A Semianalytical Model for the Simulation of Polymers

Size: px
Start display at page:

Download "A Semianalytical Model for the Simulation of Polymers"

Transcription

1 A Semianalytical Model for the Simulation of Polymers Paul Du Bois 3, Stefan Kolling 1, Markus Feucht 1 & André Haufe 2 1 DaimlerChrysler AG, Sindelfingen, Germany 2 Dynamore GmbH, Stuttgart, Germany 3 Consultant, Offenbach, Germany 4. LS DYNA FORUM 25, Oktober 25, Bamberg

2 Overview Introduction and motivation Discussion of appropriate p yield surfaces Details of a new material model A few examples Conclusions 4. LS DYNA FORUM, Oktober 25, Bamberg S. 2

3 Motivation More and more structural parts are made from plastics. At present important crashworthiness applications are: Pedestrian protection (bumper, fascia, hood, adhesives) Passenger protection (cockpit, internal structures) Their mechanical behaviour is strongly dependent on Underlaying chemical structure and production process Temperature, strain rate, humidity etc. Many thousand different blends are available today!! Shell-like but rib reinforced structures 4. LS DYNA FORUM, Oktober 25, Bamberg S. 3

4 V&V processes for complete FE models Semi Analytical Model for Polymers V&V process of each individual part of the numerical model necessary: Global solution strategy Constitutive model Element formulation, type & size Discretisation depth & modeling techniques more In engineering practise the numerical model shall correlate to experimental data close enough, to allow sound predictions in a predefined range of model variations. 4. LS DYNA FORUM, Oktober 25, Bamberg S. 4

5 Identification challenge: Structures made of plastics Plastics is a group name comprising many different materials Mechanical response at room temperature may be glassy or rubbery, brittle or viscous ε& T st tress 4 5 thermoset plastic (Duroplast) thermoplastic elastomer strain 1 glasslike behaviour 2 plastic or viscous flow 3 low ductility 4 high ductility 5 rubbery crystalline thermoplastic amorphous thermoplastic Fiber reinforcement may causeanisotropic anisotropic response Rib reinforcements represent an important modeling effort 4. LS DYNA FORUM, Oktober 25, Bamberg S. 5

6 Mechanical behaviour of thermoplastics (uniaxial loading) True Stress Yield curve AND Young s Modulus are strain rate dependent d Non linear elasticity Uniform necking due to stabilisation True Stre ess True strain Visco elasto visco plasticity Different yielding under tension/compression (and shear) Plastic incompressibility for compression only (ν p 5).5) Under tension foam like (ν p ) True strain Tensile Test Compression Test No Von Mises type of plasticity! 4. LS DYNA FORUM, Oktober 25, Bamberg S. 6

7 Simulation of a tensile test: thermoplastic response Von Mises (piecewise linear) plasticity, linear elastic visco plastic, input of strain rate dependent test data (= state of the art: MAT24 in LS DYNA) Generally good representation of tensile responses 4. LS DYNA FORUM, Oktober 25, Bamberg S. 7

8 Simulation of a tensile test: thermoplastic response Positive curvature in the hardening curve causes stabilisation of the cross section after necking 4. LS DYNA FORUM, Oktober 25, Bamberg S. 8

9 Deficiencies of Von Mises plasticity to describe plastics Plastic incompressibility not correct for thermoplastics No Von Mises relationship between yield stress in tension, compression, shear σ c σ t σ b σ t σ Loss of isotropy during hardening due to reorientation of molecules (load induced anisotropy) Crazing ( volumetric plasticity and low biaxial strength) cannot be described Modulus is rate dependent (viscosity below the yield surface) Modulus of elasticity it depends d on plastic df deformation ( damage) s σ t 3 4. LS DYNA FORUM, Oktober 25, Bamberg S. 9

10 Major concerns for the simulation of plastic parts Bending stiffness is usually underestimated Under biaxial loads (punching) the plastic tends to develop crazes Important elastic rebound is currently the major stumbling block 4. LS DYNA FORUM, Oktober 25, Bamberg S. 1

11 SAMP 1 : goals and limitations Semi Analytical Model for Polymers Describe isotropic ductile thermoplastic materials Implement for solid and shell (plane stress) elements Fully tabulated input data Most general quadratic isotropic yield surface formulation, allows to fit 3 experiments exactly and 4 approximately (least squares) Damage model to simulate unloading response Tabulated visco plasticity Not suited for the simulation of fiber reinforced structures with high anisotropy and low rupture strain Load induced anisotropy neglected Large plastic deformation expected : rate dependency in elastic region is neglected No sophisticated failure model yet 4. LS DYNA FORUM, Oktober 25, Bamberg S. 11

12 SAMP A Semi Analytical Model for Polymers Hardening curves: tabulated data σ y ε& σ y σ c σ y σ s σ t d l l l l h tensile hardening curve from tensile test at different strain rates σt ε pt = ε t, ε t = E l ln l ε pt ε pc compressive hardening curve from compression test shear hardening curve from shear test ε ps c l ε = σ σ 1 x& s 1 d pc εc, εc = ln ε = = = E l ps εs, εs dt 2G 2 y 2 h difficult! 4. LS DYNA FORUM, Oktober 25, Bamberg S. 12

13 General isotropic quadratic yield surface: SAMP 1 f = tension q shear compression Yield surface rface(modified Schlimmer): (,, pl 2 2 f p σ ε ) = σ A A p A p vm vm p To achieve a fast and easy calibration i process, test results from tension, compression and shear tests can be fd fed directly into SAMP 1 via table definitions: σt σc σs Tension test data Compression test data Shear test data ε t ε c ε s Therefore the yield surface coefficients A,1,2 are calculated directly from stresses gained from a table lookup. A 2 c t t c s = σ A = 9( σ ) A = 9( ) 2 3 s 1 s σ σ σ σ c t 4. LS DYNA FORUM, Oktober 25, Bamberg S σ σ 3σ σ σ t c

14 General isotropic quadratic yield surface: special cases Von Mises q Drucker Prager q f = f = 3 tension tension 1 3 compression 1 p p σ t σ t σ c Tension test data Tension test data Compression test data ε t εt εc alternatively υ p.5 σt σs Tension test data Shear test data ε t ε s 4. LS DYNA FORUM, Oktober 25, Bamberg S. 14

15 General isotropic quadratic yield surface: SAMP 1 f = q tension q shear compression Yield surface: (,, pl 2 2 f p σ ε ) = σ A A p A p vm vm 1 2 Biaxial tension 3 1 Plastic potential: g = σ α p 2 2 vm p To achieve a fast and easy calibration process, test results from tension, compression and shear tests can be fed directly into SAMP 1 via table definitions: σ t σt σc σs Tension test data Biaxial test data Compression test data Shear test data ε t ε t ε c ε s Therefore the yield surface coefficients A 12,1,2 are calculated each time step by a least squares approach fitting the yield stress values obtained by a table lookup 4. LS DYNA FORUM, Oktober 25, Bamberg S. 15

16 General isotropic quadratic yield surface: anything goes! f = q Drucker Prager q tension q shear compression f = Biaxial tension 3 tension 1 biaxial 3 1 p p σ t σ t σ c σ t σ t Tension test data Biaxial test data Compression test data Tension test data Biaxial test data ε ε t ε t ε c ε t ε t σ t σ t σ s Tension test data Biaxial test data Shear test data ε t εt εs 4. LS DYNA FORUM, Oktober 25, Bamberg S. 16

17 General isotropic quadratic yield surface: convexity f = q compression tension q shear A 2 Yield surface: (,, pl 2 2 f p σ ε ) = σ A A p A p vm vm 1 2 Biaxial tension 3 1 A 2 2 Condition for convexity : A 2 σ s σ σ t 3 c p In the numerical algorithm, a unique solution is guaranteed only for convex yield surfaces In order to avoid numerical problems convexity can be enforced in SAMP 1 by a user controlled flag The hardening curve in shear is then scaled as necessary every timestep This allows to achieve robust numerical behaviour under most loading conditions 4. LS DYNA FORUM, Oktober 25, Bamberg S. 17

18 SAMP 1: Flow rule & g g = & λ F = σ = q vm σ c ε p σ plastic potential: ti g=const. σ t σ s m = g σσ g = 2 2 q A A1 p A2 p associated 2 2 q + αpα p non associated σ t 3 σ c 3 p flow parameter correlates to plastic ν p Poisson s ratio: l 9 2α α υ p = α l l 4. LS DYNA FORUM, Oktober 25, Bamberg S. 18 ε pt

19 SAMP 1: Flow rule & g g = & λ F = σ = q vm σ c ε p σ plastic potential: ti g=const. σ t σ s m = g σσ g = 2 2 q A A1 p A2 p associated 2 2 q + αpα p non associated σ t 3 σ c 3 p flow parameter correlates to plastic ν p Poisson s ratio: l 9 2α α υ p = α l l 4. LS DYNA FORUM, Oktober 25, Bamberg S. 19 ε pt

20 SAMP1: Visco plasticity Elastoplastic consistency condition f ( ) 2 2 λ, & λ = = σ A A p A p vm 1 2 σ y ε& Viscoplastic constitutive law: & λ = f Φ( f ) 2η ( ) 1 λ, & λ Φ ( 2ηλ& ) = σ t l ε pt l 1 Φ ( 2ηλ& ) = f ( λ, & λ) f ( λ,) 2 = A ( λ, & λ) + A ( λ, & λ) p + A ( λ, & λ) p A ( λ, ) A ( λ, ) p A ( λ, ) p LS DYNA FORUM, Oktober 25, Bamberg S. 2

21 ,, 1, 2, 3, 4, 5 Semi Analytical Model for Polymers Unloading test: (1 d) damage damage model: Basics E E eff1 E eff2 Schädigung d 1 Tabulated damage curve: d(ε pl ) =1 - E eff / E wahre True Spann St nung tress [MPa] d,8,6,4,2 Test Versuch Input Simulation data 125 Test % Streckgrenze 8% Approximated Versagendehnung effective modulus of elasticity 75% Streckgrenze,,1,2,3,4,5 Plastic strain ε pl plastische Dehnung True strain wahre Dehnung [-] Damage parameter d : E eff = E (1 d) d = 1 E eff / E σ eff y σ y = 1 d 4. LS DYNA FORUM, Oktober 25, Bamberg S. 21

22 SAMP 1: Damage and failure Semi Analytical Model for Polymers Failure onset defined by the parameter further fading of the element defined by d c p Δ ε rupt d 1. d c Δ ε p rupt ε p 4. LS DYNA FORUM, Oktober 25, Bamberg S. 22

23 Yield surfaces: experiment vs. SAMP Polyvinyl Chloride (PVC) 4. LS DYNA FORUM, Oktober 25, Bamberg S. 23

24 Experimental data vs. SAMP Polystyrene (PS) 4. LS DYNA FORUM, Oktober 25, Bamberg S. 24

25 Experimental data vs. SAMP Polycarbonate (PC) 4. LS DYNA FORUM, Oktober 25, Bamberg S. 25

26 Experimental data vs. SAMP Polypropylene (PP) 4. LS DYNA FORUM, Oktober 25, Bamberg S. 26

27 Experimental data vs. SAMP Polyethylene (PE) 4. LS DYNA FORUM, Oktober 25, Bamberg S. 27

28 Experimental datavs vs. SAMP Acrylonitrile Butadiene Styrene (ABS) 4. LS DYNA FORUM, Oktober 25, Bamberg S. 28

29 Verification and validation of PP EPDM Quasi static tensile tests with unloading tensile tests with unloading experiment unloading simulation with damage simulation no damage 35 8x2 mm 48.6 mm [N] force displacement [mm] 4. LS DYNA FORUM, Oktober 25, Bamberg S. 29

30 Verification and validation of PP EPDM Compression test F DKI PP_EPDM compression tests : 2.5mm mesh experiment simulation 2 force [N N] 1.5 4x6 mm 1.5 F displacement [mm] 4. LS DYNA FORUM, Oktober 25, Bamberg S. 3

31 Verification and validation of PP EPDM Shear test F 5 45 PP_EPDM - Shear Test experiment simulation 4 35 force N F displacement mm 4. LS DYNA FORUM, Oktober 25, Bamberg S. 31

32 Verification and validation of PP EPDM SAMP 1: experimental results (tension and compression test) has been used directly as input data for this three point bending test. Tensile Test Compression Test Specimen size 1 x 133 x 3.8 mm Downward prescribed displacement (quasi static) 3 integration points across thickness direction 4. LS DYNA FORUM, Oktober 25, Bamberg S. 32

33 Unloading test: (1 d) damage damage model: Results Flow curve definition and failure parameters for a simple dogbone tension test at different loading velocities including proper unloading behaviour 6 5 u 4 u 3 F-x_dyn (test data) F-x_static (test data) 2 F-x_dyn_dam (SAMP-) F-x_static_dam (SAMP-) t LS DYNA FORUM, Oktober 25, Bamberg S. 33

34 Other applications Material model: SAMP not only valid for thermoplastics It covers metals as well Also suitable for Adhesives (if you have a clue how to model) Structural foams Crushable foams Example: validation of a high strength, low density, expandable epoxy polymer (CORE Products) using a single material input card of SAMP 4. LS DYNA FORUM, Oktober 25, Bamberg S. 34

35 Material laws for crushable foams in LS DYNA No. keyword formulation input 5,14 MAT_SOIL_AND_FOAM isotropic, el pl parameter 26,126 MAT_HONEYCOMB anisotropic, el pl LC 53 MAT_CLOSED_CELL_FOAM CELL isotropic, el pl LC 63,163 MAT_CRUSHABLE_FOAM isotropic, el pl LC / table υ variable 75 MAT_BILKHU/DUBOIS_FOAM _ isotropic, el pl LC strain rate parameter 142 MAT_TRANSVERSELY_ANISO TROPIC_CRUSHABLE_FOAM anisotropic el pl LC 144 MAT_PITZER_CRUSHABLE isotropic, el pl LC + strain rate _FOAM υ variable parameter user MAT_SAMP isotropic, el pl variable LC / table υ 4. LS DYNA FORUM, Oktober 25, Bamberg S. 35

36 Validation of structural high density foam (CORE) 45 4 FOAM compression experiment simulation 6 FOAM tension experiment simulation 35 5 Fad force [kn] force [kn] ading out via damage formulation on displacement [mm] FOAM shear displacement [mm] experiment simulation -1 force [kn] displacement [mm] 4. LS DYNA FORUM, Oktober 25, Bamberg S. 36

37 Conclusions and outlook Semi Analytical Model for Polymers Most critical issues have been addressed with SAMP 1 Damage and strain rate dependency Failure and unloading General quadratic yield condition Pressure dependent plastic potential First shot at crazing Features still missing: Transition to anisotropic behaviour Rate dependency in elastic region Future work: Further testing of material ilmodel dl Calibration and validation of more polymers Simulation of more component tests SAMP 1 will be available in the next release of LS DYNA (971) 4. LS DYNA FORUM, Oktober 25, Bamberg S. 37

38 Thanks for your attention! Semi Analytical Model for Polymers This presentation was pedagogical valuable or somehow 4. LS DYNA FORUM, Oktober 25, Bamberg S. 38

WORKSHOP Introduction to material characterization

WORKSHOP Introduction to material characterization WORKSHOP Introduction to material characterization Martin Helbig, David Koch DYNAmore GmbH, Germany 15 th German LS-DYNA Forum 2018 Bamberg, October 15, 2018 1 Motivation Example of material usage in a

More information

Development, implementation and Validation of 3-D Failure Model for Aluminium 2024 for High Speed Impact Applications

Development, implementation and Validation of 3-D Failure Model for Aluminium 2024 for High Speed Impact Applications Development, implementation and Validation of -D Failure Model for Aluminium 2024 for High Speed Impact Applications Paul Du Bois, Murat Buyuk, Jeanne He, Steve Kan NCAC-GWU th International LS-DYNA Users

More information

Enhancing Prediction Accuracy In Sift Theory

Enhancing 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 information

Module-4. Mechanical Properties of Metals

Module-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 information

A Constitutive Model for Plastics with Piecewise Linear Yield Surface and Damage

A Constitutive Model for Plastics with Piecewise Linear Yield Surface and Damage 6. LS-DYNA Anwenderforum, Frankenthal 2007 Crash II - Schadensmodellierung A Constitutive Model for Plastics with Piecewise Linear Yield Surface and Damage M. Vogler 1, S. Kolling 2, A. Haufe 3 1 Leibniz

More information

Anisotropic modeling of short fibers reinforced thermoplastics materials with LS-DYNA

Anisotropic modeling of short fibers reinforced thermoplastics materials with LS-DYNA Anisotropic modeling of short fibers reinforced thermoplastics materials with LS-DYNA Alexandre Hatt 1 1 Faurecia Automotive Seating, Simplified Limited Liability Company 1 Abstract / Summary Polymer thermoplastics

More information

INCREASING RUPTURE PREDICTABILITY FOR ALUMINUM

INCREASING RUPTURE PREDICTABILITY FOR ALUMINUM 1 INCREASING RUPTURE PREDICTABILITY FOR ALUMINUM Influence of anisotropy Daniel Riemensperger, Adam Opel AG Paul Du Bois, PDB 2 www.opel.com CONTENT Introduction/motivation Isotropic & anisotropic material

More information

Recent Developments in Damage and Failure Modeling with LS-DYNA

Recent Developments in Damage and Failure Modeling with LS-DYNA Recent evelopments in amage and Failure Modeling with LS-YNA r. André Haufe ynamore GmbH Frieder Neukamm, r. Markus Feucht aimler AG Paul ubois Consultant r. Thomas Borvall ERAB 1 Technological challenges

More information

Anisotropic plasticity, anisotropic failure and their application to the simulation of aluminium extrusions under crash loads

Anisotropic plasticity, anisotropic failure and their application to the simulation of aluminium extrusions under crash loads Anisotropic plasticity, anisotropic failure and their application to the simulation of aluminium extrusions under crash loads Paul Du Bois, Consulting engineer Oasys LS-DYNA Users Meeting 28th January

More information

Enhancement of Spot Weld Modeling using MAT 100 DAI

Enhancement of Spot Weld Modeling using MAT 100 DAI 7. LS-DYNA Anwenderforum, Bamberg 2008 Crash II - Verbindungstechnik, Versagen Enhancement of Spot Weld Modeling using MAT 100 DAI Falko Seeger a, Markus Feucht a, George Dumitru b, Tobias Graf b a Daimler

More information

Crash and Vibration Analysis of rotors in a Roots Vacuum Booster

Crash and Vibration Analysis of rotors in a Roots Vacuum Booster Crash and Vibration Analysis of rotors in a Roots Vacuum Booster Manuel Roth 1, Stefan Kolling 2 1 Pfeiffer Vacuum GmbH, R&D Backing Pumps, Asslar, Germany 2 Giessen University of Applied Sciences, Laboratory

More information

EQUIVALENT FRACTURE ENERGY CONCEPT FOR DYNAMIC RESPONSE ANALYSIS OF PROTOTYPE RC GIRDERS

EQUIVALENT FRACTURE ENERGY CONCEPT FOR DYNAMIC RESPONSE ANALYSIS OF PROTOTYPE RC GIRDERS EQUIVALENT FRACTURE ENERGY CONCEPT FOR DYNAMIC RESPONSE ANALYSIS OF PROTOTYPE RC GIRDERS Abdul Qadir Bhatti 1, Norimitsu Kishi 2 and Khaliq U Rehman Shad 3 1 Assistant Professor, Dept. of Structural Engineering,

More information

An orthotropic damage model for crash simulation of composites

An orthotropic damage model for crash simulation of composites High Performance Structures and Materials III 511 An orthotropic damage model for crash simulation of composites W. Wang 1, F. H. M. Swartjes 1 & M. D. Gan 1 BU Automotive Centre of Lightweight Structures

More information

Introduction to Engineering Materials ENGR2000. Dr. Coates

Introduction to Engineering Materials ENGR2000. Dr. Coates Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed

More information

Simulation of Adhesives

Simulation of Adhesives Fakultät Maschinenwesen Institut für Festkörpermechanik, Professur für Nichtlineare Festkörpermechanik Dynamore USER Forum in Bamberg 2014 Karl Plangger, Prof. Dr.-Ing. habil. V. Ulbricht Agenda 1. Problem

More information

Chapter 7. Highlights:

Chapter 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 information

GISSMO Material Modeling with a sophisticated Failure Criteria

GISSMO Material Modeling with a sophisticated Failure Criteria GISSMO Material Modeling with a sophisticated Failure Criteria André Haufe, Paul DuBois, Frieder Neukamm, Markus Feucht Dynamore GmbH Industriestraße 2 70565 Stuttgart http://www.dynamore.de Motivation

More information

Mechanical Properties of Polymers. Scope. MSE 383, Unit 3-1. Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept.

Mechanical Properties of Polymers. Scope. MSE 383, Unit 3-1. Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept. Mechanical Properties of Polymers Scope MSE 383, Unit 3-1 Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept. Structure - mechanical properties relations Time-dependent mechanical

More information

14. LS-DYNA Forum 2016

14. LS-DYNA Forum 2016 14. LS-DYNA Forum 2016 A Novel Approach to Model Laminated Glass R. Böhm, A. Haufe, A. Erhart DYNAmore GmbH Stuttgart 1 Content Introduction and Motivation Common approach to model laminated glass New

More information

Modelling the behaviour of plastics for design under impact

Modelling 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 information

Plastic Instability of Rate-Dependent Materials - A Theoretical Approach in Comparison to FE-Analyses -

Plastic Instability of Rate-Dependent Materials - A Theoretical Approach in Comparison to FE-Analyses - Plastic Instability of Rate-Dependent Materials - A Theoretical Approach in Comparison to FE-Analyses - Christian Keller 1, Uwe Herbrich 1 1 Bundesanstalt für Materialforschung und -prüfung 12200 Berlin,

More information

NUMERICAL SIMULATION OF DAMAGE IN THERMOPLASTIC COMPOSITE MATERIALS

NUMERICAL SIMULATION OF DAMAGE IN THERMOPLASTIC COMPOSITE MATERIALS 5 th European LS-DYNA Users Conference Composites NUMERICAL SIMULATION OF DAMAGE IN THERMOPLASTIC COMPOSITE MATERIALS Kevin Brown 1, Richard Brooks, Nicholas Warrior School of Mechanical, Materials and

More information

ME 2570 MECHANICS OF MATERIALS

ME 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 information

Composite Materials 261 and 262

Composite Materials 261 and 262 Composite Materials 261 and 262 Stefan Hartmann 1 David Moncayo 2 1 DYNAmore GmbH, Stuttgart, Germany 2 Daimler AG, Sindelfingen, Germany 11. LS-DYNA Forum 2012, 9. - 10. Oktober 2012, Ulm 1 Outline Introduction

More information

Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur

Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 9 Table of Contents 1. Plasticity:... 3 1.1 Plastic Deformation,

More information

Outline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour

Outline. 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 information

An overview of Carbon Fiber modeling in LS-DYNA. John Zhao October 23 th 2017

An overview of Carbon Fiber modeling in LS-DYNA. John Zhao October 23 th 2017 An overview of Carbon Fiber modeling in LS-DYNA John Zhao zhao@lstc.com October 23 th 2017 Outline Manufacturing of Carbon Fiber Compression molding *MAT_277 & 278 *MAT_293 *MAT_249 Resin transform molding

More information

The Significance of the Production Process of FRP Parts for the Performance in Crashworthiness

The Significance of the Production Process of FRP Parts for the Performance in Crashworthiness 14 th International LS-DYNA Users Conference Session: Simulation The Significance of the Production Process of FRP Parts for the Performance in Crashworthiness Christian Liebold, Andrea Erhart, André Haufe

More information

Mechanical Properties of Materials

Mechanical Properties of Materials Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of

More information

Lecture #6: 3D Rate-independent Plasticity (cont.) Pressure-dependent plasticity

Lecture #6: 3D Rate-independent Plasticity (cont.) Pressure-dependent plasticity Lecture #6: 3D Rate-independent Plasticity (cont.) Pressure-dependent plasticity by Borja Erice and Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering, Chair of Computational Modeling

More information

Modelling the nonlinear shear stress-strain response of glass fibrereinforced composites. Part II: Model development and finite element simulations

Modelling the nonlinear shear stress-strain response of glass fibrereinforced composites. Part II: Model development and finite element simulations Modelling the nonlinear shear stress-strain response of glass fibrereinforced composites. Part II: Model development and finite element simulations W. Van Paepegem *, I. De Baere and J. Degrieck Ghent

More information

CONSTITUTIVE MODELING AND OPTIMAL DESIGN OF POLYMERIC FOAMS FOR CRASHWORTHINESS

CONSTITUTIVE MODELING AND OPTIMAL DESIGN OF POLYMERIC FOAMS FOR CRASHWORTHINESS CONSTITUTIVE MODELING AND OPTIMAL DESIGN OF POLYMERIC FOAMS FOR CRASHWORTHINESS Jun Zhang December 19, 1997 Computational Mechanics Laboratory Department of Mechanical Engineering and Applied Mechanics

More information

In Situ Ultrasonic NDT of Fracture and Fatigue in Composites

In Situ Ultrasonic NDT of Fracture and Fatigue in Composites ECNDT 26 - Mo.2.6.5 In Situ Ultrasonic NDT of Fracture and Fatigue in Composites I. SOLODOV, K. PFLEIDERER, and G. BUSSE Institute for Polymer Testing and Polymer Science (IKP), Non-destructive Testing

More information

Card Variable MID RO E PR ECC QH0 FT FC. Type A8 F F F F F F F. Default none none none 0.2 AUTO 0.3 none none

Card Variable MID RO E PR ECC QH0 FT FC. Type A8 F F F F F F F. Default none none none 0.2 AUTO 0.3 none none Note: This is an extended description of MAT_273 input provided by Peter Grassl It contains additional guidance on the choice of input parameters beyond the description in the official LS-DYNA manual Last

More information

Digimat material model for short fiber reinforced plastics at Volvo Car Corporation

Digimat material model for short fiber reinforced plastics at Volvo Car Corporation Digimat material model for short fiber reinforced plastics at Volvo Car Corporation Mats Landervik DYNAmore Nordic Johan Jergeus Volvo Car Corporation June 2, 2015 26TH SICOMP CONFERENCE, GOTHENBURG 1

More information

Constitutive models: Incremental plasticity Drücker s postulate

Constitutive models: Incremental plasticity Drücker s postulate Constitutive models: Incremental plasticity Drücker s postulate if consistency condition associated plastic law, associated plasticity - plastic flow law associated with the limit (loading) surface Prager

More information

*MAT_PAPER - a new orthotropic elastoplastic model for paper materials

*MAT_PAPER - a new orthotropic elastoplastic model for paper materials *MAT_PAPER - a new orthotropic elastoplastic model for paper materials Jesper Karlsson, Dynamore Nordic Mikael Schill, Dynamore Nordic Johan Tryding, Tetra Pak *MAT_PAPER (*MAT_274) A new orthotropic elastoplastic

More information

Chapter 6: Plastic Theory

Chapter 6: Plastic Theory OHP Mechanical Properties of Materials Chapter 6: Plastic Theory Prof. Wenjea J. Tseng 曾文甲 Department of Materials Engineering National Chung Hsing University wenjea@dragon.nchu.edu.tw Reference: W. F.

More information

MECHANICS OF POLYMERS

MECHANICS OF POLYMERS MECHANICS OF POLYMERS by Stefan Kolling Technische Universität Darmstadt, WS 3/4 contact: stefan.kolling@me.thm.de Course Contents and Goals Topics Basics on continuum mechanics (no chemistry!) Classification

More information

Coupling of plasticity and damage in glass fibre reinforced polymer composites

Coupling of plasticity and damage in glass fibre reinforced polymer composites EPJ Web of Conferences 6, 48 1) DOI: 1.151/epjconf/1648 c Owned by the authors, published by EDP Sciences, 1 Coupling of plasticity and damage in glass fibre reinforced polymer composites R. Kvale Joki

More information

SIMPLIFIED CONCRETE MODELING WITH *MAT_CONCRET_DAMAGE_REL3

SIMPLIFIED CONCRETE MODELING WITH *MAT_CONCRET_DAMAGE_REL3 SIMPLIFIED CONCRETE MODELING WITH *MAT_CONCRET_DAMAGE_REL3 Leonard E Schwer Schwer Engineering & Consulting Services, Windsor CA, USA and L. Javier Malvar Karagozian & Case Structural Engineers, Burbank

More information

Lecture #8: Ductile Fracture (Theory & Experiments)

Lecture #8: Ductile Fracture (Theory & Experiments) Lecture #8: Ductile Fracture (Theory & Experiments) by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering, Chair of Computational Modeling of Materials in Manufacturing 2015 1 1 1 Ductile

More information

ANSYS Mechanical Basic Structural Nonlinearities

ANSYS 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 information

CONSIDERATIONS CONCERNING YIELD CRITERIA INSENSITIVE TO HYDROSTATIC PRESSURE

CONSIDERATIONS CONCERNING YIELD CRITERIA INSENSITIVE TO HYDROSTATIC PRESSURE CONSIDERATIONS CONCERNING YIELD CRITERIA INSENSITIVE TO HYDROSTATIC PRESSURE ADRIAN SANDOVICI, PAUL-DORU BARSANESCU Abstract. For distinguishing between pressure insensitive and pressure sensitive criteria,

More information

Evaluation of Material Models to Predict Material Failure in LS-DYNA

Evaluation of Material Models to Predict Material Failure in LS-DYNA Department of Construction Sciences Solid Mechanics ISRN LUTFD2/TFHF-16/5209-SE(1-55) Evaluation of Material Models to Predict Material Failure in LS-DYNA Master s Dissertation by Hjalmar Sandberg Oscar

More information

Multiscale modeling of failure in ABS materials

Multiscale modeling of failure in ABS materials Institute of Mechanics Multiscale modeling of failure in ABS materials Martin Helbig, Thomas Seelig 15. International Conference on Deformation, Yield and Fracture of Polymers Kerkrade, April 2012 Institute

More information

Impact and Crash Modeling of Composite Structures: A Challenge for Damage Mechanics

Impact and Crash Modeling of Composite Structures: A Challenge for Damage Mechanics Impact and Crash Modeling of Composite Structures: A Challenge for Damage Mechanics Dr. A. Johnson DLR Dr. A. K. Pickett ESI GmbH EURO-PAM 99 Impact and Crash Modelling of Composite Structures: A Challenge

More information

MHA042 - Material mechanics: Duggafrågor

MHA042 - Material mechanics: Duggafrågor MHA042 - Material mechanics: Duggafrågor 1) For a static uniaxial bar problem at isothermal (Θ const.) conditions, state principle of energy conservation (first law of thermodynamics). On the basis of

More information

Mechanical properties of polymers: an overview. Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore

Mechanical properties of polymers: an overview. Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore Mechanical properties of polymers: an overview Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore UGC-NRCM Summer School on Mechanical Property Characterization- June 2012 Overview of polymer

More information

Performance Evaluation of Fu Chang and Low Density Foam Model for Expanded Polypropylene

Performance Evaluation of Fu Chang and Low Density Foam Model for Expanded Polypropylene MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 2014, pp. 49 53 49 Performance Evaluation of Fu Chang and Low Density Foam Model for Expanded Polypropylene Vivek Srivastava

More information

Numerical simulation the bottom structures. grounding test by LS-DYNA

Numerical simulation the bottom structures. grounding test by LS-DYNA 5 th European LS-DYNA Users Conference Methods and Techniques (3) Numerical simulation the bottom structures grounding test by LS-DYNA Ainian Zhang Graduate School of Frontier Sciences, The University

More information

A Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials

A Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials Dublin, October 2010 A Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials FracMan Technology Group Dr Mark Cottrell Presentation Outline Some Physical

More information

Elements of Polymer Structure and Viscoelasticity. David M. Parks Mechanics and Materials II February 18, 2004

Elements of Polymer Structure and Viscoelasticity. David M. Parks Mechanics and Materials II February 18, 2004 Elements of Polymer Structure and Viscoelasticity David M. Parks Mechanics and Materials II 2.002 February 18, 2004 Outline Elements of polymer structure Linear vs. branched; Vinyl polymers and substitutions

More information

Short Introduction of a New Generalized Damage Model

Short Introduction of a New Generalized Damage Model Short Introduction of a New Generalized Damage Model Tobias Erhart 1, Paul Du Bois 2, Filipe Andrade 1 1 Dynamore GmbH, Stuttgart 2 Consulting Engineer, Offenbach 1 Introduction Sound numerical models

More information

ALGORITHM FOR NON-PROPORTIONAL LOADING IN SEQUENTIALLY LINEAR ANALYSIS

ALGORITHM FOR NON-PROPORTIONAL LOADING IN SEQUENTIALLY LINEAR ANALYSIS 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-9 Chenjie Yu, P.C.J. Hoogenboom and J.G. Rots DOI 10.21012/FC9.288 ALGORITHM FOR NON-PROPORTIONAL LOADING

More information

Unified Constitutive Model for Engineering- Pavement Materials and Computer Applications. University of Illinois 12 February 2009

Unified Constitutive Model for Engineering- Pavement Materials and Computer Applications. University of Illinois 12 February 2009 Unified Constitutive Model for Engineering- Pavement Materials and Computer Applications Chandrakant S. Desai Kent Distinguished i Lecture University of Illinois 12 February 2009 Participation in Pavements.

More information

Lecture #10: Anisotropic plasticity Crashworthiness Basics of shell elements

Lecture #10: Anisotropic plasticity Crashworthiness Basics of shell elements Lecture #10: 151-0735: Dynamic behavior of materials and structures Anisotropic plasticity Crashworthiness Basics of shell elements by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering,

More information

Finite Element Modeling of a Thermoplastic Seal at High Temperature and Pressure

Finite Element Modeling of a Thermoplastic Seal at High Temperature and Pressure Finite Element Modeling of a Thermoplastic Seal at High Temperature and Pressure Jorgen Bergstrom 1, Ph.D. Brun Hilbert 2, Ph.D., P.E. Email: jorgen@polymerfem.com 1 Veryst Engineering, LLC Needham, MA

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading

EMA 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 information

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

More information

A RHEOLOGICAL ANALYSIS OF SOLID POLYMERS USING AN INVERSE METHOD APPLIED TO A FINITE ELEMENT MODEL OF THE TORSION AND TENSILE TESTS

A RHEOLOGICAL ANALYSIS OF SOLID POLYMERS USING AN INVERSE METHOD APPLIED TO A FINITE ELEMENT MODEL OF THE TORSION AND TENSILE TESTS THE PULISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume, Number 4/2, pp. 363 37 A RHEOLOGICAL ANALYSIS OF SOLID POLYMERS USING AN INVERSE METHOD APPLIED TO A FINITE

More information

CLOSED SIMULATION PROCESS CHAIN FOR SHORT FIBER REINFORCED PLASTIC COMPONENTS WITH LS-DYNA

CLOSED SIMULATION PROCESS CHAIN FOR SHORT FIBER REINFORCED PLASTIC COMPONENTS WITH LS-DYNA CLOSED SIMULATION PROCESS CHAIN FOR SHORT FIBER REINFORCED PLASTIC COMPONENTS WITH LS-DYNA B. Lauterbach 1, M. Erzgräber 1, C. Liebold 2, M. Helbig 2, A. Haufe 2 1 Adam Opel AG 2 DYNAmore GmbH www.opel.com

More information

Accurate Finite Element Simulations of PTFE Components

Accurate Finite Element Simulations of PTFE Components Accurate Finite Element Simulations of PTFE Components Jörgen S. Bergström, Ph.D. Veryst Engineering, LLC, 47A Kearney Rd, Needham, MA 02494 Abstract: Fluoropolymers is an import class of thermoplastics

More information

Simulation and Test Validation of Windscreen Subject to Pedestrian Head Impact

Simulation and Test Validation of Windscreen Subject to Pedestrian Head Impact 12 th International LS-DYNA Users Conference Occupant Safety Simulation and Test Validation of Windscreen Subject to Pedestrian Head Impact Qi Liu, Junyong Liu, Qiang Miao, Dazhi Wang, Xiaodong Tang SAIC

More information

Lecture 7, Foams, 3.054

Lecture 7, Foams, 3.054 Lecture 7, Foams, 3.054 Open-cell foams Stress-Strain curve: deformation and failure mechanisms Compression - 3 regimes - linear elastic - bending - stress plateau - cell collapse by buckling yielding

More information

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3

MECE 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 information

Non-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 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 information

The design of a formula student front impact attenuator

The design of a formula student front impact attenuator The design of a formula student front impact attenuator J.M.J. Schormans MT 10.06 Supervisors: dr. ir. Varvara Kouznetsova Eindhoven University of Technology Department of Mechanical Engineering Computational

More information

Chapter 6: Mechanical Properties of Metals. Dr. Feras Fraige

Chapter 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

IMPACT RESPONSE ANALYSIS OF LARGE SCALE RC GIRDER WITH SAND CUSHION

IMPACT RESPONSE ANALYSIS OF LARGE SCALE RC GIRDER WITH SAND CUSHION -Technical Paper- IMPACT RESPONSE ANALYSIS OF LARGE SCALE RC GIRDER WITH SAND CUSHION Abdul Qadir BHATTI *1, Norimitsu KISHI *2, Shin-ya OKADA *3 and Hisashi KONNO *4 ABSTRACT In order to establish a proper

More information

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 Viscous (fluid) Behavior http://manoa.hawaii.edu/graduate/content/slide-lava

More information

University of Sheffield The development of finite elements for 3D structural analysis in fire

University 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 information

Tensile stress strain curves for different materials. Shows in figure below

Tensile 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 information

Practice Final Examination. Please initial the statement below to show that you have read it

Practice Final Examination. Please initial the statement below to show that you have read it EN175: Advanced Mechanics of Solids Practice Final Examination School of Engineering Brown University NAME: General Instructions No collaboration of any kind is permitted on this examination. You may use

More information

MODELING OF CONCRETE MATERIALS AND STRUCTURES. Kaspar Willam. Uniaxial Model: Strain-Driven Format of Elastoplasticity

MODELING OF CONCRETE MATERIALS AND STRUCTURES. Kaspar Willam. Uniaxial Model: Strain-Driven Format of Elastoplasticity MODELING OF CONCRETE MATERIALS AND STRUCTURES Kaspar Willam University of Colorado at Boulder Class Meeting #3: Elastoplastic Concrete Models Uniaxial Model: Strain-Driven Format of Elastoplasticity Triaxial

More information

Outline. Tension test of stainless steel type 301. Forming including the TRIP-effect

Outline. Tension test of stainless steel type 301. Forming including the TRIP-effect Outline Erweiterte Kontaktformulierung, User-Reibmodell und thermische Analyse Simulationsmöglichkeiten zur Werkzeugauslegung mit LS-DYNA Workshop Simulation in der Umformtechnik Institut für Statik und

More information

Mechanical analysis of timber connection using 3D finite element model

Mechanical analysis of timber connection using 3D finite element model Mechanical analysis of timber connection using 3D finite element model Bohan XU Ph.D Student Civil Engineering Laboratory (CUST) Clermont-Ferrand, France Mustapha TAAZOUNT Dr-Ing Civil Engineering Laboratory

More information

A Constitutive Model for DYNEEMA UD composites

A Constitutive Model for DYNEEMA UD composites A Constitutive Model for DYNEEMA UD composites L Iannucci 1, D J Pope 2, M Dalzell 2 1 Imperial College, Department of Aeronautics London, SW7 2AZ l.iannucci@imperial.ac.uk 2 Dstl, Porton Down, Salisbury,

More information

Experimental and theoretical characterization of Li 2 TiO 3 and Li 4 SiO 4 pebbles

Experimental and theoretical characterization of Li 2 TiO 3 and Li 4 SiO 4 pebbles Experimental and theoretical characterization of Li 2 TiO 3 and Li 4 SiO 4 s D. Aquaro 1 N. Zaccari ABSTRACT Dipartimento di Ingegneria Meccanica Nucleare e della Produzione University of Pisa (Italy)

More information

NUMERICAL SIMULATIONS OF CORNERS IN RC FRAMES USING STRUT-AND-TIE METHOD AND CDP MODEL

NUMERICAL SIMULATIONS OF CORNERS IN RC FRAMES USING STRUT-AND-TIE METHOD AND CDP MODEL Numerical simulations of corners in RC frames using Strut-and-Tie Method and CDP model XIII International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XIII E. Oñate, D.R.J.

More information

Theory at a Glance (for IES, GATE, PSU)

Theory at a Glance (for IES, GATE, PSU) 1. Stress and Strain Theory at a Glance (for IES, GATE, PSU) 1.1 Stress () When a material is subjected to an external force, a resisting force is set up within the component. The internal resistance force

More information

*MAT_PAPER and *MAT_COHESIVE_PAPER: Two New Models for Paperboard Materials

*MAT_PAPER and *MAT_COHESIVE_PAPER: Two New Models for Paperboard Materials 14 th International LS-DYNA Users Conference Session: Constitutive Modeling *MAT_PAPER and *MAT_COHESIVE_PAPER: Two New Models for Paperboard Materials Jesper Karlsson 1, Mikael Schill 1, Johan Tryding

More information

3-D Finite Element Analysis of Instrumented Indentation of Transversely Isotropic Materials

3-D Finite Element Analysis of Instrumented Indentation of Transversely Isotropic Materials 3-D Finite Element Analysis of Instrumented Indentation of Transversely Isotropic Materials Abstract: Talapady S. Bhat and T. A. Venkatesh Department of Material Science and Engineering Stony Brook University,

More information

Discrete Element Modelling of a Reinforced Concrete Structure

Discrete Element Modelling of a Reinforced Concrete Structure Discrete Element Modelling of a Reinforced Concrete Structure S. Hentz, L. Daudeville, F.-V. Donzé Laboratoire Sols, Solides, Structures, Domaine Universitaire, BP 38041 Grenoble Cedex 9 France sebastian.hentz@inpg.fr

More information

Constitutive model for quasi-static deformation of metallic sandwich cores

Constitutive model for quasi-static deformation of metallic sandwich cores INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2004; 61:2205 2238 Published online 18 October 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1142

More information

Crashworthy Design of Composite Structures Using CAE Process Chain

Crashworthy Design of Composite Structures Using CAE Process Chain 0 th European LS-DYNA Conference 205, Würzburg, Germany Crashworthy Design of Composite Structures Using CAE Process Chain Madhukar Chatiri, Thorsten Schuetz 2, Anton Matzenmiller 3 CADFEM GmbH, Grafing

More information

Calibration and Experimental Validation of LS-DYNA Composite Material Models by Multi Objective Optimization Techniques

Calibration and Experimental Validation of LS-DYNA Composite Material Models by Multi Objective Optimization Techniques 9 th International LS-DYNA Users Conference Optimization Calibration and Experimental Validation of LS-DYNA Composite Material Models by Multi Objective Optimization Techniques Stefano Magistrali*, Marco

More information

Loading σ Stress. Strain

Loading σ Stress. Strain hapter 2 Material Non-linearity In this chapter an overview of material non-linearity with regard to solid mechanics is presented. Initially, a general description of the constitutive relationships associated

More information

Failure surface according to maximum principal stress theory

Failure surface according to maximum principal stress theory Maximum Principal Stress Theory (W. Rankin s Theory- 1850) Brittle Material The maximum principal stress criterion: Rankin stated max principal stress theory as follows- a material fails by fracturing

More information

4.MECHANICAL PROPERTIES OF MATERIALS

4.MECHANICAL PROPERTIES OF MATERIALS 4.MECHANICAL PROPERTIES OF MATERIALS The diagram representing the relation between stress and strain in a given material is an important characteristic of the material. To obtain the stress-strain diagram

More information

Lecture #7: Basic Notions of Fracture Mechanics Ductile Fracture

Lecture #7: Basic Notions of Fracture Mechanics Ductile Fracture Lecture #7: Basic Notions of Fracture Mechanics Ductile Fracture by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering, Chair of Computational Modeling of Materials in Manufacturing

More information

An experimental and constitutive modeling study on the large strain deformation and fracture behavior of PC/ABS blends

An experimental and constitutive modeling study on the large strain deformation and fracture behavior of PC/ABS blends An experimental and constitutive modeling study on the large strain deformation and fracture behavior of PC/ABS blends J. Hund, J. Naumann, Th. Seelig 1 Institute of Mechanics, Karlsruhe Institute of Technology,

More information

Fracture mechanics fundamentals. Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design

Fracture mechanics fundamentals. Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design Fracture mechanics fundamentals Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design Failure modes Failure can occur in a number of modes: - plastic deformation

More information

Prediction of Elastic Constants on 3D Four-directional Braided

Prediction of Elastic Constants on 3D Four-directional Braided Prediction of Elastic Constants on 3D Four-directional Braided Composites Prediction of Elastic Constants on 3D Four-directional Braided Composites Liang Dao Zhou 1,2,* and Zhuo Zhuang 1 1 School of Aerospace,

More information

ScienceDirect. Bauschinger effect during unloading of cold-rolled copper alloy sheet and its influence on springback deformation after U-bending

ScienceDirect. Bauschinger effect during unloading of cold-rolled copper alloy sheet and its influence on springback deformation after U-bending Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 81 (2014 ) 969 974 11th International Conference on Technology of Plasticity, ICTP 2014, 19-24 October 2014, Nagoya Congress

More information

SEMM Mechanics PhD Preliminary Exam Spring Consider a two-dimensional rigid motion, whose displacement field is given by

SEMM Mechanics PhD Preliminary Exam Spring Consider a two-dimensional rigid motion, whose displacement field is given by SEMM Mechanics PhD Preliminary Exam Spring 2014 1. Consider a two-dimensional rigid motion, whose displacement field is given by u(x) = [cos(β)x 1 + sin(β)x 2 X 1 ]e 1 + [ sin(β)x 1 + cos(β)x 2 X 2 ]e

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS Third E CHAPTER 2 Stress MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University and Strain Axial Loading Contents Stress & Strain:

More information

Lecture No. (1) Introduction of Polymers

Lecture No. (1) Introduction of Polymers Lecture No. (1) Introduction of Polymers Polymer Structure Polymers are found in nature as proteins, cellulose, silk or synthesized like polyethylene, polystyrene and nylon. Some natural polymers can also

More information

Nonlinear FE Analysis of Reinforced Concrete Structures Using a Tresca-Type Yield Surface

Nonlinear FE Analysis of Reinforced Concrete Structures Using a Tresca-Type Yield Surface Transaction A: Civil Engineering Vol. 16, No. 6, pp. 512{519 c Sharif University of Technology, December 2009 Research Note Nonlinear FE Analysis of Reinforced Concrete Structures Using a Tresca-Type Yield

More information

MSC Elastomers Seminar Some Things About Elastomers

MSC 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 information