the science of deformation and flow – The forces involved could be tensile, compressive, shear or bulk (uniform external pressure) • Food rheology is the material science of food – This can involve fluid or semi-solid foods • A rheometer is used to determine rheological properties (how a material flows under different conditions) – Viscometers are a sub-set of rheometers 3 1 Applications of Rheology • Process engineering calculations – Pumping requirements, extrusion, mixing, heat transfer, homogenization, spray coating • Determination of ingredient functionality – Consistency, stickiness etc. • Quality control of ingredients or final product – By measurement of viscosity, compressive strength etc. • Determination of shelf life – By determining changes in texture • Correlations to sensory tests – Mouthfeel 4 Stress and Strain • Stress: Force per unit area (Units: N/m2 or Pa) • Strain: (Change in dimension)/(Original dimension) (Units: None) • Strain rate: Rate -
Computational Rheology (4K430)
Computational Rheology (4K430) dr.ir. M.A. Hulsen [email protected] Website: http://www.mate.tue.nl/~hulsen under link ‘Computational Rheology’. – Section Polymer Technology (PT) / Materials Technology (MaTe) – Introduction Computational Rheology important for: B Polymer processing B Rheology & Material science B Turbulent flow (drag reduction phenomena) B Food processing B Biological flows B ... Introduction (Polymer Processing) Analysis of viscoelastic phenomena essential for predicting B Flow induced crystallization kinetics B Flow instabilities during processing B Free surface flows (e.g.extrudate swell) B Secondary flows B Dimensional stability of injection moulded products B Prediction of mechanical and optical properties Introduction (Surface Defects on Injection Molded Parts) Alternating dull bands perpendicular to flow direction with high surface roughness (M. Bulters & A. Schepens, DSM-Research). Introduction (Flow Marks, Two Color Polypropylene) Flow Mark Side view Top view Bottom view M. Bulters & A. Schepens, DSM-Research Introduction (Simulation flow front) 1 0.5 Steady Perturbed H 2y 0 ___ −0.5 −1 0 0.5 1 ___2x H Introduction (Rheology & Material Science) Simulation essential for understanding and predicting material properties: B Polymer blends (morphology, viscosity, normal stresses) B Particle filled viscoelastic fluids (suspensions) B Polymer architecture macroscopic properties (Brownian dynamics (BD), molecular dynamics (MD),⇒ Monte Carlo, . ) Multi-scale. ⇒ Introduction (Solid particles in a viscoelastic fluid) B Microstructure (polymer, particles) B Bulk rheology B Flow induced crystallization Introduction (Multiple particles in a viscoelastic fluid) Introduction (Flow induced crystallization) Introduction (Multi-phase flows) Goal and contents of the course Goal: Introduction of the basic numerical techniques used in Computational Rheology using the Finite Element Method (FEM). -
Monday, July 26
USNCCM16 Technical Program (as of July 27, 2021) To find specific authors, use the search function in the pdf file. All times listed are in Central Daylight Saving Time. Monday, July 26 1 TS 1: MONDAY MORNING, JULY 26 10:00 AM 10:20 AM 10:40 AM 11:00 AM 11:20 AM Symposium Honoring J. Tinsley Oden's Monumental Contributions to Computational #M103 Mechanics, Chair(s): Romesh Batra Keynote presentation: On the Equivalence On the Coupling of Fiber-Reinforced Analysis and Between the Multiplicative Hyper-Elasto-Plasticity Classical and Non- Composites: Interface Application of and the Additive Hypo-Elasto-Plasticity Based on Local Models for Failures, Convergence Peridynamics to the Modified Kinetic Logarithmic Stress Rate Applications in Issues, and Sensitivity Fracture in Solids and Computational Analysis Granular Media Mechanics Jacob Fish*, Yang Jiao Serge Prudhomme*, Maryam Shakiba*, Prashant K Jha*, Patrick Diehl Reza Sepasdar Robert Lipton #M201 Imaging-Based Methods in Computational Medicine, Chair(s): Jessica Zhang Keynote presentation: Image-Based A PDE-Constrained Image-Based Polygonal Cardiac Motion Computational Modeling of Prostate Cancer Optimization Model for Lattices for Mechanical Estimation from Cine Growth to Assist Clinical Decision-Making the Material Transport Modeling of Biological Cardiac MR Images Control in Neurons Materials: 2D Based on Deformable Demonstrations Image Registration and Mesh Warping Guillermo Lorenzo*, Thomas J. R. Hughes, Angran Li*, Yongjie Di Liu, Chao Chen, Brian Wentz, Roshan Alessandro Reali, -
Rheology of Frictional Grains
Rheology of frictional grains Dissertation zur Erlangung des mathematisch-naturwissenschaftlichen Doktorgrades “Doctor rerum naturalium” der Georg-August-Universität Göttingen im Promotionsprogramm ProPhys der Georg-August University School of Science (GAUSS) vorgelegt von Matthias Grob aus Mühlhausen Göttingen, 2016 Betreuungsausschuss: • Prof. Dr. Annette Zippelius, Institut für Theoretische Physik, Georg-August-Universität Göttingen • Dr. Claus Heussinger, Institut für Theoretische Physik, Georg-August-Universität Göttingen Mitglieder der Prüfungskommission: • Referentin: Prof. Dr. Annette Zippelius, Institut für Theoretische Physik, Georg-August-Universität Göttingen • Korreferent: Prof. Dr. Reiner Kree, Institut für Theoretische Physik, Georg-August-Universität Göttingen Weitere Mitglieder der Prüfungskommission: • PD Dr. Timo Aspelmeier, Institut für Mathematische Stochastik, Georg-August-Universität Göttingen • Prof. Dr. Stephan Herminghaus, Dynamik Komplexer Fluide, Max-Planck-Institut für Dynamik und Selbstorganisation • Dr. Claus Heussinger, Institut für Theoretische Physik, Georg-August-Universität Göttingen • Prof. Cynthia A. Volkert, PhD, Institut für Materialphysik, Georg-August-Universität Göttingen Tag der mündlichen Prüfung: 09.08.2016 Zusammenfassung Diese Arbeit behandelt die Beschreibung des Fließens und des Blockierens von granularer Materie. Granulare Materie kann einen Verfestigungsübergang durch- laufen. Dieser wird Jamming genannt und ist maßgeblich durch vorliegende Spannungen sowie die Packungsdichte der Körner, -
Lecture 1: Introduction
Lecture 1: Introduction E. J. Hinch Non-Newtonian fluids occur commonly in our world. These fluids, such as toothpaste, saliva, oils, mud and lava, exhibit a number of behaviors that are different from Newtonian fluids and have a number of additional material properties. In general, these differences arise because the fluid has a microstructure that influences the flow. In section 2, we will present a collection of some of the interesting phenomena arising from flow nonlinearities, the inhibition of stretching, elastic effects and normal stresses. In section 3 we will discuss a variety of devices for measuring material properties, a process known as rheometry. 1 Fluid Mechanical Preliminaries The equations of motion for an incompressible fluid of unit density are (for details and derivation see any text on fluid mechanics, e.g. [1]) @u + (u · r) u = r · S + F (1) @t r · u = 0 (2) where u is the velocity, S is the total stress tensor and F are the body forces. It is customary to divide the total stress into an isotropic part and a deviatoric part as in S = −pI + σ (3) where tr σ = 0. These equations are closed only if we can relate the deviatoric stress to the velocity field (the pressure field satisfies the incompressibility condition). It is common to look for local models where the stress depends only on the local gradients of the flow: σ = σ (E) where E is the rate of strain tensor 1 E = ru + ruT ; (4) 2 the symmetric part of the the velocity gradient tensor. The trace-free requirement on σ and the physical requirement of symmetry σ = σT means that there are only 5 independent components of the deviatoric stress: 3 shear stresses (the off-diagonal elements) and 2 normal stress differences (the diagonal elements constrained to sum to 0). -
Rheometry SLIT RHEOMETER
Rheometry SLIT RHEOMETER Figure 1: The Slit Rheometer. L > W h. ∆P Shear Stress σ(y) = y (8-30) L −∆P h Wall Shear Stress σ = −σ(y = h/2) = (8-31) w L 2 NEWTONIAN CASE 6Q Wall Shear Rateγ ˙ = −γ˙ (y = h/2) = (8-32) w h2w σ −∆P h3w Viscosity η = w = (8-33) γ˙ w L 12Q 1 Rheometry SLIT RHEOMETER NON-NEWTONIAN CASE Correction for the real wall shear rate is analogous to the Rabinowitch correction. 6Q 2 + β Wall Shear Rateγ ˙ = (8-34a) w h2w 3 d [log(6Q/h2w)] β = (8-34b) d [log(σw)] σ −∆P h3w Apparent Viscosity η = w = γ˙ w L 4Q(2 + β) NORMAL STRESS DIFFERENCE The normal stress difference N1 can be determined from the exit pressure Pe. dPe N1(γ ˙ w) = Pe + σw (8-45) dσw d(log Pe) N1(γ ˙ w) = Pe 1 + (8-46) d(log σw) These relations were calculated assuming straight parallel streamlines right up to the exit of the die. This assumption is not found to be valid in either experiment or computer simulation. 2 Rheometry SLIT RHEOMETER NORMAL STRESS DIFFERENCE dPe N1(γ ˙ w) = Pe + σw (8-45) dσw d(log Pe) N1(γ ˙ w) = Pe 1 + (8-46) d(log σw) Figure 2: Determination of the Exit Pressure. 3 Rheometry SLIT RHEOMETER NORMAL STRESS DIFFERENCE Figure 3: Comparison of First Normal Stress Difference Values for LDPE from Slit Rheometer Exit Pressure (filled symbols) and Cone&Plate (open symbols). The poor agreement indicates that the more work is needed in order to use exit pressures to measure normal stress differences. -
20. Rheology & Linear Elasticity
20. Rheology & Linear Elasticity I Main Topics A Rheology: Macroscopic deformation behavior B Linear elasticity for homogeneous isotropic materials 10/29/18 GG303 1 20. Rheology & Linear Elasticity Viscous (fluid) Behavior http://manoa.hawaii.edu/graduate/content/slide-lava 10/29/18 GG303 2 20. Rheology & Linear Elasticity Ductile (plastic) Behavior http://www.hilo.hawaii.edu/~csav/gallery/scientists/LavaHammerL.jpg http://hvo.wr.usgs.gov/kilauea/update/images.html 10/29/18 GG303 3 http://upload.wikimedia.org/wikipedia/commons/8/89/Ropy_pahoehoe.jpg 20. Rheology & Linear Elasticity Elastic Behavior https://thegeosphere.pbworks.com/w/page/24663884/Sumatra http://www.earth.ox.ac.uk/__Data/assets/image/0006/3021/seismic_hammer.jpg 10/29/18 GG303 4 20. Rheology & Linear Elasticity Brittle Behavior (fracture) 10/29/18 GG303 5 http://upload.wikimedia.org/wikipedia/commons/8/89/Ropy_pahoehoe.jpg 20. Rheology & Linear Elasticity II Rheology: Macroscopic deformation behavior A Elasticity 1 Deformation is reversible when load is removed 2 Stress (σ) is related to strain (ε) 3 Deformation is not time dependent if load is constant 4 Examples: Seismic (acoustic) waves, http://www.fordogtrainers.com rubber ball 10/29/18 GG303 6 20. Rheology & Linear Elasticity II Rheology: Macroscopic deformation behavior A Elasticity 1 Deformation is reversible when load is removed 2 Stress (σ) is related to strain (ε) 3 Deformation is not time dependent if load is constant 4 Examples: Seismic (acoustic) waves, rubber ball 10/29/18 GG303 7 20. Rheology & Linear Elasticity II Rheology: Macroscopic deformation behavior B Viscosity 1 Deformation is irreversible when load is removed 2 Stress (σ) is related to strain rate (ε ! ) 3 Deformation is time dependent if load is constant 4 Examples: Lava flows, corn syrup http://wholefoodrecipes.net 10/29/18 GG303 8 20.