Transactions on Modelling and Simulation vol 10, 1995 WIT Press, ISSN X
|
|
- Kerry Williamson
- 5 years ago
- Views:
Transcription
1 Modelling the behaviour of rubber-like materials to obtain correlation with rigidity modulus tests S.J. Jerrams, J. Bowen School of Engineering, Coventry University, Coventry England Abstract Finite element software for analysing components made from rubber-like materials employ strain energy functions to enable the determination of stress and displacement. Most use Mooney-Rivlin constants to define the material behaviour and these constants are simply related to the rigidity modulus for a given material. The statistical theory for the stress-strain relationship for rubbers implies that the material will obey Hooke's Law in shear though not in tension or compression. Previous research suggests that the modulus ofrigidityremains constant for shear strains up to 1.0. Values forrigiditymodulus for a 60IRHD rubber are determined from standard tests on dual-lap and quad-lap specimens. These are compared with the value given by the manufacturer, that determined from the quoted Mooney-Rivlin constants and those obtained from two-dimensional plane strain and three dimensionalfiniteelement analyses conducted using ANSYS software. Increasingly, nonlinear rather than linear finite element stress analyses are required by industry. Hyperelastic materials are less well understood than Hookean materials by engineers and without commensurate testing and consequent revision of input data,finiteelement analysis could not be trusted. Finally disparities between testing and analyses are discussed and the implications for hyperelastic analyses considered with respect to ongoing research requirements. 1 Introduction Engineers lack confidence infiniteelement analyses of elastomers due to the sparsity of test results and standard analytical solutions for nonlinear materials.
2 512 Computational Methods and Experimental Measurements Verification of linear elastic analyses are not problematical as material behaviour and constants are well understood. This is less so for nonlinear stresses and strains, though increasingly FEA solutions are required for situations where components exhibit plastic or hyperelastic deformations. Rubber-like materials subjected to tensile and compressive loads do not possess a constant modulus of elasticity for any part of a stress-strain curve. However linearity for shear strains up to 1.0 ( 100% ) have been observed when shear stress (i ) is plotted against shear strain ( y )fromtensile test results ( Treloar 1975 [ 1 ]). The statistical theory of rubber deformation suggests a constant value of shear modulus for long-chain molecules subjected to moderate extensions, but for higher extensions this theory becomes inadequate. Typical discrepancy between theory and experimentation is shown in Fig. 1. 1,6 - THEORY/ TEST 1,2-0,8-0,4-0,0 I I 3 4 SHEAR STRAIN Figure 1: Relationship between shear stress and shear strain determined from tensile test data and from statistical theory for a typical rubber. Hyperelastic finite element analyses use strain energy ( density ) functions to predict stresses and deformations. The inclusion of more terms in a function improves accuracy, but higher-order models require more complex determination of material coefficients. The strain energy function used by ANSYS is of the form shown below. W = Cio(I-3) + Co,(H-3) + X(l/IIl2-l) + Y(III-l)2 (1) where W = work of deformation ( strain energy function ) I, II and III are invariants of the right Cauchy-Green deformation tensor and are expressed in terms of A^, A^ and A^ the principal stretch ratios CIQ, CQI, X and Y are Mooney-Rivlin constants.
3 Computational Methods and Experimental Measurements 513 = 1/2 1-2v where v = Poisson's ratio ( ANSYS Tutorial - Hyperelastic Elements [ 2 ] ) If the material is virtually incompressible the third and fourth terms in the righthand side of equation 1 are insignificant since III is almost unity. Thefirsttwo Mooney-Rivlin constants for an incompressible material are related to the initial Shear Modulus by the formula Shear Modulus ( Rigidity Modulus ) G - 2 ( C,o + Q,, ) ( N / mm^ ) ( MARC software also uses Mooney-Rivlin constants in a two parameter model and a five parameter model where the additional constants are determined from material tests. However, the strain energy functions determined from Mooney- Rivlin constants are derived solely on even powers of the extension ratios, which is based on expedience rather than rationality Ogden wrote a strain energy function in series form to avoid this difficulty ( Treloar 1975 [ 3 ] ). The function, given below is offered by MARC and the values of the constants c^ and Pa are determined from tensile tests... _ A,3«n-3) (3) a" n Research is underway to determine if tactile sensors, employed in Robotics, can use stresses and deformations in compliant materials to recognise the shape of components. Further, it is hoped that FEA can model and predict these deformations to provide information for the sensors. Previous research has assumed that pads holding the sensors were subject to linear deformations ( Fearing 1983 [ 4 ], Fearing and Hollerbach 1985 [5] and Speeter 1992 [6]) Initial analyses into contact stresses in elastomers suggest that component shapes can be identified at specific depths in compliant media ( Jerrams and Hookes 1993 [ 7 ]), but physical tests are needed to verify this work and to provide information for subsequent modelling. Thus it is essential that software allows the determination of material behaviour at high stretch ratios. A sample of 60IRHD medium hard rubber was provided by Metalastik, Dunlop Ltd., conforming to the specification shown below. Material: First grade natural rubber compound Ref N Shore A hardness
4 514 Computational Methods and Experimental Measurements Poisson's ratio ( v ) = Mooney-Rivlin constants CJQ = MPa CQI = MPa. Hence the theoretical value of G, obtainedfromthe relationship G = [ 2 ( C^ + C<>i ) ] is MPa As afirststep toward confirming the accuracy of analyses, dual-lap and quad-lap rigidity modulus tests to BS 903: Part A14 ( or ISO 1827: 1991(E) which is identical) [ 8 ] have been modelled and analysed. The results are compared with those obtained from tests on specimens produced from the sample. Recommendations for the verification of shear modulus and hence material constants for rubber-like materials are made. This allows for improved understanding of FEA modelling of elastomers when applying the technique to more complex problems. 2 Rigidity modulus tests and analyses Before conducting the shear modulus tests, a simple tensile test was carried out to verify the Mooney-Rivlin constants. The gauge length for the test-piece was 20mm, the cross-section 19 x 5.85mm and the rate of traverse 500mm/min. The test-piece was extended to a stretch ratio (1) of approximately six. If a graph of ( > versus 1/X is plotted ( Figure 2 ), the slope of the straight line portion yields the constant CQI and the intercept on the vertical axis at 1 A, = 1 gives the value of CIQ + Qi- Normally CQI is small, but the test results gave a slope close to unity, suggesting that the supplied values of Co * and CJQ could be transposed. MARC UK also analysed the tensile test results and determined C^ and CQI for different values of K. Their evaluation confirmed that for the sample tested the Mooney-Rivlin constants appeared transposed ( CQI > C^ ), though the constants calculated resulted in an under stiff model. MARC also determined Ogden constants from the test results which gave an overstiff model for high strains. To improve this model more points would need to befittedto the curve and this will form the basis of future work. An evaluation of the suppliers method of determining the constants appeared to show that they miscalculated the value ofc^ which would also have a small effect on the determination of the initial shear modulus. The test-piece was cut from a block 300mm square by 50mm deep, unlike a conventional test-piece which would be pressed from a rolled strip, so some change in properties, surface damage and small dimensional variations were unavoidable. However, the test should still be broadly representative of material behaviour. Hyperelastic constants should not be assumed when undertaking afiniteelement stress analysis of a rubber component. Of course, typical components are not
5 Computational Methods and Experimental Measurements 515 manufactured from test grade rubber, reinforcing the need to tensile test a piece of rubber taken from an actual component. To consider the disparity between quoted and determined constants a finite element model of the tensile test was carried out and the simulations of shear modulus tests were made with Mooney- Rivlin constants entered as quoted and transposed. The simulations of the tensile test proved of little value because predicted displacements were far smaller for both 2D and 3D finite element models. The 2D model could be expected to be overstiff because a plane stress option is not available for ANSYS 2D hyperelastic analyses and the plane strain option used would not simulate a Poisson's effect in the third plane. The 3D model, inexplicably gave even smaller displacements. This suggests that hyperelastic elements configured to give a constant shear modulus are unable to model other modes of deformation accurately. Dual-lap and quad-lap test-pieces were manufactured as shown in Figure 3 to the British and international standards. The rubber was bonded to therigidmetal plates using Methyl-2-cyanoacrylate adhesive. Normally when conducting dual and quad-lap shear modulus tests, this bonding takes place during vulcanisation. Since the rubber parallelepipeds were cut from the same large block this was not possible. Consequently, failure of the bond could be expected at a lower shear strain than would usually obtain Slope C\, * = L = c10 (4) where: A, = stretch ratio = strained length unstrained length f = tensile stress based on unstrained cross- sectional area ( N / Figure 2: Tensile test result for rubber sample To avoid errors induced by stress relaxation, the test-pieces were pulled apart at a constant rate of 5mm per minute and it was observed that for each type of test the bonds initially failed at shear strains between 50% and 60%. Though these
6 516 Computational Methods and Experimental Measurements failures did not allow the shear modulus to be determined at strains above 1.0, Figures 4 and 5 show clearly that the modulus ceases to be approximately constant for relatively low strains, linearity ceasing in the range of 6-8% shear strain. The initial slopes ( shear stress / shear strain ) achieved in the tests give Figure 3: Dual-lap and Quad-lap Test-pieces for Shear Modulus Tests 1.4 Test Shear Mode. ~~ A - 1: Ansys 2D Model, Ansys 3D Model, Theory with MPa. 2: Theory with 1.5 MPa. 3: Test Y % Shear Strain = T / y = / 0.25 = MPa Figure 4: Shear Stress versus Shear Strain from Dual-lap Test : Ansys 2D Model, Ansys 3D Model Theory with MPa 2: Theory with 1.5 MPa. 3: Test 25% Shear Strain = %/y = 0.372/0.25 = 1.49 MPa Figure 5: Shear Stress versus Shear Strain from Quad-lap Tests
7 Computational Methods and Experimental Measurements 517 values of G averaging MPa, which is very similar to MPa, that determined from the Mooney-Rivlin constants supplied by the manufacturer. The mean value of rigidity modulus from each set of tests at the shear strain stipulated by the standards ( 25% ) is MPa, which is virtually that quoted by Metalastik ( 1.5MPa ). To interrogate the performance of hyperelastic elements supported by ANSYS, each test was modelled in two and three dimensions. The dual-lap tests distort the parallelepipeds in simple shear as shown in Figure 4, whilst the quad-lap tests simulate pure shear (Figure 5 ). Thus both 3D and a 2D plane strain, half model analysis of the dual-lap test could be considered accurate representations, whilst a 2D plane strain, quarter model of the quad-lap test would have small errors due to the presence of strain in the Z direction. The 2D and 3D models comprised eight noded quadrilateral and brick elements respectively, though a 2D element without midside nodes is available and each element type has degenerate forms. Each model was load stepped to a maximum shear strain of 150% and the stress/strain curves obtained are shown in figures 4 and 5. Mooney-Rivlin constants were varied for all the models to alter the tensile properties of the rubber. Their sum was unaltered to keep the value of the initial shear modulus predicted by statistical theory unchanged ( Table 1 ). C,o Q, Assumed G 2(C,0 + C01) (MPa) Table 1 Mooney-Rivlin constants input forrigiditymodulus test simulations Shear stresses plotted against shear strains predictably give straight lines virtually sharing the same slope for each analysis and variations in constants. So analyses and test diverge at values of y of 6 to 8% and the predicted values of i are 59% in error at 50% shear strain (y = 0.5 ). Verification of hyperelastic analyses It is clear that for any large displacement hyperelastic finite element analysis, the use of strain energy ( density) functions based on Mooney-Rivlin constants will only give satisfactory results if the component is predominantly subjected to shear and then only if the shear modulus is constant for a large strain range. The value of either Mooney-Rivlin constant ( C^ or C<>i ) is largely irrelevant to an analysis predicting deformation in shear, providing the sum of the constants results in the same initial shear modulus. Thus it is obvious that a model using
8 518 Computational Methods and Experimental Measurements Mooney-Rivlin constants that accurately predicts behaviour in shear over a small strain range may prove utterly inadequate for other modes of deformation and for greater strain ranges. Manufacturers quoted material constants can be unreliable and tests on material taken from a component should be conducted whenever possible. Since the phenomenological theory of the behaviour of rubber assumes a constant shear modulus, benchmark testing of punch problems should indicate whether indentation can be accurately modelled and if so, over what strain ranges for individual rubbers. Unfortunately, it is evident that the requirement to correctly simulate the physical behaviour of rubber in all modes and working environments remains unrealised. References 1. Treloar L.R.G. 7%f Physics of Rubber Elasticity ( 3^ edition) pp Claredon Press, Oxford Marx F J ANSYSRevision 4.3 Tutorial, Hyerelastic Elements pp Swanson Analysis Systems Inc Treloar L.R.G. The Physics of Rubber Elasticity ( 3>'<* edition) pp Claredon Press, Oxford Fearing R.S. Touch processing for determining a stable grasp. Master's thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science Fearing R.S. and Hollerbach JM Basic Solid Mechanics of tactile sensing. The International Journal of Robotics Research, Vol 4, No Specter T.H. Three-dimensional finite element analysis of elastic continua for tactile sensing. The International Journal of Robotics Research, vol 11, No Jerrams S. J and Hookes D. The computer simulation of the indentation of compliant surfaces in production engineering. CAD, CAM, Robotics and Autonomous Factories, Vol. 4. pp New Delhi British and international standards. BS903; part A14: 1992 and ISO 1827: 1991 ( E ) Rubber, \wlcanisedor thermoplastic - Determination of modulus in shear or adhesion to rigid plates - Quadruple shear method.
Benchmarkingfiniteelement simulation of rigid indenters in elastomers S.J. Jerrams, N. Reece-Pinchin
Benchmarkingfiniteelement simulation of rigid indenters in elastomers S.J. Jerrams, N. Reece-Pinchin Abstract Verifications of finite element techniques applied to elastomers are difficult to achieve since
More informationA Review On Methodology Of Material Characterization And Finite Element Modelling Of Rubber-Like Materials
IOSR Journal of Engineering (IOSRJEN) ISSN (e): 50-301, ISSN (p): 78-8719 PP 06-10 www.iosrjen.org A Review On Methodology Of Material Characterization And Finite Element Modelling Of Rubber-Like Materials
More informationEXPERIMENTAL IDENTIFICATION OF HYPERELASTIC MATERIAL PARAMETERS FOR CALCULATIONS BY THE FINITE ELEMENT METHOD
Journal of KONES Powertrain and Transport, Vol. 7, No. EXPERIMENTAL IDENTIFICATION OF HYPERELASTIC MATERIAL PARAMETERS FOR CALCULATIONS BY THE FINITE ELEMENT METHOD Robert Czabanowski Wroclaw University
More informationA strategy for benchmarkingfiniteelement analysis of nitrile rubbers
A strategy for benchmarkingfiniteelement analysis of nitrile rubbers S.J. Jerrams & S.J. Harvey Rubber Research and Technology Unit, Coventry University, Priory St., Coventry CV1 5FB, England Email: cex076@coventry.ac.uk
More informationComparative Study of Variation of Mooney- Rivlin Hyperelastic Material Models under Uniaxial Tensile Loading
Comparative Study of Variation of Mooney- Rivlin Hyperelastic Material Models under Uniaxial Tensile Loading A. N. Jadhav 1, Dr. S.R. Bahulikar, N.H. Sapate 3 1 M Tech Design Engg, Mechanical Engineering,
More informationCOMPARISON OF CONSTITUTIVE HYPER-ELASTIC MATERIAL MODELS IN FINITE ELEMENT THEORY
OTEKON 2012 6. Otomotiv Teknolojileri Kongresi 04 05 Haziran 2012, BURSA COMPARISON O CONSTITUTIVE HYPER-ELASTIC MATERIAL MODELS IN INITE ELEMENT THEORY ABSTRACT Savaş Kayacı, Ali Kamil Serbest Las-Par
More information2.1 Strain energy functions for incompressible materials
Chapter 2 Strain energy functions The aims of constitutive theories are to develop mathematical models for representing the real behavior of matter, to determine the material response and in general, to
More informationSimulation of the mechanical behavior of a rubber pumping system under large deformations.
Simulation of the mechanical behavior of a rubber pumping system under large deformations. Author: Ing. Andrea Romeo LPA Consorzio per la promozione della cultura plastica Proplast Str. Comunale Savonesa,
More informationThe strain response of silicone dielectric elastomer actuators
The strain response of silicone dielectric elastomer actuators G. Yang a, G. Yao b, W. Ren a, G. Akhras b, J.P. Szabo c and B.K. Mukherjee a* a Department of Physics, Royal Military College of Canada,
More informationProject PAJ2 Dynamic Performance of Adhesively Bonded Joints. Report No. 3 August Proposed Draft for the Revision of ISO
NPL Report CMMT(A)81 Project PAJ2 Dynamic Performance of Adhesively Bonded Joints Report No. 3 August 1997 Proposed Draft for the Revision of ISO 11003-2 Adhesives - Determination of Shear Behaviour of
More informationMEASUREMENT METHODS FOR OBTAINING VOLUMETRIC COEFFICIENTS FOR HYPERELASTIC MODELLING OF FLEXIBLE ADHESIVES
MEASUREMENT METHODS FOR OBTAINING VOLUMETRIC COEFFICIENTS FOR HYPERELASTIC MODELLING OF FLEXIBLE ADHESIVES by Louise Crocker and Bruce Duncan Project PAJex2 - Flexible Adhesives PAJex2 Report No 3 January
More informationNonlinear Modeling for Health Care Applications Ashutosh Srivastava Marc Horner, Ph.D. ANSYS, Inc.
Nonlinear Modeling for Health Care Applications Ashutosh Srivastava Marc Horner, Ph.D. ANSYS, Inc. 2 Motivation 12 Motivation Linear analysis works well for only small number of applications. The majority
More informationTesting and Analysis
Testing and Analysis Testing Elastomers for Hyperelastic Material Models in Finite Element Analysis 2.6 2.4 2.2 2.0 1.8 1.6 1.4 Biaxial Extension Simple Tension Figure 1, A Typical Final Data Set for Input
More informationFEM model of pneumatic spring assembly
FEM model of pneumatic spring assembly Tien Tran Xuan 1, David Cirkl 2 Department of Applied Mechanics, Faculty of Mechanical Engineering, Technical University of Liberec, Liberec, Czech Republic 1 Corresponding
More informationNORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.
NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric
More informationConstitutive Modelling of Elastomeric Seal Material under Compressive Loading
Modeling and Numerical Simulation of Material Science, 206, 6, 28-40 Published Online April 206 in SciRes. http://www.scirp.org/journal/mnsms http://dx.doi.org/0.4236/mnsms.206.62004 Constitutive Modelling
More informationHIGHLY ADAPTABLE RUBBER ISOLATION SYSTEMS
th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 24 Paper No. 746 HIGHLY ADAPTABLE RUBBER ISOLATION SYSTEMS Luis DORFMANN, Maria Gabriella CASTELLANO 2, Stefan L. BURTSCHER,
More informationDetermination of Mechanical Properties of Elastomers Using Instrumented Indentation
Determination of Mechanical Properties of Elastomers Using Instrumented Indentation, Antonios E. Giannakopoulos and Dimitrios Bourntenas University of Thessaly, Department of Civil Engineering, Volos 38334,
More informationModelling the behaviour of plastics for design under impact
Modelling the behaviour of plastics for design under impact G. Dean and L. Crocker MPP IAG Meeting 6 October 24 Land Rover door trim Loading stages and selected regions Project MPP7.9 Main tasks Tests
More informationUniversity of Sheffield The development of finite elements for 3D structural analysis in fire
The development of finite elements for 3D structural analysis in fire Chaoming Yu, I. W. Burgess, Z. Huang, R. J. Plank Department of Civil and Structural Engineering StiFF 05/09/2006 3D composite structures
More informationMaterial testing and hyperelastic material model curve fitting for Ogden, Polynomial and Yeoh models
Material testing and hyperelastic material model curve fitting for Ogden, Polynomial and Yeoh models ScilabTEC 2015, Paris, France Michael Rackl rackl@fml.mw.tum.de Technische Universität München (TUM)
More informationChapter 7. Highlights:
Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true
More informationComparative Study of Hyper Elastic Material Models
International Journal of Engineering and Manufacturing Science. ISSN 2249-3115 Volume 7, Number 2 (2017), pp. 149-170 Research India Publications http://www.ripublication.com Comparative Study of Hyper
More informationMITOCW MITRES2_002S10nonlinear_lec15_300k-mp4
MITOCW MITRES2_002S10nonlinear_lec15_300k-mp4 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources
More informationMSC Elastomers Seminar Some Things About Elastomers
MSC Elastomers Seminar Some Things About Elastomers Kurt Miller, Axel Products, Inc. www.axelproducts.com Visit us at: axelproducts.com 2 Your Presenter Kurt Miller Founded Axel Products 1994 Instron Corporation,
More informationSIMULATION OF MECHANICAL TESTS OF COMPOSITE MATERIAL USING ANISOTROPIC HYPERELASTIC CONSTITUTIVE MODELS
Engineering MECHANICS, Vol. 18, 2011, No. 1, p. 23 32 23 SIMULATION OF MECHANICAL TESTS OF COMPOSITE MATERIAL USING ANISOTROPIC HYPERELASTIC CONSTITUTIVE MODELS Tomáš Lasota*, JiříBurša* This paper deals
More informationA COMPARATIVE STUDY OF HYPERELASTIC CONSTITUTIVE MODELS FOR AN AUTOMOTIVE COMPONENT MATERIAL
A COMPARATIVE STUDY OF HYPERELASTIC CONSTITUTIVE MODELS FOR AN AUTOMOTIVE COMPONENT MATERIAL Rafael Tobajas (a), Daniel Elduque (b), Carlos Javierre (c), Elena Ibarz (d), Luis Gracia (e) (a),(b),(c),(d),(e)
More informationSTANDARD SAMPLE. Reduced section " Diameter. Diameter. 2" Gauge length. Radius
MATERIAL PROPERTIES TENSILE MEASUREMENT F l l 0 A 0 F STANDARD SAMPLE Reduced section 2 " 1 4 0.505" Diameter 3 4 " Diameter 2" Gauge length 3 8 " Radius TYPICAL APPARATUS Load cell Extensometer Specimen
More informationThe elastic behavior of a rubber-like material for composite glass
The elastic behavior of a rubber-like material for composite glass Silvia Briccoli Bati 1, Mario Fagone 1, Giovanna Ranocchiai 1 1 Department of Costruzioni, University of Florence, Italy E-mail: silvia.briccolibati@unifi.it
More information[5] Stress and Strain
[5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law
More informationModule 4 : Nonlinear elasticity Lecture 25 : Inflation of a baloon. The Lecture Contains. Inflation of a baloon
Lecture 25 : Inflation of a baloon The Lecture Contains Inflation of a baloon 1. Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues with examples, M. F Beatty, App.
More informationOpen-hole compressive strength prediction of CFRP composite laminates
Open-hole compressive strength prediction of CFRP composite laminates O. İnal 1, A. Ataş 2,* 1 Department of Mechanical Engineering, Balikesir University, Balikesir, 10145, Turkey, inal@balikesir.edu.tr
More informationCHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS
CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. A rectangular bar having a cross-sectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress
More informationME 2570 MECHANICS OF MATERIALS
ME 2570 MECHANICS OF MATERIALS Chapter III. Mechanical Properties of Materials 1 Tension and Compression Test The strength of a material depends on its ability to sustain a load without undue deformation
More informationStress-Strain Behavior
Stress-Strain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.
More informationOutline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour
Tensile-Test Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress - true strain (flow curve) mechanical properties: - Resilience - Ductility - Toughness - Hardness A standard
More informationStatic and Time Dependent Failure of Fibre Reinforced Elastomeric Components. Salim Mirza Element Materials Technology Hitchin, UK
Static and Time Dependent Failure of Fibre Reinforced Elastomeric Components Salim Mirza Element Materials Technology Hitchin, UK Introduction Fibre reinforced elastomers are used in many applications,
More informationTesting Elastomers and Plastics for Marc Material Models
Testing Elastomers and Plastics for Marc Material Models Presented by: Kurt Miller Axel Products, Inc. axelproducts.com We Measure Structural Properties Stress Strain Time-Temperature Test Combinations
More informationINTRODUCTION TO STRAIN
SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,
More informationNUMERICAL MODELLING AND EXPERIMENTAL INFLATION VALIDATION OF A BIAS TWO-WHEEL TIRE
Journal of Engineering Science and Technology 4 th EURECA 05 Special Issue February (06) 70-8 School of Engineering, Taylor s University NUMERICAL MODELLING AND EXPERIMENTAL INFLATION VALIDATION OF A BIAS
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Statics
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS
EDEXCEL NATIONAL CERTIICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQ LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS 1. Be able to determine the effects of loading in static engineering
More informationMechanical properties 1 Elastic behaviour of materials
MME131: Lecture 13 Mechanical properties 1 Elastic behaviour of materials A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Deformation of material under the action of a mechanical
More informationSTRUCTURAL OPTIMIZATION OF A MATERIAL EXHIBITING NEGATIVE STIFFNESS
International Conference on Engineering Vibration Ljubljana, Slovenia, 7-0 September 05 STRUCTURAL OPTIMIZATION OF A MATERIAL EXHIBITING NEGATIVE STIFFNESS Zuzana Dimitrovová*, Jan Heczo, Helder C. Rodrigues
More informationLectures on. Constitutive Modelling of Arteries. Ray Ogden
Lectures on Constitutive Modelling of Arteries Ray Ogden University of Aberdeen Xi an Jiaotong University April 2011 Overview of the Ingredients of Continuum Mechanics needed in Soft Tissue Biomechanics
More informationISO 178 INTERNATIONAL STANDARD. Plastics Determination of flexural properties. Plastiques Détermination des propriétés en flexion
INTERNATIONAL STANDARD ISO 178 Fourth edition 2001-12-15 Plastics Determination of flexural properties Plastiques Détermination des propriétés en flexion Reference number ISO 2001 PDF disclaimer This PDF
More informationGB/T / ISO 527-1:1993
Translated English of Chinese Standard: GB/T1040.1-2006 www.chinesestandard.net Sales@ChineseStandard.net GB NATIONAL STANDARD OF THE PEOPLE S REPUBLIC OF CHINA ICS 83.080.01 G 31 GB/T 1040.1-2006 / ISO
More informationPhysical Properties Testing Technical Bulletin
Technical Bulletin MANUFACTURER Raven Lining Systems 13105 E. 61 st Street, Suite A Broken Arrow, OK 74012 (918) 615-0020 TENSILE TESTING OF PLASTICS ASTM D638, ISO 527 Tensile tests measure the force
More informationSize Effects In the Crushing of Honeycomb Structures
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 19-22 April 2004, Palm Springs, California AIAA 2004-1640 Size Effects In the Crushing of Honeycomb Structures Erik C.
More informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011
Interlaminar failure analysis of FRP cross ply laminate with elliptical cutout Venkateswara Rao.S 1, Sd. Abdul Kalam 1, Srilakshmi.S 1, Bala Krishna Murthy.V 2 1 Mechanical Engineering Department, P. V.
More informationBending Load & Calibration Module
Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of
More informationMechanical Properties of Polymer Rubber Materials Based on a New Constitutive Model
Mechanical Properties of Polymer Rubber Materials Based on a New Constitutive Model Mechanical Properties of Polymer Rubber Materials Based on a New Constitutive Model J.B. Sang*, L.F. Sun, S.F. Xing,
More informationBIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS
BIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS H. Kumazawa and T. Takatoya Airframes and Structures Group, Japan Aerospace Exploration Agency 6-13-1, Ohsawa, Mitaka,
More information, causing the length to increase to l 1 R U M. L Q P l 2 l 1
1 1 Which of the following correctly defines the terms stress, strain and oung modulus? stress strain oung modulus (force) x (area) (extension) x (original length) (stress) / (strain) (force) x (area)
More informationUnderstanding Frequency Domain Viscoelasticity in Abaqus
Paper # 12 Understanding Frequency Domain Viscoelasticity in Abaqus By Saurabh Bahuguna, Randy Marlow*, and Tod Dalrymple Dassault Systèmes Simulia Corp., Great Lakes Region Presented at the Fall 172 nd
More informationA CRITERION OF TENSILE FAILURE FOR HYPERELASTIC MATERIALS AND ITS APPLICATION TO VISCOELASTIC-VISCOPLASTIC MATERIALS
MTS ADHESIVES PROGRAMME 1996-1999 PERFORMANCE OF ADHESIVE JOINTS Project: PAJ1; Failure Criteria and their Application to Visco-Elastic/Visco-Plastic Materials Report 2 A CRITERION OF TENSILE FAILURE FOR
More information1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine Spring 2004 LABORATORY ASSIGNMENT NUMBER 6
1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine MIT Spring 2004 LABORATORY ASSIGNMENT NUMBER 6 COMPRESSION TESTING AND ANISOTROPY OF WOOD Purpose: Reading: During this laboratory
More informationUpon Impact Numerical Modeling of Foam Materials
Upon Impact Numerical Modeling of Foam Materials VASILE NASTASESCU*, SILVIA MARZAVAN Military Technical Academy, 81-83 George Cosbuc Blvd., 050141, Bucharest, Romania The paper presents some theoretical
More informationLITERATURE SURVEY SUMMARY OF HYPERELASTIC MODELS FOR PDMS
LITERATURE SURVEY SUMMARY OF HYPERELASTIC MODELS FOR PDMS ZHAO Feihu feihu.zhao@tut.fi 0 P age CONTENT 1. Mooney- Rivlin Model-----------------------------------------------------------------------------------------
More informationMECE 3321 MECHANICS OF SOLIDS CHAPTER 3
MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.
More informationA Numerical Study of Finite Element Calculations for Incompressible Materials under Applied Boundary Displacements
A Numerical Study of Finite Element Calculations for Incompressible Materials under Applied Boundary Displacements A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment
More informationX has a higher value of the Young modulus. Y has a lower maximum tensile stress than X
Bulk Properties of Solids Old Exam Questions Q1. The diagram shows how the stress varies with strain for metal specimens X and Y which are different. Both specimens were stretched until they broke. Which
More informationQUESTION BANK Composite Materials
QUESTION BANK Composite Materials 1. Define composite material. 2. What is the need for composite material? 3. Mention important characterits of composite material 4. Give examples for fiber material 5.
More informationANSYS Mechanical Basic Structural Nonlinearities
Lecture 4 Rate Independent Plasticity ANSYS Mechanical Basic Structural Nonlinearities 1 Chapter Overview The following will be covered in this Chapter: A. Background Elasticity/Plasticity B. Yield Criteria
More informationCode_Aster. SSNP161 Biaxial tests of Kupfer
Titre : SSNP161 Essais biaxiaux de Kupfer Date : 10/10/2012 Page : 1/8 SSNP161 Biaxial tests of Kupfer Summary: Kupfer [1] is interested to characterize the performances of the concrete under biaxial loadings.
More informationClassification of Prostate Cancer Grades and T-Stages based on Tissue Elasticity Using Medical Image Analysis. Supplementary Document
Classification of Prostate Cancer Grades and T-Stages based on Tissue Elasticity Using Medical Image Analysis Supplementary Document Shan Yang, Vladimir Jojic, Jun Lian, Ronald Chen, Hongtu Zhu, Ming C.
More informationFlexural properties of polymers
A2 _EN BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS FACULTY OF MECHANICAL ENGINEERING DEPARTMENT OF POLYMER ENGINEERING Flexural properties of polymers BENDING TEST OF CHECK THE VALIDITY OF NOTE ON
More informationFinite-Element Analysis of Stress Concentration in ASTM D 638 Tension Specimens
Monika G. Garrell, 1 Albert J. Shih, 2 Edgar Lara-Curzio, 3 and Ronald O. Scattergood 4 Journal of Testing and Evaluation, Vol. 31, No. 1 Paper ID JTE11402_311 Available online at: www.astm.org Finite-Element
More informationModelling Rubber Bushings Using the Parallel Rheological Framework
Modelling Rubber Bushings Using the Parallel Rheological Framework Javier Rodríguez 1, Francisco Riera 1, and Jon Plaza 2 1 Principia, Spain; 2 Cikatek, Spain Abstract: Bushings are anti vibration components
More informationPredicting the dynamic material constants of Mooney-Rivlin model in broad frequency range for elastomeric components
1983 Predicting the dynamic material constants of Mooney-Rivlin model in broad frequency range for elastomeric components Abstract In this paper, dynamic material constants of 2-parameter Mooney-Rivlin
More information3.22 Mechanical Properties of Materials Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 3.22 Mechanical Properties of Materials Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Quiz #1 Example
More informationTensile stress strain curves for different materials. Shows in figure below
Tensile stress strain curves for different materials. Shows in figure below Furthermore, the modulus of elasticity of several materials effected by increasing temperature, as is shown in Figure Asst. Lecturer
More informationEnhancing Prediction Accuracy In Sift Theory
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS Enhancing Prediction Accuracy In Sift Theory J. Wang 1 *, W. K. Chiu 1 Defence Science and Technology Organisation, Fishermans Bend, Australia, Department
More informationA comparison of the Hart-Smith model with the Arruda-Boyce and Gent formulations for rubber elasticity
A comparison of the Hart-Smith model with the Arruda-Boyce and Gent formulations for rubber elasticity Grégory Chagnon, Gilles Marckmann, Erwan Verron To cite this version: Grégory Chagnon, Gilles Marckmann,
More informationElectromechanically Coupled Finite Element Model of a Circular Electro-active Polymer Actuator. by Aseem Pralhad Deodhar
ABSTRACT DEODHAR, ASEEM PRALHAD. Electromechanically Coupled Finite Element (FE) Model of a Circular Electro-active Polymer Actuator. (Under the direction of Dr. Stefan Seelecke). This thesis presents
More informationFinal Project: Indentation Simulation Mohak Patel ENGN-2340 Fall 13
Final Project: Indentation Simulation Mohak Patel ENGN-2340 Fall 13 Aim The project requires a simulation of rigid spherical indenter indenting into a flat block of viscoelastic material. The results from
More informationElastic Properties of Solid Materials. Notes based on those by James Irvine at
Elastic Properties of Solid Materials Notes based on those by James Irvine at www.antonine-education.co.uk Key Words Density, Elastic, Plastic, Stress, Strain, Young modulus We study how materials behave
More informationPRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses
OPTIMAT BLADES Page 1 of 24 PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses first issue Peter Joosse CHANGE RECORD Issue/revision date pages Summary of changes draft 24-10-02
More informationExperimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives
Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives Mark Oliver October 19, 2016 Adhesives and Sealants Council Fall Convention contact@veryst.com www.veryst.com Outline
More informationMECHANICAL AND RHEOLOGICAL PROPERTIES
MECHANICAL AND RHEOLOGICAL PROPERTIES MECHANICAL PROPERTIES OF SOLIDS Extension Shear δ τ xy l 0 l l 0 θ σ Hooke's law σ = Eε Hooke's law τ = G γ xy xy MECHANICAL AND RHEOLOGICAL PROPERTIES RHEOLOGICAL
More informationTheoretical Manual Theoretical background to the Strand7 finite element analysis system
Theoretical Manual Theoretical background to the Strand7 finite element analysis system Edition 1 January 2005 Strand7 Release 2.3 2004-2005 Strand7 Pty Limited All rights reserved Contents Preface Chapter
More informationSTRENGTH OF MATERIALS-I. Unit-1. Simple stresses and strains
STRENGTH OF MATERIALS-I Unit-1 Simple stresses and strains 1. What is the Principle of surveying 2. Define Magnetic, True & Arbitrary Meridians. 3. Mention different types of chains 4. Differentiate between
More informationElastic Properties of Solids (One or two weights)
Elastic properties of solids Page 1 of 8 Elastic Properties of Solids (One or two weights) This is a rare experiment where you will get points for breaking a sample! The recommended textbooks and other
More informationEffect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test
Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test M. Praveen Kumar 1 and V. Balakrishna Murthy 2* 1 Mechanical Engineering Department, P.V.P. Siddhartha Institute of Technology,
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 1 - STATIC AND DYNAMIC FORCES TUTORIAL 3 STRESS AND STRAIN
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 1 - STATIC AND DYNAMIC FORCES TUTORIAL 3 STRESS AND STRAIN 1 Static and dynamic forces Forces: definitions of: matter, mass, weight,
More informationENGINEERING FOR RURAL DEVELOPMENT Jelgava, MECHANICAL BEHAVIOR OF RUBBER SAMPLES UNDER RELAXATION
MECHANICAL BEHAVIOR OF RUBBER SAMPLES UNDER RELAXATION Ruslan Askarbekov, David Herak, Cestmir Mizera Czech University of Life Sciences Prague askarbekovu@gmail.com, herak@tf.czu.cz, mizera@tf.czu.cz Abstract.
More informationINTRODUCTION (Cont..)
INTRODUCTION Name : Mohamad Redhwan Abd Aziz Post : Lecturer @ DEAN CENTER OF HND STUDIES Subject : Solid Mechanics Code : BME 2033 Room : CENTER OF HND STUDIES OFFICE H/P No. : 019-2579663 W/SITE : Http://tatiuc.edu.my/redhwan
More informationThe Design of Polyurethane Parts: Using Closed Solutions and Finite Element Analysis to Obtain Optimal Results
The Design of Polyurethane Parts: Using Closed Solutions and Finite Element Analysis to Obtain Optimal Results By: Richard Palinkas George Nybakken Ian Laskowitz Chemtura Corporation Overview How does
More informationTENSILE TESTS (ASTM D 638, ISO
MODULE 4 The mechanical properties, among all the properties of plastic materials, are often the most important properties because virtually all service conditions and the majority of end-use applications
More informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More informationExample-3. Title. Description. Cylindrical Hole in an Infinite Mohr-Coulomb Medium
Example-3 Title Cylindrical Hole in an Infinite Mohr-Coulomb Medium Description The problem concerns the determination of stresses and displacements for the case of a cylindrical hole in an infinite elasto-plastic
More informationContinuum Mechanics and Theory of Materials
Peter Haupt Continuum Mechanics and Theory of Materials Translated from German by Joan A. Kurth Second Edition With 91 Figures, Springer Contents Introduction 1 1 Kinematics 7 1. 1 Material Bodies / 7
More informationThe science of elasticity
The science of elasticity In 1676 Hooke realized that 1.Every kind of solid changes shape when a mechanical force acts on it. 2.It is this change of shape which enables the solid to supply the reaction
More informationThe University of Melbourne Engineering Mechanics
The University of Melbourne 436-291 Engineering Mechanics Tutorial Four Poisson s Ratio and Axial Loading Part A (Introductory) 1. (Problem 9-22 from Hibbeler - Statics and Mechanics of Materials) A short
More informationActivity Tensile Testing SIM
Activity 2.3.2 Tensile Testing SIM Introduction Tensile testing provides engineers with the ability to verify and establish material properties related to a specific material. This verification process
More information22 Which of the following correctly defines the terms stress, strain and Young modulus? stress strain Young modulus
PhysicsndMathsTutor.com Which of the following correctly defines the terms stress, strain and Young modulus? 97/1/M/J/ stress strain Young modulus () x (area) (extension) x (original length) (stress) /
More informationModule-4. Mechanical Properties of Metals
Module-4 Mechanical Properties of Metals Contents ) Elastic deformation and Plastic deformation ) Interpretation of tensile stress-strain curves 3) Yielding under multi-axial stress, Yield criteria, Macroscopic
More informationNon-linear and time-dependent material models in Mentat & MARC. Tutorial with Background and Exercises
Non-linear and time-dependent material models in Mentat & MARC Tutorial with Background and Exercises Eindhoven University of Technology Department of Mechanical Engineering Piet Schreurs July 7, 2009
More informationHyperelasticity and the Failure of Averages
Paper 204 Civil-Comp Press, 2015 Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing, J. Kruis, Y. Tsompanakis and B.H.V. Topping, (Editors),
More informationChapter 6: Mechanical Properties of Metals. Dr. Feras Fraige
Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness
More information