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

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

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

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 meso-scale model for concrete in which they modeled the aggregates and mortar matrix. 2012, Potyondy, D. O. The Bonded-Particle 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 Face-Centered 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.

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: 2315-4713 Series Editors: Shaofan Li (University of California, Berkeley, USA) Wing Kam Liu (Northwestern University, USA)

More information

This thesis is approved, and it is acceptable in quality and form for publication:

This 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 information

Numerical Characterization of Concrete Heterogeneity

Numerical Characterization of Concrete Heterogeneity Vol. Materials 5, No. Research, 3, 2002Vol. 5, No. 3, Statistical 309-314, 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.

/tvsb Transactions of the VŠB Technical University of Ostrava Civil Engineering Series,Vol. 16, No. 10.1515/tvsb-2016-0020 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 information

Elastic 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 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 information

VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS

VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR 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 NON-LINEAR MATERIALS K.

More information

PDLAMMPS - made easy

PDLAMMPS - 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 information

Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas

Análisis 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 information

Fracture Mechanics of Non-Shear Reinforced R/C Beams

Fracture Mechanics of Non-Shear Reinforced R/C Beams Irina Kerelezova Thomas Hansen M. P. Nielsen Fracture Mechanics of Non-Shear Reinforced R/C Beams DANMARKS TEKNISKE UNIVERSITET Report BYG DTU R-154 27 ISSN 161-2917 ISBN 97887-7877-226-5 Fracture Mechanics

More information

6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS

6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS 6. NON-LINEAR PSEUDO-STATIC 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 in-plane loads. The displacement

More information

Game Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost

Game 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 information

Chapter 12. Static Equilibrium and Elasticity

Chapter 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 information

Dynamic 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 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 information

Irregular lattice model for quasistatic crack propagation

Irregular 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 information

Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering

Mechanics 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 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

Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7

Civil 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 information

Studies of Bimaterial Interface Fracture with Peridynamics Fang Wang 1, Lisheng Liu 2, *, Qiwen Liu 1, Zhenyu Zhang 1, Lin Su 1 & Dan Xue 1

Studies 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 information

The concept of Representative Volume for elastic, hardening and softening materials

The 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 information

NUMERICAL SIMULATION OF CONCRETE EXPOSED TO HIGH TEMPERATURE DAMAGE AND EXPLOSIVE SPALLING

NUMERICAL 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 information

A 3D distinct lattice spring model for elasticity and dynamic failure

A 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 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

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

MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING

MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING CD02-003 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 information

BACKGROUNDS. Two Models of Deformable Body. Distinct Element Method (DEM)

BACKGROUNDS. Two Models of Deformable Body. Distinct Element Method (DEM) BACKGROUNDS Two Models of Deformable Body continuum rigid-body spring deformation expressed in terms of field variables assembly of rigid-bodies connected by spring Distinct Element Method (DEM) simple

More information

Two-Direction Cracking Shear-Friction Membrane Model for Finite Elment Analysis of Reinforced concrete

Two-Direction Cracking Shear-Friction 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 Two-Direction Cracking Shear-Friction Membrane Model for Finite Elment Analysis

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

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

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture

five 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 information

A RATE-DEPENDENT MULTI-SCALE CRACK MODEL FOR CONCRETE

A RATE-DEPENDENT MULTI-SCALE CRACK MODEL FOR CONCRETE VIII International Conference on Fracture echanics of Concrete and Concrete Structures FraCoS-8 J.G.. Van ier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang (Eds) A RATE-DEPENDENT ULTI-SCALE CRACK ODEL FOR

More information

Chapter 26 Elastic Properties of Materials

Chapter 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 information

Stress-Strain Behavior

Stress-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 information

**********************************************************************

********************************************************************** Department of Civil and Environmental Engineering School of Mining and Petroleum Engineering 3-33 Markin/CNRL Natural Resources Engineering Facility www.engineering.ualberta.ca/civil Tel: 780.492.4235

More information

THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?

THEME 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 information

A STUDY ON FATIGUE CRACK GROWTH IN CONCRETE IN THE PRE-PARIS REGION

A STUDY ON FATIGUE CRACK GROWTH IN CONCRETE IN THE PRE-PARIS REGION VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-8 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 information

CHAPTER 6: ULTIMATE LIMIT STATE

CHAPTER 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 information

Some recent developments in computational modelling of concrete fracture

Some 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 information

Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods of Structural Analysis

Review 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 information

Unit I - Properties of Matter

Unit 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 information

TENSILE CRACKING VIEWED AS BIFURCATION AND INSTABILITY IN A DISCRETE INTERFACE MODEL

TENSILE CRACKING VIEWED AS BIFURCATION AND INSTABILITY IN A DISCRETE INTERFACE MODEL Fracture Mechanics of Concrete Structures Proceeding FRAMCOS-3 AEDIFICATIO Publishers, D-79104 Frei burg, Germany TENSILE CRACKING VIEWED AS BIFURCATION AND INSTABILITY IN A DISCRETE INTERFACE MODEL A.

More information

Strain-Based Design Model for FRP-Confined Concrete Columns

Strain-Based Design Model for FRP-Confined Concrete Columns SP-230 57 Strain-Based Design Model for FRP-Confined Concrete Columns by N. Saenz and C.P. Pantelides Synopsis: A constitutive strain-based confinement model is developed herein for circular concrete columns

More information

Nonlinear static analysis PUSHOVER

Nonlinear static analysis PUSHOVER Nonlinear static analysis PUSHOVER Adrian DOGARIU European Erasmus Mundus Master Course Sustainable Constructions under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC Structural

More information

Laboratory 4 Bending Test of Materials

Laboratory 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 information

Pushover Seismic Analysis of Bridge Structures

Pushover 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 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

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

3D 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 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 information

Railroad Concrete Tie Failure Analysis

Railroad 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 3-5, 2014 The National Transportation Systems

More information

Application to modeling brittle materials

Application 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 information

Limit 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 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 information

Failure interaction curves for combined loading involving torsion, bending, and axial loading

Failure 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 information

Strength of Material. Shear Strain. Dr. Attaullah Shah

Strength 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 information

How materials work. Compression Tension Bending Torsion

How 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 information

REPRESENTING MATRIX CRACKS THROUGH DECOMPOSITION OF THE DEFORMATION GRADIENT TENSOR IN CONTINUUM DAMAGE MECHANICS METHODS

REPRESENTING MATRIX CRACKS THROUGH DECOMPOSITION OF THE DEFORMATION GRADIENT TENSOR IN CONTINUUM DAMAGE MECHANICS METHODS 20 th International Conference on Composite Materials Copenhagen, 19-24 th July 2015 REPRESENTING MATRIX CRACKS THROUGH DECOMPOSITION OF THE DEFORMATION GRADIENT TENSOR IN CONTINUUM DAMAGE MECHANICS METHODS

More information

STRAIN ASSESSMENT USFOS

STRAIN 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 information

Special edition paper

Special 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 information

Finite element analyses for limit state design of concrete structures

Finite 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 information

Elastic 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 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 information

Flexure: Behavior and Nominal Strength of Beam Sections

Flexure: 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 (kip-in.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015

More information

CRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES

CRACK 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 information

CFRP. FRP FRP. Abaqus

CFRP. 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 information

MECHANICS OF MATERIALS. EQUATIONS AND THEOREMS

MECHANICS OF MATERIALS. EQUATIONS AND THEOREMS 1 MECHANICS OF MATERIALS. EQUATIONS AND THEOREMS Version 2011-01-14 Stress tensor Definition of traction vector (1) Cauchy theorem (2) Equilibrium (3) Invariants (4) (5) (6) or, written in terms of principal

More information

1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I)

1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm If Mechanics was the answer, what was the question? Traditional: Structural Engineering Geotechnics Structural Design

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

Mechanical Models for Asphalt Behavior and Performance

Mechanical 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 information

X has a higher value of the Young modulus. Y has a lower maximum tensile stress than X

X 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 information

Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design

Seismic 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 information

MATERIALS. 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? 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 information

Influence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes

Influence 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 information

FCP 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 FCP Short Course Ductile and Brittle Fracture Stephen D. Downing Mechanical Science and Engineering 001-015 University of Illinois Board of Trustees, All Rights Reserved Agenda Limit theorems Plane Stress

More information

Constitutive Modeling of Reinforced Concrete Panel Behavior under Cyclic Loading

Constitutive 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 information

Studies of dynamic crack propagation and crack branching with peridynamics

Studies of dynamic crack propagation and crack branching with peridynamics Int J Fract (2010) 162:229 244 DOI 10.1007/s10704-010-9442-4 ORIGINAL PAPER Studies of dynamic crack propagation and crack branching with peridynamics Youn Doh Ha Florin Bobaru Received: 31 August 2009

More information

Objectives: After completion of this module, you should be able to:

Objectives: 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 information

Sean Carey Tafe No Lab Report: Hounsfield Tension Test

Sean 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 test-piece. It is mostly used for tensile

More information

Lecture-08 Gravity Load Analysis of RC Structures

Lecture-08 Gravity Load Analysis of RC Structures Lecture-08 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 information

Static 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 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 information

sottotitolo Department of Civil and Environmental Engineering

sottotitolo Department of Civil and Environmental Engineering A thirty-year 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 information

6.4 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 ( 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 information

Brittle Deformation. Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm

Brittle 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 information

A NEW SIMPLIFIED AND EFFICIENT TECHNIQUE FOR FRACTURE BEHAVIOR ANALYSIS OF CONCRETE STRUCTURES

A NEW SIMPLIFIED AND EFFICIENT TECHNIQUE FOR FRACTURE BEHAVIOR ANALYSIS OF CONCRETE STRUCTURES Fracture Mechanics of Concrete Structures Proceedings FRAMCOS-3 AEDFCATO Publishers, D-79104 Freiburg, Germany A NEW SMPLFED AND EFFCENT TECHNQUE FOR FRACTURE BEHAVOR ANALYSS OF CONCRETE STRUCTURES K.

More information

Cracking and Fracture of Concrete at Meso-level using Zero-thickness Interface Elements

Cracking and Fracture of Concrete at Meso-level using Zero-thickness Interface Elements Cracking and Fracture of Concrete at Meso-level using Zero-thickness Interface Elements Ignacio Carol*, Andrés Idiart**, Carlos López* and Antonio Caballero*** * School of Civil Engineering (ETSECCPB),

More information

1.050 Content overview Engineering Mechanics I Content overview. Selection of boundary conditions: Euler buckling.

1.050 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 information

Chapter 3. Load and Stress Analysis

Chapter 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 information

SERVICEABILITY OF BEAMS AND ONE-WAY SLABS

SERVICEABILITY OF BEAMS AND ONE-WAY SLABS CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach - Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONE-WAY SLABS A. J. Clark School of Engineering Department of Civil

More information

Behavior and Modeling of Existing Reinforced Concrete Columns

Behavior 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

*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

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

SHEAR 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 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 information

Mechanical properties 1 Elastic behaviour of materials

Mechanical 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 information

Cohesive band model: a triaxiality-dependent cohesive model for damage to crack transition in a non-local implicit discontinuous Galerkin framework

Cohesive band model: a triaxiality-dependent cohesive model for damage to crack transition in a non-local implicit discontinuous Galerkin framework University of Liège Aerospace & Mechanical Engineering Cohesive band model: a triaxiality-dependent cohesive model for damage to crack transition in a non-local implicit discontinuous Galerkin framework

More information

NONLINEAR MATERIAL MECHANICS

NONLINEAR 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 information

3.091 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 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 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

MODELING OF CONCRETE MATERIALS AND STRUCTURES. Kaspar Willam. Isotropic Elastic Models: Invariant vs Principal Formulations

MODELING 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

(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 information

ELAS - Elasticity

ELAS - 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 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

CDPM2: A damage-plasticity approach to modelling the failure of concrete

CDPM2: A damage-plasticity approach to modelling the failure of concrete CDPM2: A damage-plasticity 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 [cond-mat.mtrl-sci] 26

More information

Concrete 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 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