Cohesive Particle Model milauer using the Discrete Element Method - PowerPoint PPT Presentation

Cohesive particle model & Yade Václav Cohesive Particle Model Šmilauer using the Discrete Element Method DEM on the Yade platform CPM Overview Stresses Calibration Yade Introduction Václav Šmilauer Simulation Code Functionality CTU Prague & UJF Grenoble Yade- powered projects 24 June 2010 Past Present

Outline Cohesive 1 Discrete Element Method particle model & Yade 2 Cohesive Particle Model Václav Overview Šmilauer Stresses DEM Calibration CPM Overview 3 Yade Stresses Calibration Introduction Yade Introduction Simulation Simulation Code Code Functionality Functionality Yade- powered projects 4 Yade-powered projects Past Present Past Present

Particle models history Cohesive particle model & Yade Václav in mechanics since 1970 (Cundall, soil Šmilauer mechanics) DEM continuum=particles+contacts, CPM Overview relatively simple contact laws Stresses Calibration suitable for “discontinua” behavior Yade Introduction different flavors of particle methods Simulation Code (DOF number, static/dynamic problem, Functionality Yade- particle type) powered projects Past Present

Classification Cohesive particle model & Yade lattice models (no mass, 3/6 DOFs, Václav Šmilauer spring/beam links between particles; 2D variants) DEM mass-spring (3 DOFs, explicit CPM Overview dynamics) Stresses Calibration DEM (discrete element method) — Yade Introduction particles with 6 DOFs, rigid shape Simulation Code (rigid), inter-particle collisions Functionality Yade- DEM+FEM (“multi-body dynamics”) powered projects — particles are deformable (FEM) and Past collide (DEM) Present

Classification Cohesive particle model & Yade lattice models (no mass, 3/6 DOFs, Václav spring/beam links between particles; 2D Šmilauer variants) DEM mass-spring (3 DOFs, explicit CPM dynamics) Overview Stresses Calibration DEM (discrete element method) — Yade particles with 6 DOFs, rigid shape Introduction Simulation (rigid), inter-particle collisions Code Functionality DEM+FEM (“multi-body dynamics”) Yade- powered — particles are deformable (FEM) and projects Past collide (DEM) Present

Classification Cohesive particle model & Yade lattice models (no mass, 3/6 DOFs, Václav spring/beam links between particles; 2D Šmilauer variants) DEM mass-spring (3 DOFs, explicit CPM dynamics) Overview Stresses Calibration DEM (discrete element method) — Yade particles with 6 DOFs, rigid shape Introduction Simulation (rigid), inter-particle collisions Code Functionality DEM+FEM (“multi-body dynamics”) Yade- powered — particles are deformable (FEM) and projects Past collide (DEM) Present

Classification Cohesive particle model & Yade lattice models (no mass, 3/6 DOFs, Václav spring/beam links between particles; 2D Šmilauer variants) DEM mass-spring (3 DOFs, explicit CPM dynamics) Overview Stresses Calibration DEM (discrete element method) — Yade particles with 6 DOFs, rigid shape Introduction Simulation (rigid), inter-particle collisions Code Functionality DEM+FEM (“multi-body dynamics”) Yade- powered — particles are deformable (FEM) and projects Past collide (DEM) Present

DEM and DEMs Cohesive particle model & Yade smooth Václav Šmilauer collision prediction t – between collisions DEM restitution equations CPM Overview gas dynamics (few contacts) Stresses Calibration non-smooth Yade collision as shape overlaps Introduction Simulation t – a given ∆ t Code Functionality repulsive force, integration of motion Yade- equations powered projects dense packings Past Present

DEM and DEMs Cohesive particle model & Yade smooth Václav Šmilauer collision prediction t – between collisions DEM restitution equations CPM Overview gas dynamics (few contacts) Stresses Calibration non-smooth Yade collision as shape overlaps Introduction Simulation t – a given ∆ t Code Functionality repulsive force, integration of motion Yade- equations powered projects dense packings Past Present

Outline Cohesive 1 Discrete Element Method particle model & Yade 2 Cohesive Particle Model Václav Overview Šmilauer Stresses DEM Calibration CPM Overview 3 Yade Stresses Calibration Introduction Yade Introduction Simulation Simulation Code Code Functionality Functionality Yade- powered projects 4 Yade-powered projects Past Present Past Present

Overview Cohesive particle model & Yade Václav concrete (generally cohesive-frictional materials) Šmilauer contacts have 3 DOFs: normal and shear strains ε N , ε T DEM and stresses σ N , σ T CPM model features: Overview Stresses Calibration tensile damage + visco-damage Yade compressive plasticity Introduction shear plasticity + visco-plasticity Simulation Code Functionality parameters mostly with a physical meaning Yade- powered calibration procedures designed projects Past Present

Normal stress evaluation Cohesive particle model & σ N = [ 1 − ω H ( ε N )] k N ε N + σ Nv ( ˙ ε Nd ) Yade Václav Šmilauer ε N normal strain DEM CPM k N contact normal modulus Overview Stresses ω internal damage variable, ε N > 0 Calibration ω = g ( κ ) , κ = max ε N Yade Introduction ε T g ( κ ) damage evolution function Simulation Code (parameters ε 0 and ε f ) Functionality Yade- σ Nv damage overstress, powered projects ε T evaluated iteratively from Past Present induced damage strain rate ε Nd ( τ d , M d ) ε N < 0 ˙

Normal stress evaluation Cohesive particle model & σ N = [ 1 − ω H ( ε N )] k N ε N + σ Nv ( ˙ ε Nd ) Yade Václav Šmilauer ε N normal strain DEM CPM k N contact normal modulus Overview 3000000 σ N Stresses ω internal damage variable, Calibration 2000000 ω = g ( κ ) , κ = max ε N Yade Introduction 1000000 g ( κ ) damage evolution function Simulation σ N Code (parameters ε 0 and ε f ) Functionality 0 ε 0 ε f Yade- σ Nv damage overstress, powered − 1000000 projects evaluated iteratively from Past − 2000000 − 0.00010 − 0.00005 0.00000 0.00005 0.00010 0.00015 0.00020 0.00025 0.00030 Present ε N induced damage strain rate ε Nd ( τ d , M d ) ˙

Normal stress evaluation Cohesive particle model & σ N = [ 1 − ω H ( ε N )] k N ε N + σ Nv ( ˙ ε Nd ) Yade Václav Šmilauer 1.0 ε N normal strain ω DEM 0.8 CPM k N contact normal modulus 0.6 ω ( ε N ) Overview Stresses 0.4 ω internal damage variable, Calibration 0.2 ω = g ( κ ) , κ = max ε N Yade 0.0 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 Introduction ε N g ( κ ) damage evolution function Simulation Code Functionality (parameters ε 0 and ε f ) Yade- ω = g ( κ ) = σ Nv damage overstress, powered projects � � evaluated iteratively from 1 − ε f − κ − ε 0 Past κ exp Present induced damage strain rate ε f ε Nd ( τ d , M d ) ˙

Normal stress evaluation Cohesive particle σ N = [ 1 − ω H ( ε N )] k N ε N + σ Nv ( ˙ ε Nd ) model & Yade Václav Šmilauer 5000000 ε N τ d = 100 ˙ ε N normal strain DEM ε N τ d = 10 ˙ ε N τ d = 1 ˙ 4000000 CPM ε N τ d = 0.1 ˙ k N contact normal modulus ε N τ d = 0.001 ˙ Overview ε N τ d = 10 − 6 ˙ 3000000 Stresses ε N τ d = 10 − 12 ˙ ω internal damage variable, Calibration σ N Yade 2000000 ω = g ( κ ) , κ = max ε N Introduction Simulation g ( κ ) damage evolution function 1000000 Code Functionality (parameters ε 0 and ε f ) 0 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 Yade- ε N powered σ Nv damage overstress, projects evaluated iteratively from Past Present ε Nd � M d induced damage strain rate σ Nv ( ˙ ε Nd ) = k N ε 0 � τ d ˙ ε Nd ( τ d , M d ) ˙

Shear stress evalution (after σ N ) Cohesive Shear stress, plasticity function, plastic flow rule particle model & Yade σ T = k T ( ε T − ε Tp ) Václav Šmilauer f ( σ N , σ T ) = | σ T | − ( c T 0 ( 1 − ω ) − σ N tan ϕ ) DEM λ σ T ε Tp = ˙ ˙ CPM | σ T | Overview Stresses Calibration Yade × 10 7 3 Introduction linear, ω =0 Simulation linear, ω =1 ˙ ε Tp Code ε Tp ˙ 2 log+lin, ω =0 ± | σ T | σ T2 f = 0 log+lin, ω =1 Functionality 1 Yade- c T0 r pl powered ϕ ± | σ T | 0 projects σ N σ T1 Past − 1 f = 0 Present − 2 − 3 − 3.0 − 2.5 − 2.0 − 1.5 − 1.0 − 0.5 0.0 0.5 σ N × 10 7

Model parameters Cohesive Elastic parameters particle model & Yade moduli k N , k T , interaction radius R I . Václav Šmilauer Plasticity+damage parameters DEM limit elastic strain ε 0 , damage evolution parameter ε f ; friction CPM Overview angle ϕ , cohesion c T 0 . Stresses Calibration Yade Viscosity parameters Introduction Simulation Code characteristic time τ d , exponent M d ; ( τ pl , M pl ) Functionality Yade- powered projects Confinement parameters Past Present hardening strain ε s , hardening modulus ˜ K s , plasticity function parameter Y 0 .