Anthony R. Ingraffea Symposium September 27, State Based Peridynamic Lattice Modeling of Reinforced Concrete Structures ! 1


 Alvin Daniel
 1 years ago
 Views:
Transcription
1 Anthony R. Ingraffea Symposium September 27, 2014 State Based Peridynamic Lattice Modeling of Reinforced Concrete Structures Walter Gerstle Department of Civil Engineering University of New Mexico, U.S.A. 1
2 Scope Claude Louis Navier and Augustin Louis Cauchy, State Based Peridynamic Lattice Model Elasticity Damage Plasticity Examples Conclusions Navier Cauchy 2
3 Navier,
4 Navier s assumption of spatial continuity 4
5 Does this look continuous to you? concrete.blogspot.com/2010_10_01_archive.html 5
6 Cauchy s Concept of Stress R 2 Traction: Stress: R 1 6
7 Continuous function 7
8 Discontinuous Displacement across Crack u(x) is continuous above crack u(x) is discontinuous across crack 8
9 There is no physical reason why solids should deform continuously (in space) So why do we teach continuum mechanics? Because continuum mechanics yields analytical solutions (for a few simple problems) Computers are now ubiquitous But computers use discrete arithmetic So let us use discrete (particle) mechanics But we want some regular structure for our particles Let us use a particle lattice 9
10 Discrete models for solid mechanics 1941, Hrennikoff, A., Solution of problems of elasticity by the framework method 1977, Burt, N. J. & Dougill, J. W., Progressive Failure in a Model Heterogeneous Medium 1989, Herrmann, H. J.; Hansen, A. & Roux, S., Fracture of disordered, elastic lattices in two dimensions 1992, Schlangen, E. and J. G. M. Van Mier modeled the concrete as discrete lattice of beams. 1993, Itasca consulting group, Universal Discrete Element Code (UDEC). 1995, Jirásek, M. and Z. P. Bažant used a particle model with random geometry. 1998, Bolander, J. E. and S. Saito modeled the concrete as spring networks with random geometry. 2011, Cusatis, G. and coworkers proposed a mesoscale model for concrete in which they modeled the aggregates and mortar matrix. 2012, Potyondy, D. O. The BondedParticle Model (many others) 10
11 Peridynamics peri = near dynamic = force In 2000, S. A. Silling of Sandia National Laboratories introduced continuum peridynamic theory. In 2007, Silling introduced state based continuum peridynamic theory. Peridynamics reformulates continuum mechanics theory to overcome deficiencies in modeling of deformation discontinuities. 11
12 Peridynamic physical description Terminology for peridynamic model. Peridynamic mathematical description (Equation of motion for particle i) 12
13 Peridynamic states The original peridynamic model included only a bond based model for materials. In 2007, S. A. Silling introduced the concept of peridynamic states to generalize the original bond based peridynamic model. In peridynamic state based model, the interaction between two particles i and j, also, depends upon the state of other particles, k, in the neighborhood. State based peridynamics is capable of modeling broader material behaviors such as plasticity. 13
14 Lattice Model Y 1 FaceCentered Cubic (FCC) Z X 2 3 Hexagonal Close Packed (HCP) Newton s laws are applied to each lattice particle 14
15 Quasi brittle materials deform discontinuously in most regimes of interest. Original peridynamics has not discarded the continuum paradigm entirely. Computational implementation of peridynamics requires ad hoc discretization decisions. The lattice model discards the spatial continuum completely. The lattice model is computationally straightforward. 15
16 Solid models, like computer graphics, pixilated edge vertex volume face 16
17 Implemented so far: Constitutive models for concrete Linear elasticity Damage Plasticity Damping 17
18 Face Centered Cubic Particle Lattice 18
19 Stretch State, Y 19
20 Force State, T 20
21 Relationship between stretch state, Y, and strain, ε For a homogeneous (small) strain field, (For a spatially non homogeneous strain field, stretch state and strain are not directly comparable.) 21
22 22
23 Linear Elastic Lattice Model 23
24 Decomposition of Stretch and Force States 24
25 Tensile Damage 1 1 S 1 S 2 S 3 Damage Potential versus Elastic Volumetric Stretch S 1 S 2 S 3 Bond Force versus Elastic Volumetric Stretch 25
26 Plasticity 26
27 Damping Internal damping force External damping force 27
28 Modeling of reinforcing bars and bond Steel particles interact with concrete particles within material horizon. Steel is one dimensional elasto plastic peridynamic lattice. Stiffness of peridynamic steel concrete bonds similar to that of concrete concrete bonds. Bond between steel and concrete is elastic in compression, but sustains no tension. Bond of reinforcement (red) to concrete (black) using peridynamic interactions (tan). 28
29 Reinforced Concrete Beam 29
30 Show Movies of Reinforced Concrete Beam in Bending and Torsion 30
31 (SPLM = State based Peridynamic Lattice Model) SPLM can simulate major features of concrete: (Dynamics, stability, large deformations, damage, fracture, plasticity, post peak mechanisms) Simplicity of SPLM makes it potentially applicable for practicing engineers: (Meshless method, no convergence studies needed, few material parameters) SPLM requires a lot of computational power, which is becoming cheap. SPLM competes with traditional approaches: (continuum mechanics, finite elements, fracture mechanics) SPLM in the classroom? Conclusions 31
32 Acknowledgements Dr. Susan Atlas, Department of Physics and Astronomy, UNM Dr. Stewart Silling, Sandia National Laboratories Center for Advanced Research Computing, UNM Graduate Students: Nicolas Sau, Eduardo Aguilera, Navid Sakhavand, Vijay Janardhanam, Kiran Tuniki, Asifur Rahman, Hossein Honarvar, Raybeau Richardson, Aziz Asadollahi 32
Introduction to Practical Peridynamics Downloaded from by on 12/30/17. For personal use only.
Frontier Research in Computation and Mechanics of Materials and Biology ISSN: 23154713 Series Editors: Shaofan Li (University of California, Berkeley, USA) Wing Kam Liu (Northwestern University, USA)
More informationThis thesis is approved, and it is acceptable in quality and form for publication:
Bhanu Kiran Tuniki Candidate Civil Engineering Department This thesis is approved, and it is acceptable in quality and form for publication: Approved by the Thesis Committee: Dr. Walter H. Gerstle, Chairperson
More informationNumerical Characterization of Concrete Heterogeneity
Vol. Materials 5, No. Research, 3, 2002Vol. 5, No. 3, Statistical 309314, 2002. Characterization of the Concrete Numerical Modeling of Size Effect In Heterogeneity 2002 309 Numerical Characterization
More information/tvsb Transactions of the VŠB Technical University of Ostrava Civil Engineering Series,Vol. 16, No.
10.1515/tvsb20160020 Transactions of the VŠB Technical University of Ostrava Civil Engineering Series,Vol. 16, No. 2, 2016 paper #20 Josef KVĚTOŇ 1, Jan ELIÁŠ 2 DISCRETE MODEL FOR CONCRETE FRACTURE:
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.antonineeducation.co.uk Key Words Density, Elastic, Plastic, Stress, Strain, Young modulus We study how materials behave
More informationVORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NONLINEAR MATERIALS
The 4 th World Conference on Earthquake Engineering October 7, 008, Beijing, China VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NONLINEAR MATERIALS K.
More informationPDLAMMPS  made easy
PDLAMMPS  made easy R. Rahman 1, J. T. Foster 1, and S. J. Plimpton 2 1 The University of Texas at San Antonio 2 Sandia National Laboratory February 12, 2014 1 Peridynamic theory of solids The peridynamic
More informationAnálisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas
San Miguel de Tucuman, Argentina September 14 th, 2011 Seminary on Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas Antonio Caggiano 1, Guillermo Etse 2, Enzo
More informationFracture Mechanics of NonShear Reinforced R/C Beams
Irina Kerelezova Thomas Hansen M. P. Nielsen Fracture Mechanics of NonShear Reinforced R/C Beams DANMARKS TEKNISKE UNIVERSITET Report BYG DTU R154 27 ISSN 1612917 ISBN 9788778772265 Fracture Mechanics
More information6. NONLINEAR PSEUDOSTATIC ANALYSIS OF ADOBE WALLS
6. NONLINEAR PSEUDOSTATIC ANALYSIS OF ADOBE WALLS Blondet et al. [25] carried out a cyclic test on an adobe wall to reproduce its seismic response and damage pattern under inplane loads. The displacement
More informationGame Physics. Game and Media Technology Master Program  Utrecht University. Dr. Nicolas Pronost
Game and Media Technology Master Program  Utrecht University Dr. Nicolas Pronost Soft body physics Soft bodies In reality, objects are not purely rigid for some it is a good approximation but if you hit
More informationChapter 12. Static Equilibrium and Elasticity
Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial
More informationDynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models
Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models I. Rhee, K.J. Willam, B.P. Shing, University of Colorado at Boulder ABSTRACT: This paper examines the global
More informationIrregular lattice model for quasistatic crack propagation
PHYSICAL REVIEW B 71, 094106 2005 Irregular lattice model for quasistatic crack propagation J. E. Bolander* and N. Sukumar Department of Civil and Environmental Engineering, University of California, Davis
More informationMechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationIntroduction 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 informationCivil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7
Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Introduction... 3 1.1 Background... 3 1.2 Failure Modes... 5 1.3 Design Aspects...
More informationStudies of Bimaterial Interface Fracture with Peridynamics Fang Wang 1, Lisheng Liu 2, *, Qiwen Liu 1, Zhenyu Zhang 1, Lin Su 1 & Dan Xue 1
International Power, Electronics and Materials Engineering Conference (IPEMEC 2015) Studies of Bimaterial Interface Fracture with Peridynamics Fang Wang 1, Lisheng Liu 2, *, Qiwen Liu 1, Zhenyu Zhang 1,
More informationThe concept of Representative Volume for elastic, hardening and softening materials
The concept of Representative Volume for elastic, hardening and softening materials Inna M. Gitman Harm Askes Lambertus J. Sluys Oriol Lloberas Valls i.gitman@citg.tudelft.nl Abstract The concept of the
More informationNUMERICAL SIMULATION OF CONCRETE EXPOSED TO HIGH TEMPERATURE DAMAGE AND EXPLOSIVE SPALLING
NUMERICAL SIMULATION OF CONCRETE EXPOSED TO HIGH TEMPERATURE DAMAGE AND EXPLOSIVE SPALLING Prof. Joško Ožbolt 1 Josipa Bošnjak 1, Goran Periškić 1, Akanshu Sharma 2 1 Institute of Construction Materials,
More informationA 3D distinct lattice spring model for elasticity and dynamic failure
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. (2010) Published online in Wiley InterScience (www.interscience.wiley.com)..930 A 3D distinct
More informationNUMERICAL SIMULATIONS OF CORNERS IN RC FRAMES USING STRUTANDTIE METHOD AND CDP MODEL
Numerical simulations of corners in RC frames using StrutandTie Method and CDP model XIII International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XIII E. Oñate, D.R.J.
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 informationMODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING
CD02003 MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING B. Ghiassi 1, M. Soltani 2, A. A. Tasnimi 3 1 M.Sc. Student, School of Engineering, Tarbiat Modares
More informationBACKGROUNDS. Two Models of Deformable Body. Distinct Element Method (DEM)
BACKGROUNDS Two Models of Deformable Body continuum rigidbody spring deformation expressed in terms of field variables assembly of rigidbodies connected by spring Distinct Element Method (DEM) simple
More informationTwoDirection Cracking ShearFriction Membrane Model for Finite Elment Analysis of Reinforced concrete
Washington University in St. Louis Washington University Open Scholarship All Theses and Dissertations (ETDs) January 2010 TwoDirection Cracking ShearFriction Membrane Model for Finite Elment Analysis
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 informationfive 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 informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More informationA RATEDEPENDENT MULTISCALE CRACK MODEL FOR CONCRETE
VIII International Conference on Fracture echanics of Concrete and Concrete Structures FraCoS8 J.G.. Van ier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang (Eds) A RATEDEPENDENT ULTISCALE CRACK ODEL FOR
More informationChapter 26 Elastic Properties of Materials
Chapter 26 Elastic Properties of Materials 26.1 Introduction... 1 26.2 Stress and Strain in Tension and Compression... 2 26.3 Shear Stress and Strain... 4 Example 26.1: Stretched wire... 5 26.4 Elastic
More informationStressStrain Behavior
StressStrain 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 information**********************************************************************
Department of Civil and Environmental Engineering School of Mining and Petroleum Engineering 333 Markin/CNRL Natural Resources Engineering Facility www.engineering.ualberta.ca/civil Tel: 780.492.4235
More informationTHEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?
CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M  N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO
More informationA STUDY ON FATIGUE CRACK GROWTH IN CONCRETE IN THE PREPARIS REGION
VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS8 J.G.M. Van Mier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang (Eds) A STUDY ON FATIGUE CRACK GROWTH IN CONCRETE
More informationCHAPTER 6: ULTIMATE LIMIT STATE
CHAPTER 6: ULTIMATE LIMIT STATE 6.1 GENERAL It shall be in accordance with JSCE Standard Specification (Design), 6.1. The collapse mechanism in statically indeterminate structures shall not be considered.
More informationSome recent developments in computational modelling of concrete fracture
International Journal of Fracture 86: 5 36, 1997. c 1997 Kluwer Academic Publishers. Printed in the Netherlands. Some recent developments in computational modelling of concrete fracture RENÉ DE BORST Delft
More informationReview of Strain Energy Methods and Introduction to Stiffness Matrix Methods of Structural Analysis
uke University epartment of Civil and Environmental Engineering CEE 42L. Matrix Structural Analysis Henri P. Gavin Fall, 22 Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods
More informationUnit I  Properties of Matter
Unit I  Properties of Matter Elasticity: Elastic and plastic materials Hooke s law elastic behavior of a material stress  strain diagram factors affecting elasticity. Three moduli of elasticity Poisson
More informationTENSILE CRACKING VIEWED AS BIFURCATION AND INSTABILITY IN A DISCRETE INTERFACE MODEL
Fracture Mechanics of Concrete Structures Proceeding FRAMCOS3 AEDIFICATIO Publishers, D79104 Frei burg, Germany TENSILE CRACKING VIEWED AS BIFURCATION AND INSTABILITY IN A DISCRETE INTERFACE MODEL A.
More informationStrainBased Design Model for FRPConfined Concrete Columns
SP230 57 StrainBased Design Model for FRPConfined Concrete Columns by N. Saenz and C.P. Pantelides Synopsis: A constitutive strainbased confinement model is developed herein for circular concrete columns
More informationNonlinear static analysis PUSHOVER
Nonlinear static analysis PUSHOVER Adrian DOGARIU European Erasmus Mundus Master Course Sustainable Constructions under Natural Hazards and Catastrophic Events 520121120111CZERA MUNDUSEMMC Structural
More informationLaboratory 4 Bending Test of Materials
Department of Materials and Metallurgical Engineering Bangladesh University of Engineering Technology, Dhaka MME 222 Materials Testing Sessional.50 Credits Laboratory 4 Bending Test of Materials. Objective
More informationPushover Seismic Analysis of Bridge Structures
Pushover Seismic Analysis of Bridge Structures Bernardo Frère Departamento de Engenharia Civil, Arquitectura e Georrecursos, Instituto Superior Técnico, Technical University of Lisbon, Portugal October
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 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 information3D Finite Element analysis of stud anchors with large head and embedment depth
3D Finite Element analysis of stud anchors with large head and embedment depth G. Periškić, J. Ožbolt & R. Eligehausen Institute for Construction Materials, University of Stuttgart, Stuttgart, Germany
More informationRailroad Concrete Tie Failure Analysis
Railroad Concrete Tie Failure Analysis Hailing Yu, David Jeong, Brian Marquis, and Michael Coltman 2014 International Crosstie & Fastening System Symposium June 35, 2014 The National Transportation Systems
More informationApplication to modeling brittle materials
1.01, 3.01, 10.333,.00 Introduction to Modeling and Simulation Spring 011 Part I Continuum and particle methods Application to modeling brittle materials Lecture 7 Markus J. Buehler Laboratory for Atomistic
More informationLimit analysis of brick masonry shear walls with openings under later loads by rigid block modeling
Limit analysis of brick masonry shear walls with openings under later loads by rigid block modeling F. Portioli, L. Cascini, R. Landolfo University of Naples Federico II, Italy P. Foraboschi IUAV University,
More informationFailure interaction curves for combined loading involving torsion, bending, and axial loading
Failure interaction curves for combined loading involving torsion, bending, and axial loading W M Onsongo Many modern concrete structures such as elevated guideways are subjected to combined bending, torsion,
More informationStrength of Material. Shear Strain. Dr. Attaullah Shah
Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume
More informationHow materials work. Compression Tension Bending Torsion
Materials How materials work Compression Tension Bending Torsion Elemental material atoms: A. Composition a) Nucleus: protons (+), neutrons (0) b) Electrons () B. Neutral charge, i.e., # electrons = #
More informationREPRESENTING MATRIX CRACKS THROUGH DECOMPOSITION OF THE DEFORMATION GRADIENT TENSOR IN CONTINUUM DAMAGE MECHANICS METHODS
20 th International Conference on Composite Materials Copenhagen, 1924 th July 2015 REPRESENTING MATRIX CRACKS THROUGH DECOMPOSITION OF THE DEFORMATION GRADIENT TENSOR IN CONTINUUM DAMAGE MECHANICS METHODS
More informationSTRAIN ASSESSMENT USFOS
1 STRAIN ASSESSMENT IN USFOS 2 CONTENTS: 1 Introduction...3 2 Revised strain calculation model...3 3 Strain predictions for various characteristic cases...4 3.1 Beam with concentrated load at mid span...
More informationSpecial edition paper
Development of New Aseismatic Structure Using Escalators Kazunori Sasaki* Atsushi Hayashi* Hajime Yoshida** Toru Masuda* Aseismatic reinforcement work is often carried out in parallel with improvement
More informationFinite element analyses for limit state design of concrete structures
Finite element analyses for limit state design of concrete structures Posibilities and limitations with SOLVIA Masther s Thesis in the International Master s programme Structural Engineering FERNANDO LOPEZ
More informationElastic parameters prediction under dynamic loading based on the. unit cell of composites considering end constraint effect
Elastic parameters prediction under dynamic loading based on the unit cell of composites considering end constraint effect Wang Meng 1,, Fei Qingguo 1,, Zhang Peiwei 1, (1. Institute of Aerospace Machinery
More informationFlexure: Behavior and Nominal Strength of Beam Sections
4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kipin.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015
More informationCRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES
S. Kakay et al. Int. J. Comp. Meth. and Exp. Meas. Vol. 5 No. (017) 116 14 CRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES SAMDAR KAKAY DANIEL BÅRDSEN
More informationCFRP. FRP FRP. Abaqus
C Epoxy C baqus C FE baqus C amene.kia@gmail.com EROG 1 Debonding : / C (mm) E c (MPa) f' c (MPa) f' t (MPa) a S L d h b 1 2 3 1 2 3 baqus C Leong Kok Leong Kok CDP E p (GPa) (MPa) E a (MPa) G a (MPa)
More informationMECHANICS OF MATERIALS. EQUATIONS AND THEOREMS
1 MECHANICS OF MATERIALS. EQUATIONS AND THEOREMS Version 20110114 Stress tensor Definition of traction vector (1) Cauchy theorem (2) Equilibrium (3) Invariants (4) (5) (6) or, written in terms of principal
More information1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I)
Mechanics of Material Systems (Mechanics and Durability of Solids I) FranzJosef Ulm If Mechanics was the answer, what was the question? Traditional: Structural Engineering Geotechnics Structural Design
More informationAnisotropic modeling of short fibers reinforced thermoplastics materials with LSDYNA
Anisotropic modeling of short fibers reinforced thermoplastics materials with LSDYNA Alexandre Hatt 1 1 Faurecia Automotive Seating, Simplified Limited Liability Company 1 Abstract / Summary Polymer thermoplastics
More informationMechanical Models for Asphalt Behavior and Performance
Mechanical Models for Asphalt Behavior and Performance All Attendees Are Muted Questions and Answers Please type your questions into your webinar control panel We will read your questions out loud, and
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 informationSeismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design
Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Elmer E. Marx, Alaska Department of Transportation and Public Facilities Michael Keever, California Department
More informationMATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?
MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition
More informationInfluence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes
October 2014 Influence of residual stresses in the structural behavior of Abstract tubular columns and arches Nuno Rocha Cima Gomes Instituto Superior Técnico, Universidade de Lisboa, Portugal Contact:
More informationFCP Short Course. Ductile and Brittle Fracture. Stephen D. Downing. Mechanical Science and Engineering
FCP Short Course Ductile and Brittle Fracture Stephen D. Downing Mechanical Science and Engineering 001015 University of Illinois Board of Trustees, All Rights Reserved Agenda Limit theorems Plane Stress
More informationConstitutive Modeling of Reinforced Concrete Panel Behavior under Cyclic Loading
Constitutive Modeling of Reinforced Concrete Panel Behavior under Cyclic Loading K. Orakcal & D. Ulugtekin Bogazici University, Istanbul, Turkey L. M. Massone University of Chile, Santiago, Chile SUMMARY:
More informationStudies of dynamic crack propagation and crack branching with peridynamics
Int J Fract (2010) 162:229 244 DOI 10.1007/s1070401094424 ORIGINAL PAPER Studies of dynamic crack propagation and crack branching with peridynamics Youn Doh Ha Florin Bobaru Received: 31 August 2009
More informationObjectives: After completion of this module, you should be able to:
Chapter 12 Objectives: After completion of this module, you should be able to: Demonstrate your understanding of elasticity, elastic limit, stress, strain, and ultimate strength. Write and apply formulas
More informationSean Carey Tafe No Lab Report: Hounsfield Tension Test
Sean Carey Tafe No. 366851615 Lab Report: Hounsfield Tension Test August 2012 The Hounsfield Tester The Hounsfield Tester can do a variety of tests on a small testpiece. It is mostly used for tensile
More informationLecture08 Gravity Load Analysis of RC Structures
Lecture08 Gravity Load Analysis of RC Structures By: Prof Dr. Qaisar Ali Civil Engineering Department UET Peshawar www.drqaisarali.com 1 Contents Analysis Approaches Point of Inflection Method Equivalent
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 informationsottotitolo Department of Civil and Environmental Engineering
A thirtyyear Titolo survey presentazione of Microplane Models sottotitolo Milano, Dr. Giovanni XX mese Di Luzio 20XX Department of Civil and Environmental Engineering Origin of microplane models Slip
More information6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and
6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile
More informationBrittle Deformation. Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm
Lecture 6 Brittle Deformation Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm WW Norton, unless noted otherwise Brittle deformation EarthStructure (2 nd
More informationA NEW SIMPLIFIED AND EFFICIENT TECHNIQUE FOR FRACTURE BEHAVIOR ANALYSIS OF CONCRETE STRUCTURES
Fracture Mechanics of Concrete Structures Proceedings FRAMCOS3 AEDFCATO Publishers, D79104 Freiburg, Germany A NEW SMPLFED AND EFFCENT TECHNQUE FOR FRACTURE BEHAVOR ANALYSS OF CONCRETE STRUCTURES K.
More informationCracking and Fracture of Concrete at Mesolevel using Zerothickness Interface Elements
Cracking and Fracture of Concrete at Mesolevel using Zerothickness Interface Elements Ignacio Carol*, Andrés Idiart**, Carlos López* and Antonio Caballero*** * School of Civil Engineering (ETSECCPB),
More information1.050 Content overview Engineering Mechanics I Content overview. Selection of boundary conditions: Euler buckling.
.050 Content overview.050 Engineering Mechanics I Lecture 34 How things fail and how to avoid it Additional notes energy approach I. Dimensional analysis. On monsters, mice and mushrooms Lectures 3. Similarity
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationSERVICEABILITY OF BEAMS AND ONEWAY SLABS
CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach  Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONEWAY SLABS A. J. Clark School of Engineering Department of Civil
More informationBehavior and Modeling of Existing Reinforced Concrete Columns
Behavior and Modeling of Existing Reinforced Concrete Columns Kenneth J. Elwood University of British Columbia with contributions from Jose Pincheira, Univ of Wisconsin John Wallace, UCLA Questions? What
More information*MAT_PAPER and *MAT_COHESIVE_PAPER: Two New Models for Paperboard Materials
14 th International LSDYNA 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 informationLecture 7, Foams, 3.054
Lecture 7, Foams, 3.054 Opencell foams StressStrain curve: deformation and failure mechanisms Compression  3 regimes  linear elastic  bending  stress plateau  cell collapse by buckling yielding
More informationSHEAR CAPACITY OF REINFORCED CONCRETE COLUMNS RETROFITTED WITH VERY FLEXIBLE FIBER REINFORCED POLYMER WITH VERY LOW YOUNG S MODULUS
SHEAR CAPACITY OF REINFORCED CONCRETE COLUMNS RETROFITTED WITH VERY FLEXILE FIER REINFORCED POLYMER WITH VERY LOW YOUNG S MODULUS Hu Shaoqing Supervisor: Susumu KONO ** MEE8165 ASTRACT FRP with low Young
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 informationCohesive band model: a triaxialitydependent cohesive model for damage to crack transition in a nonlocal implicit discontinuous Galerkin framework
University of Liège Aerospace & Mechanical Engineering Cohesive band model: a triaxialitydependent cohesive model for damage to crack transition in a nonlocal implicit discontinuous Galerkin framework
More informationNONLINEAR MATERIAL MECHANICS
Graduate course NONLINEAR MATERIAL MECHANICS November 6 th 8 th 2017 November 13 th 15 th 2017 Hosted by: Faculty of Engineering Technology University of Twente General This course is an initiative of
More information3.091 Introduction to Solid State Chemistry. Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS
3.091 Introduction to Solid State Chemistry Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS 1. INTRODUCTION Crystals are held together by interatomic or intermolecular bonds. The bonds can be covalent,
More information4.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 stressstrain diagram
More informationMODELING OF CONCRETE MATERIALS AND STRUCTURES. Kaspar Willam. Isotropic Elastic Models: Invariant vs Principal Formulations
MODELING OF CONCRETE MATERIALS AND STRUCTURES Kaspar Willam University of Colorado at Boulder Class Meeting #2: Nonlinear Elastic Models Isotropic Elastic Models: Invariant vs Principal Formulations Elastic
More information(MPa) compute (a) The traction vector acting on an internal material plane with normal n ( e1 e
EN10: Continuum Mechanics Homework : Kinetics Due 1:00 noon Friday February 4th School of Engineering Brown University 1. For the Cauchy stress tensor with components 100 5 50 0 00 (MPa) compute (a) The
More informationELAS  Elasticity
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2017 295  EEBE  Barcelona East School of Engineering 737  RMEE  Department of Strength of Materials and Structural Engineering
More informationLecture #10: Anisotropic plasticity Crashworthiness Basics of shell elements
Lecture #10: 1510735: 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 informationCDPM2: A damageplasticity approach to modelling the failure of concrete
CDPM2: A damageplasticity approach to modelling the failure of concrete Peter Grassl 1, Dimitrios Xenos 1, Ulrika Nyström 2, Rasmus Rempling 2, Kent Gylltoft 2 arxiv:1307.6998v1 [condmat.mtrlsci] 26
More informationConcrete Technology Prof. B. Bhattacharjee Department of Civil Engineering Indian Institute of Technology, Delhi
Concrete Technology Prof. B. Bhattacharjee Department of Civil Engineering Indian Institute of Technology, Delhi Lecture  25 Strength of Concrete: Factors Affecting Test Results Welcome to module 6, lecture
More information