BACKGROUNDS. Two Models of Deformable Body. Distinct Element Method (DEM)
|
|
- Dwain Mason
- 6 years ago
- Views:
Transcription
1 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 treatment of failure: breakage of spring non-rigorous determination of spring constants breakage of spring deformable body particle modeling DEM analysis spring constant need to be determined in terms of material parameters
2 MATHEMATICAL INTERPLETATION OF RIGID-BODY SPRING MODEL Non-Overlapping Functions for Discretization ordinary FEM u 1 DEM u 1 u 2 u 2 smooth but overlapping functions are used for discretization characteristic functions of domain are used for discretization
3 PARTICLE DISCRETIZATION FOR FUNCTION AND DERIVATIVE Discretization of Function f(x) in terms of {ϕ (x)} form of discretization f d ( x) = f ϕ ( x) Discretization of Derivative f,i (x) in terms of {ψ (x)} form of discretization g d i ( x) = g ψ i ( x) different from {ϕ } E f ({f }) = (f ( x) f V minimize E f d ( x)) 2 ds derivative of {ϕ } is not bounded but integratable f = V 1 fϕ ds ϕ ds V g i β ( ) β ψ ϕ ds = f 1 ψ ds V V,i β optimal coefficients for given Voronoi blocks {ϕ } and Delaunay triangles {ψ }
4 1-D PARTICLE DISCRETIZATION x n x n+1 mother points f d ( x) = f ϕ ( x) average value taken over interval for ϕ is coefficient of characteristic function ϕ df dx ( x) = g( x) = g ψ ( x) y n-1 y n y n+1 average slope of interval for ψ is coefficient of characteristic function ψ middle point of neighboring mother points
5 2-D PARTICLE DISCRETIZATION dual domain decomposition Voronoi blocks for function Delaunay triangles for derivative function and derivative are discretized in terms of sets of non-overlapping characteristic functions, such that function and derivative are uniform in Voronoi blocks and Delaunay triangles,
6 COMPARISON OF PARTICLE DISCRETIZATION WITH ORDINARY DISCRETIZATION f 1 f 2 f = f 1 ordinary discretization with linear function f 1 f 2 f = f 2 x 1 f 3 particle discretization x 2 x 3 particle discretization of derivative derivative of particle discretization coincides with slope of plane which is formed by linearly connecting Voronoi mother points
7 PARTICLE DISCRETIZATION TO CONTINUUM MECHANICS PROBLEM Conjugate Functional J(u, σ) = V σ ij ε ij 1 2 σ ij c ijkl σ kl ds u σ i ij = = u i σ ij ϕ ψ hypo-voronoi for displacement Delaunay for stress: coefficients are analytically obtained by stationarizing J FEM-β: FEM with Particle Discretization stiffness matrix of FEM-β coincides with stiffness matrix of FEM with uniform triangular element including rigid-body-rotation, FEM-β gives accurate and efficient computation for field with singularity
8 FAILURE ANALYSIS OF FEM-β stiffness matrix of FEM-β [k [k [k ] ] ] [k [k [k ] ] ] [k [k [k ] ] ] strain energy due to relative deformation of Ω 1 and Ω 2 through movement of Ω 3 for indirect interaction for direct interaction Ω 1 x 1 ( T k ] [k ]) [ ji = ij direct [k12] = [k12 ] + [k indirect 12 ] x 2 Ω 2 Ω 3 x 3 cut two springs of direct and indirect interaction together or separately, according to certain failure criterion of continuum
9 FAILURE MODELING BY BREAKING SPRINGS region with reduced strain energy broken edge P O Φ 2 Φ 3 C R J-integral Analytical FEM-beta FEM A Φ 1 Q B Number of Elements relative error of J-integral is around a few percents
10 EXAMPLE PROBLEM Simulation of Crack Growth Check of Convergence displacement strain/strain energy Pattern of Crack Growth can small difference in initial configuration cause large difference in crack growth? uniform tension
11 CONVERGENCE OF SOLUTION ξ = Best Performance ηd ηd ξ NDF displacement norm w.r.t. mesh quality displacement norm w.r.t. NDF displacement norm: η d = B u û B û 2 2 dv dv
12 CHECK OF CRACK GROWTH pattern of crack growth ε yy evolution of normal strain distribution
13 EXAMPLE: PLATE WITH 3 HOLES simulation of crack growth: crack stems from holes case a case b slight difference in location of 3 rd hole
14 DIFFERENCE IN CRACK GROWTH: DISTRIBUTION OF NORMAL STRAIN case a case b
15 SIMULATION OF BRAZILIAN TEST Brazilian test
16 SIMULATION OF FOUR POINT BENDING TEST four point bending test σ
17 FOUR POINT BENDING WITH IDEARLY HOMOGENEOUS MATERIALS σ FEM-β puts two source of local heterogeneity, 1) mesh quality for particle discretization and 2) crack path along Voronoi boundary. An ideally homogeneous material which is modeled with best mesh quality sometimes fail to simulate crack propagation.
18 CONCLUDING REMARKS Particle Discretization discretization scheme using set of non-overlapping characteristic functions Continuum Mechanics Problem essentially same accuracy as FEM with uniform strain applicable to non-linear plasticity Failure Analysis simple but robust treatment of failure Monte-Carlo simulation for studying local heterogeneity effects on failure - candidates of failure patterns are pre-determined by spatial discretization
3D dynamic crack propagation analysis with PDS-FEM
JAMSTEC-R IFREE Special Issue, November 2009 3D dynamic crack propagation analysis with PDS-FEM 1*, Hide Sakaguchi 1, Kenji Oguni 2, Muneo Hori 2 discretizations. Keywords +81-45-778-5972 lalith@jamstec.go.jp
More informationMonte-Carlo Simulation of Failure Phenomena using Particle Discretization
Monte-Carlo Simulation of Failure Phenomena using Particle Discretization Kenji OGUNI Atsushi WAKAI Muneo HORI Earthquake Research Institute, University of Tokyo Motivation Deformation Failure x a PDF
More informationMechanics PhD Preliminary Spring 2017
Mechanics PhD Preliminary Spring 2017 1. (10 points) Consider a body Ω that is assembled by gluing together two separate bodies along a flat interface. The normal vector to the interface is given by n
More informationChapter 2. Formulation of Finite Element Method by Variational Principle
Chapter 2 Formulation of Finite Element Method by Variational Principle The Concept of Variation of FUNCTIONALS Variation Principle: Is to keep the DIFFERENCE between a REAL situation and an APPROXIMATE
More informationNONLINEAR CONTINUUM FORMULATIONS CONTENTS
NONLINEAR CONTINUUM FORMULATIONS CONTENTS Introduction to nonlinear continuum mechanics Descriptions of motion Measures of stresses and strains Updated and Total Lagrangian formulations Continuum shell
More information3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1
Math Problem a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b- True or false and why 1. if A is
More informationEshan V. Dave, Secretary of M&FGM2006 (Hawaii) Research Assistant and Ph.D. Candidate. Glaucio H. Paulino, Chairman of M&FGM2006 (Hawaii)
Asphalt Pavement Aging and Temperature Dependent Properties through a Functionally Graded Viscoelastic Model I: Development, Implementation and Verification Eshan V. Dave, Secretary of M&FGM2006 (Hawaii)
More informationFig. 1. Circular fiber and interphase between the fiber and the matrix.
Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In
More informationVariational principles in mechanics
CHAPTER Variational principles in mechanics.1 Linear Elasticity n D Figure.1: A domain and its boundary = D [. Consider a domain Ω R 3 with its boundary = D [ of normal n (see Figure.1). The problem of
More informationOutline. Advances in STAR-CCM+ DEM models for simulating deformation, breakage, and flow of solids
Advances in STAR-CCM+ DEM models for simulating deformation, breakage, and flow of solids Oleh Baran Outline Overview of DEM in STAR-CCM+ Recent DEM capabilities Parallel Bonds in STAR-CCM+ Constant Rate
More informationBy drawing Mohr s circle, the stress transformation in 2-D can be done graphically. + σ x σ y. cos 2θ + τ xy sin 2θ, (1) sin 2θ + τ xy cos 2θ.
Mohr s Circle By drawing Mohr s circle, the stress transformation in -D can be done graphically. σ = σ x + σ y τ = σ x σ y + σ x σ y cos θ + τ xy sin θ, 1 sin θ + τ xy cos θ. Note that the angle of rotation,
More informationNumerical modeling of standard rock mechanics laboratory tests using a finite/discrete element approach
Numerical modeling of standard rock mechanics laboratory tests using a finite/discrete element approach S. Stefanizzi GEODATA SpA, Turin, Italy G. Barla Department of Structural and Geotechnical Engineering,
More informationChapter 5 Structural Elements: The truss & beam elements
Institute of Structural Engineering Page 1 Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 2 Chapter Goals Learn how to formulate the Finite Element Equations
More informationEngineering Sciences 241 Advanced Elasticity, Spring Distributed Thursday 8 February.
Engineering Sciences 241 Advanced Elasticity, Spring 2001 J. R. Rice Homework Problems / Class Notes Mechanics of finite deformation (list of references at end) Distributed Thursday 8 February. Problems
More informationThe Finite Element Method
The Finite Element Method 3D Problems Heat Transfer and Elasticity Read: Chapter 14 CONTENTS Finite element models of 3-D Heat Transfer Finite element model of 3-D Elasticity Typical 3-D Finite Elements
More informationLecture notes Models of Mechanics
Lecture notes Models of Mechanics Anders Klarbring Division of Mechanics, Linköping University, Sweden Lecture 7: Small deformation theories Klarbring (Mechanics, LiU) Lecture notes Linköping 2012 1 /
More informationElastoplastic Deformation in a Wedge-Shaped Plate Caused By a Subducting Seamount
Elastoplastic Deformation in a Wedge-Shaped Plate Caused By a Subducting Seamount Min Ding* 1, and Jian Lin 2 1 MIT/WHOI Joint Program, 2 Woods Hole Oceanographic Institution *Woods Hole Oceanographic
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 informationCRITERIA FOR SELECTION OF FEM MODELS.
CRITERIA FOR SELECTION OF FEM MODELS. Prof. P. C.Vasani,Applied Mechanics Department, L. D. College of Engineering,Ahmedabad- 380015 Ph.(079) 7486320 [R] E-mail:pcv-im@eth.net 1. Criteria for Convergence.
More informationContinuum mechanics V. Constitutive equations. 1. Constitutive equation: definition and basic axioms
Continuum mechanics office Math 0.107 ales.janka@unifr.ch http://perso.unifr.ch/ales.janka/mechanics Mars 16, 2011, Université de Fribourg 1. Constitutive equation: definition and basic axioms Constitutive
More informationMeasurement of deformation. Measurement of elastic force. Constitutive law. Finite element method
Deformable Bodies Deformation x p(x) Given a rest shape x and its deformed configuration p(x), how large is the internal restoring force f(p)? To answer this question, we need a way to measure deformation
More informationBilinear Quadrilateral (Q4): CQUAD4 in GENESIS
Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS The Q4 element has four nodes and eight nodal dof. The shape can be any quadrilateral; we ll concentrate on a rectangle now. The displacement field in terms
More informationSoft Bodies. Good approximation for hard ones. approximation breaks when objects break, or deform. Generalization: soft (deformable) bodies
Soft-Body Physics Soft Bodies Realistic objects are not purely rigid. Good approximation for hard ones. approximation breaks when objects break, or deform. Generalization: soft (deformable) bodies Deformed
More informationINVERSE ANALYSIS METHODS OF IDENTIFYING CRUSTAL CHARACTERISTICS USING GPS ARRYA DATA
Problems in Solid Mechanics A Symposium in Honor of H.D. Bui Symi, Greece, July 3-8, 6 INVERSE ANALYSIS METHODS OF IDENTIFYING CRUSTAL CHARACTERISTICS USING GPS ARRYA DATA M. HORI (Earthquake Research
More informationCommon pitfalls while using FEM
Common pitfalls while using FEM J. Pamin Instytut Technologii Informatycznych w Inżynierii Lądowej Wydział Inżynierii Lądowej, Politechnika Krakowska e-mail: JPamin@L5.pk.edu.pl With thanks to: R. de Borst
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 informationMechanics of Earthquakes and Faulting
Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Overview Milestones in continuum mechanics Concepts of modulus and stiffness. Stress-strain relations Elasticity Surface and body
More informationMechanical 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 information1.050 Engineering Mechanics. Lecture 22: Isotropic elasticity
1.050 Engineering Mechanics Lecture 22: Isotropic elasticity 1.050 Content overview I. Dimensional analysis 1. On monsters, mice and mushrooms 2. Similarity relations: Important engineering tools II. Stresses
More informationA 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 informationLinear Cosserat elasticity, conformal curvature and bounded stiffness
1 Linear Cosserat elasticity, conformal curvature and bounded stiffness Patrizio Neff, Jena Jeong Chair of Nonlinear Analysis & Modelling, Uni Dui.-Essen Ecole Speciale des Travaux Publics, Cachan, Paris
More informationFinite Element Method in Geotechnical Engineering
Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps
More informationCIVL4332 L1 Introduction to Finite Element Method
CIVL L Introduction to Finite Element Method CIVL L Introduction to Finite Element Method by Joe Gattas, Faris Albermani Introduction The FEM is a numerical technique for solving physical problems such
More informationAnalytical Mechanics: Elastic Deformation
Analytical Mechanics: Elastic Deformation Shinichi Hirai Dept. Robotics, Ritsumeikan Univ. Shinichi Hirai (Dept. Robotics, Ritsumeikan Univ.) Analytical Mechanics: Elastic Deformation 1 / 60 Agenda Agenda
More informationTopics in Ship Structures
Topics in Ship Structures 8 Elastic-lastic Fracture Mechanics Reference : Fracture Mechanics by T.L. Anderson Lecture Note of Eindhoven University of Technology 17. 1 by Jang, Beom Seon Oen INteractive
More informationMacroscopic theory Rock as 'elastic continuum'
Elasticity and Seismic Waves Macroscopic theory Rock as 'elastic continuum' Elastic body is deformed in response to stress Two types of deformation: Change in volume and shape Equations of motion Wave
More informationABHELSINKI UNIVERSITY OF TECHNOLOGY
ABHELSINKI UNIVERSITY OF TECHNOLOGY TECHNISCHE UNIVERSITÄT HELSINKI UNIVERSITE DE TECHNOLOGIE D HELSINKI A posteriori error analysis for the Morley plate element Jarkko Niiranen Department of Structural
More informationVORONOI 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 informationContinuum Models of Discrete Particle Systems with Particle Shape Considered
Introduction Continuum Models of Discrete Particle Systems with Particle Shape Considered Matthew R. Kuhn 1 Ching S. Chang 2 1 University of Portland 2 University of Massachusetts McMAT Mechanics and Materials
More informationIntroduction to fracture mechanics
Introduction to fracture mechanics Prof. Dr. Eleni Chatzi Dr. Giuseppe Abbiati, Dr. Konstantinos Agathos Lecture 6-9 November, 2017 Institute of Structural Engineering, ETH Zu rich November 9, 2017 Institute
More informationLecture 8: Tissue Mechanics
Computational Biology Group (CoBi), D-BSSE, ETHZ Lecture 8: Tissue Mechanics Prof Dagmar Iber, PhD DPhil MSc Computational Biology 2015/16 7. Mai 2016 2 / 57 Contents 1 Introduction to Elastic Materials
More informationThe Virtual Element Method: an introduction with focus on fluid flows
The Virtual Element Method: an introduction with focus on fluid flows L. Beirão da Veiga Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca VEM people (or group representatives): P.
More informationHomogenization in Elasticity
uliya Gorb November 9 13, 2015 uliya Gorb Homogenization of Linear Elasticity problem We now study Elasticity problem in Ω ε R 3, where the domain Ω ε possess a periodic structure with period 0 < ε 1 and
More informationContents. Prologue Introduction. Classical Approximation... 19
Contents Prologue........................................................................ 15 1 Introduction. Classical Approximation.................................. 19 1.1 Introduction................................................................
More informationL e c t u r e. D r. S a s s a n M o h a s s e b
The Scaled smteam@gmx.ch Boundary Finite www.erdbebenschutz.ch Element Method Lecture A L e c t u r e A1 D r. S a s s a n M o h a s s e b V i s i t i n g P r o f e s s o r M. I. T. C a m b r i d g e December
More information1. Let a(x) > 0, and assume that u and u h are the solutions of the Dirichlet problem:
Mathematics Chalmers & GU TMA37/MMG800: Partial Differential Equations, 011 08 4; kl 8.30-13.30. Telephone: Ida Säfström: 0703-088304 Calculators, formula notes and other subject related material are not
More informationAnisotropic 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 informationFundamentals of Linear Elasticity
Fundamentals of Linear Elasticity Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI bluebox.ippt.pan.pl/ tzielins/ Institute of Fundamental Technological Research of the Polish Academy
More informationSimulation of Stress Concentration Problems in Laminated Plates by Quasi-Trefftz Finite Element Models
1677 Simulation of Stress Concentration Problems in Laminated Plates by Quasi-Trefftz Finite Element Models Abstract Hybrid quasi-trefftz finite elements have been applied with success to the analysis
More informationOn atomistic-to-continuum couplings without ghost forces
On atomistic-to-continuum couplings without ghost forces Dimitrios Mitsoudis ACMAC Archimedes Center for Modeling, Analysis & Computation Department of Applied Mathematics, University of Crete & Institute
More informationIntroduction to the J-integral
Introduction to the J-integral Instructor: Ramsharan Rangarajan February 24, 2016 The purpose of this lecture is to briefly introduce the J-integral, which is widely used in fracture mechanics. To the
More informationCHAPTER 5. Beam Theory
CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The Euler-Bernoulli assumptions One of its dimensions
More informationStress analysis of a stepped bar
Stress analysis of a stepped bar Problem Find the stresses induced in the axially loaded stepped bar shown in Figure. The bar has cross-sectional areas of A ) and A ) over the lengths l ) and l ), respectively.
More informationa x Questions on Classical Solutions 1. Consider an infinite linear elastic plate with a hole as shown. Uniform shear stress
Questions on Classical Solutions. Consider an infinite linear elastic plate with a hole as shown. Uniform shear stress σ xy = T is applied at infinity. Determine the value of the stress σ θθ on the edge
More informationBake, shake or break - and other applications for the FEM. 5: Do real-life experimentation using your FEM code
Bake, shake or break - and other applications for the FEM Programming project in TMA4220 - part 2 by Kjetil André Johannessen TMA4220 - Numerical solution of partial differential equations using the finite
More informationPLAXIS. Scientific Manual
PLAXIS Scientific Manual 2016 Build 8122 TABLE OF CONTENTS TABLE OF CONTENTS 1 Introduction 5 2 Deformation theory 7 2.1 Basic equations of continuum deformation 7 2.2 Finite element discretisation 8 2.3
More informationMECh300H Introduction to Finite Element Methods. Finite Element Analysis (F.E.A.) of 1-D Problems
MECh300H Introduction to Finite Element Methods Finite Element Analysis (F.E.A.) of -D Problems Historical Background Hrenikoff, 94 frame work method Courant, 943 piecewise polynomial interpolation Turner,
More informationSummary so far. Geological structures Earthquakes and their mechanisms Continuous versus block-like behavior Link with dynamics?
Summary so far Geodetic measurements velocities velocity gradient tensor (spatial derivatives of velocity) Velocity gradient tensor = strain rate (sym.) + rotation rate (antisym.) Strain rate tensor can
More informationA Locking-Free MHM Method for Elasticity
Trabalho apresentado no CNMAC, Gramado - RS, 2016. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics A Locking-Free MHM Method for Elasticity Weslley S. Pereira 1 Frédéric
More informationEDEM DISCRETIZATION (Phase II) Normal Direction Structure Idealization Tangential Direction Pore spring Contact spring SPRING TYPES Inner edge Inner d
Institute of Industrial Science, University of Tokyo Bulletin of ERS, No. 48 (5) A TWO-PHASE SIMPLIFIED COLLAPSE ANALYSIS OF RC BUILDINGS PHASE : SPRING NETWORK PHASE Shanthanu RAJASEKHARAN, Muneyoshi
More informationLecture #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 informationA HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS
A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,
More information1 Nonlinear deformation
NONLINEAR TRUSS 1 Nonlinear deformation When deformation and/or rotation of the truss are large, various strains and stresses can be defined and related by material laws. The material behavior can be expected
More informationStrain analysis.
Strain analysis ecalais@purdue.edu Plates vs. continuum Gordon and Stein, 1991 Most plates are rigid at the until know we have studied a purely discontinuous approach where plates are
More informationElements of Rock Mechanics
Elements of Rock Mechanics Stress and strain Creep Constitutive equation Hooke's law Empirical relations Effects of porosity and fluids Anelasticity and viscoelasticity Reading: Shearer, 3 Stress Consider
More informationA temperature-related homogenization technique and its implementation in the meshfree particle method for nanoscale simulations
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2007; 69:2099 2125 Published online 15 August 2006 in Wiley InterScience (www.interscience.wiley.com)..1841 A temperature-related
More informationModelling of ductile failure in metal forming
Modelling of ductile failure in metal forming H.H. Wisselink, J. Huetink Materials Innovation Institute (M2i) / University of Twente, Enschede, The Netherlands Summary: Damage and fracture are important
More informationThe Stress Variations of Granular Samples in Direct Shear Tests using Discrete Element Method
The Stress Variations of Granular Samples in Direct Shear Tests using Discrete Element Method Hoang Khanh Le 1), *Wen-Chao Huang 2), Yi-De Zeng 3), Jheng-Yu Hsieh 4) and Kun-Che Li 5) 1), 2), 3), 4), 5)
More informationComparative Analysis of Mesh Generators and MIC(0) Preconditioning of FEM Elasticity Systems
Comparative Analysis of Mesh Generators and MIC(0) Preconditioning of FEM Elasticity Systems Nikola Kosturski and Svetozar Margenov Institute for Parallel Processing, Bulgarian Academy of Sciences Abstract.
More informationBasic Equations of Elasticity
A Basic Equations of Elasticity A.1 STRESS The state of stress at any point in a loaded bo is defined completely in terms of the nine components of stress: σ xx,σ yy,σ zz,σ xy,σ yx,σ yz,σ zy,σ zx,andσ
More informationLEAST-SQUARES FINITE ELEMENT MODELS
LEAST-SQUARES FINITE ELEMENT MODELS General idea of the least-squares formulation applied to an abstract boundary-value problem Works of our group Application to Poisson s equation Application to flows
More informationAn Atomistic-based Cohesive Zone Model for Quasi-continua
An Atomistic-based Cohesive Zone Model for Quasi-continua By Xiaowei Zeng and Shaofan Li Department of Civil and Environmental Engineering, University of California, Berkeley, CA94720, USA Extended Abstract
More informationMathematical Background
CHAPTER ONE Mathematical Background This book assumes a background in the fundamentals of solid mechanics and the mechanical behavior of materials, including elasticity, plasticity, and friction. A previous
More informationBAR ELEMENT WITH VARIATION OF CROSS-SECTION FOR GEOMETRIC NON-LINEAR ANALYSIS
Journal of Computational and Applied Mechanics, Vol.., No. 1., (2005), pp. 83 94 BAR ELEMENT WITH VARIATION OF CROSS-SECTION FOR GEOMETRIC NON-LINEAR ANALYSIS Vladimír Kutiš and Justín Murín Department
More informationStructural Analysis of Truss Structures using Stiffness Matrix. Dr. Nasrellah Hassan Ahmed
Structural Analysis of Truss Structures using Stiffness Matrix Dr. Nasrellah Hassan Ahmed FUNDAMENTAL RELATIONSHIPS FOR STRUCTURAL ANALYSIS In general, there are three types of relationships: Equilibrium
More informationFinite Element simulations of a phase-field model for mode-iii fracture. by V. Kaushik
Finite Element simulations of a phase-field model for mode-iii fracture. by V. Kaushik 1 Motivation The motivation behind this model is to understand the underlying physics behind branching of cracks during
More informationCitation Key Engineering Materials, ,
NASITE: Nagasaki Universit's Ac Title Author(s) Interference Analsis between Crack Plate b Bod Force Method Ino, Takuichiro; Ueno, Shohei; Saim Citation Ke Engineering Materials, 577-578, Issue Date 2014
More informationSome improvements of Xfem for cracked domains
Some improvements of Xfem for cracked domains E. Chahine 1, P. Laborde 2, J. Pommier 1, Y. Renard 3 and M. Salaün 4 (1) INSA Toulouse, laboratoire MIP, CNRS UMR 5640, Complexe scientifique de Rangueil,
More informationComputational models of diamond anvil cell compression
UDC 519.6 Computational models of diamond anvil cell compression A. I. Kondrat yev Independent Researcher, 5944 St. Alban Road, Pensacola, Florida 32503, USA Abstract. Diamond anvil cells (DAC) are extensively
More informationMulti-scale digital image correlation of strain localization
Multi-scale digital image correlation of strain localization J. Marty a, J. Réthoré a, A. Combescure a a. Laboratoire de Mécanique des Contacts et des Strcutures, INSA Lyon / UMR CNRS 5259 2 Avenue des
More informationMMJ1153 COMPUTATIONAL METHOD IN SOLID MECHANICS PRELIMINARIES TO FEM
B Course Content: A INTRODUCTION AND OVERVIEW Numerical method and Computer-Aided Engineering; Phsical problems; Mathematical models; Finite element method;. B Elements and nodes, natural coordinates,
More information14. 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 informationFEMxDEM double scale approach with second gradient regularization applied to granular materials modeling
FEMxDEM double scale approach with second gradient regularization applied to granular materials modeling Albert Argilaga Claramunt Stefano Dal Pont Gaël Combe Denis Caillerie Jacques Desrues 16 december
More informationIntroduction to Finite Element Method
Introduction to Finite Element Method Dr. Rakesh K Kapania Aerospace and Ocean Engineering Department Virginia Polytechnic Institute and State University, Blacksburg, VA AOE 524, Vehicle Structures Summer,
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 informationDr. Parveen Lata Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India.
International Journal of Theoretical and Applied Mechanics. ISSN 973-685 Volume 12, Number 3 (217) pp. 435-443 Research India Publications http://www.ripublication.com Linearly Distributed Time Harmonic
More informationPowerful Modelling Techniques in Abaqus to Simulate
Powerful Modelling Techniques in Abaqus to Simulate Necking and Delamination of Laminated Composites D. F. Zhang, K.M. Mao, Md. S. Islam, E. Andreasson, Nasir Mehmood, S. Kao-Walter Email: sharon.kao-walter@bth.se
More informationMechanics of Earthquakes and Faulting
Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Surface and body forces Tensors, Mohr circles. Theoretical strength of materials Defects Stress concentrations Griffith failure
More informationPowder Technology 205 (2011) Contents lists available at ScienceDirect. Powder Technology. journal homepage:
Powder Technology 25 (211) 15 29 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec Numerical simulation of particle breakage of angular particles
More informationUNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich
UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Lecture - 06
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Lecture - 06 In the last lecture, we have seen a boundary value problem, using the formal
More informationMechanics of Earthquakes and Faulting
Mechanics of Earthquakes and Faulting Lectures & 3, 9/31 Aug 017 www.geosc.psu.edu/courses/geosc508 Discussion of Handin, JGR, 1969 and Chapter 1 Scholz, 00. Stress analysis and Mohr Circles Coulomb Failure
More informationFracture 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 informationDEFORMATION AND FRACTURE ANALYSIS OF ELASTIC SOLIDS BASED ON A PARTICLE METHOD
Blucher Mechanical Engineering Proceedings May 2014, vol. 1, num. 1 www.proceedings.blucher.com.br/evento/10wccm DEFORMATION AND FRACTURE ANALYSIS OF ELASTIC SOLIDS BASED ON A PARTICLE METHOD R. A. Amaro
More informationFinite Elements for Elastic Shell Models in
Elastic s in Advisor: Matthias Heinkenschloss Computational and Applied Mathematics Rice University 13 April 2007 Outline Elasticity in Differential Geometry of Shell Geometry and Equations The Plate Model
More informationLattice element method
Lattice element method Vincent Topin, Jean-Yves Delenne and Farhang Radjai Laboratoire de Mécanique et Génie Civil, CNRS - Université Montpellier 2, Place Eugène Bataillon, 34095 Montpellier cedex 05 1
More informationConservation of mass. Continuum Mechanics. Conservation of Momentum. Cauchy s Fundamental Postulate. # f body
Continuum Mechanics We ll stick with the Lagrangian viewpoint for now Let s look at a deformable object World space: points x in the object as we see it Object space (or rest pose): points p in some reference
More informationFLEXIBILITY METHOD FOR INDETERMINATE FRAMES
UNIT - I FLEXIBILITY METHOD FOR INDETERMINATE FRAMES 1. What is meant by indeterminate structures? Structures that do not satisfy the conditions of equilibrium are called indeterminate structure. These
More informationSpectral methods for fuzzy structural dynamics: modal vs direct approach
Spectral methods for fuzzy structural dynamics: modal vs direct approach S Adhikari Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Wales, UK IUTAM Symposium
More informationAnalysis of Blocky Rock Slopes with Finite Element Shear Strength Reduction Analysis
Analysis of Blocky Rock Slopes with Finite Element Shear Strength Reduction Analysis R.E. Hammah, T. Yacoub, B. Corkum & F. Wibowo Rocscience Inc., Toronto, Canada J.H. Curran Department of Civil Engineering
More information