Particle Flow Code PFC2D3D Basic Training Courseitasca相關(guān)軟件flac－flac3d－pfc－udec等培訓(xùn)資料

1、Particle Flow Code (PFC2D/3D)Basic Training Course Peter Cundall, Yanhui Han & Roger HartItasca Consulting Group, Inc.Itasca Software Training CourseTongji UniversityShanghai, ChinaOctober 27-31, 2008PFC Basic Training CourseTopic 1: PFC Features and Theoretical Basis Features TheoryTopic 2: PFC Tut

2、orial Command summary Simple PFC data files without FISH Set up PFC models in progressively complex mannerTopic 3: FISH description and tutorial FISH description Implement ball-generation algorithm Implement wall-based servo-control Modeling approaches and FishTank modeling approaches material genes

3、is material testing a compression test exampleTopic 1: PFC Features and Theoretical BasisFeaturesTheoryModeling of dynamic behavior of assemblies of arbitrarily-sized particles; particle radii may distribute uniformly or according to a Gaussian distributionProperties are associated with individual p

4、articles, allowing continuous gradations in properties and particle radiiDouble precision storage of particle coordinates and radii ensure long-term freedom from numerical driftPFC2D/3D FeaturesContact physics consists of: linear springs or simplified Hertz-Mindlin law, Coulomb sliding, and contact

5、or parallel bondingClump logic supports creation of groups of slaved particles or clumps; clumps can serve as “super particles” of general shapeAny number of arbitrarily-oriented line segments may be specified as walls, each with its own contact properties; general walls provide geometric objects; a

6、ssemblies are loaded through prescribed wall velocitiesPFC2D/3D FeaturesAutomatic timestep calculation that ensures a stable solutionCell-mapping scheme to ensure that solution time increases linearly with the number of particlesParticles and walls may be added or deleted (and properties changed) at

7、 any time during a simulationTwo types of damping available: local nonviscous and viscousPFC2D/3D FeaturesDensity scaling may be used to increase timestep and optimize solution efficiencyEnergy tracing allows observation of: body work, bond energy, boundary work, frictional work, kinetic energy, str

8、ain energyMeasurements of average stress, strain rate and porosity can be made over any number of specified circular regions PFC2D/3D FeaturesAny quantity may be traced with time and stored and plotted as a historyA quasi-static operating mode is available (in addition to fully dynamic mode) to ensu

9、re rapid convergence to steady state solutionPowerful built-in programming language (FISH) provides full access to internal state variables and allows one to customize analysesPFC2D/3D FeaturesExplicit solution scheme provides a stable solution for unstable physical processes and makes it possible t

10、o simulate the non-linear interaction of a large number of particles without excessive memory requirements or the need for an iterative procedureBuilt-in contact models include: simple viscoelastic model, simple ductile model, and displacement-softening modelPFC2D/3D FeaturesPFC (2D & 3D) models two

11、 types of objects: balls and wallsBalls are disks (3 degrees of freedom) or spheres (6 dof). Also, clumps are arbitrarily shaped groups of rigidly attached balls. The full equations of motion are solved for balls & clumps.Walls are surfaces that can interact with balls (but not with other walls), an

12、d can be planar polygons or special shapes: spiral, cylinder. Walls may move with user-specified velocities or spins, or by programmed function.The interactions between objects (ball-ball or ball-wall) can be any force/displacement law e.g., linear, Hertzian (nonlinear), hysteretic, viscous, brittle

13、-bonded, ductile-bonded, etc.PFC2D/3D TheoryContacts visualization & notationBall-ball contactBall-wall contactPFC2D/3D TheoryUnit normal vector -Distance between centroids -Overlap -The normal force is derived directly from the overlap:However, the shear force is derived incrementally:where the inc

14、remental shear displacement is:based on the relative shear velocity vector:PFC2D/3D Theory where the relative velocity vector at the contact is given by:using the following notation: Finally, the shear force is derived:And the particle forces and moments are obtained from the total contact force vec

15、tor, given by -Shear force vector corrected by contact spinPFC2D/3D TheoryContact formulations:The previous development assumed a linear spring model at contact points:(normal)(shear)This default model also allows slip, due to friction:IfthenIn addition, there are a number of other models, both buil

16、t-in and user-defined.The Hertz-Mindlin model is a nonlinear model derived from the analysis of contact between two elastic spheres:Normal secant stiffnessShear tangent stiffnessPFC2D/3D TheoryThere are two built-in bonding models: the contact-bond and the parallel-bond. Contact-bond behavior is ill

17、ustrated as follows.Normal directionShear directionThe contact bond is either intact or broken. It may be broken by either the shear or the normal strength being exceeded. If broken, the contact reverts to unbonded behavior (e.g., slip is possible).PFC2D/3D TheoryContact bonds simply associate a str

18、ength limit to shear and normal contact forces. No moment is generated.Parallel bonds assume that bonding is over a finite area of contact, so that moments may be generated in response to twisting and bending.Direct forcesMomentsPFC2D/3D TheoryThe parallel-bond forces act in parallel with the regula

19、r contact forces (described earlier), providing extra contact stiffness.Maximum fiber stresses are calculated, and the bond broken if any stress component exceeds the corresponding strength.PFC also allows user-defined contact models. These are compiled as DLLs (dynamic link libraries) and loaded in

20、to PFC as needed.Examples of user-defined models are provided with PFC e.g., a visco-elastic model and a general softening model PFC2D/3D TheoryThe general softening model provides ductile post-peak behavior, rather than the brittle behavior of the default bonding models.ForceDisplacementA single yi

21、eld condition combines both shear and normal yield (rather than separate conditions, for the default models) PFC2D/3D TheoryShear forceNormal forceThe yield envelope “softens” (contracts) as a function of plastic (irreversible) displacement: using an associated flow rule:PFC2D/3D TheoryDamping formu

22、lations:PFC may be used to simulate either static or dynamic systems. Further, there are several distinct classes of problems (e.g., impact; free-flight; flow; compact solid). Thus, several forms of damping are available.1.Default, “l(fā)ocal” damping good for general static solution of compact assembli

23、es.2.Viscous contact damping for systems in which many particles are in free flight, and then form stable assemblies.3.Hysteretic contact damping good for modeling impact of fragments, but not prolonged contact.PFC2D/3D Theorylocal damping:Velocity-proportional damping introduces body forces that ca

24、n affect the solution.Local damping is the default damping in PFC.The damping force at a ball is proportional to the magnitude of the unbalanced force with the sign set to ensure that vibrational modes are damped.PFC2D/3D TheoryDamping forces are introduced to the equations of motion:diiituFFmwhere

25、is the unbalanced force. iF sgndiiiFFu The damping force isThe unbalanced force ratio (average unbalanced force over average contact force) can be monitored to check for static equilibrium.When this ratio is less than a small value, then the model is considered to be in static equilibrium. (See the

26、SOLVE command.)local damping:PFC2D/3D TheorydiiituFFm sgndiiiFFu Two main fields of application:PFC has been applied in two main fields -1.Simulation of deformation and flow of granular material2.Fracture of brittle elastic solidsIn both of these cases the “synthetic material” (consisting of an asse

27、mbly of particles) must be calibrated by performing simulated laboratory tests.PFC2D/3D TheoryCalibration:Normally, tests are performed to match the following properties for real materials before performing full simulations:1.Elastic moduli and Poissons ratio2.Peak strengthOptionally, the following

28、properties may be matched:1.Softening slope2.Residual strength3.Fracture toughness (for a brittle solid)4.Crack initiation stress (for a brittle solid)PFC2D/3D TheoryBrittle solids relation of PFC model to LEFM conceptsThe relation of a numerical particle model to the behavior and properties of a gr

29、anular material are well-documented.However, the use of bonded-particle assemblies to represent brittle solids has hardly been justified theoretically in the literature.A theoretical link between micro-properties and LEFM mechanisms and properties (fracture toughness) is derived, as follows PFC2D/3D

30、 TheoryConclusion:PFC is a useful tool for modeling material with micro-structure. Many mechanisms evolve naturally in the PFC model, compared to a continuum model, in which each effect must be pre-programmed.A particle model of soil, rock and concrete exhibits emergent properties i.e., the macro be

31、havior is more complicated than the micro behavior, and new mechanisms emerge.PFC2D/3D TheoryTopic 2: PFC TutorialCommand summarySimple PFC data files without FISHSet up PFC models in progressively complex mannerCommand Summary (1)Command Summary (2)Command Summary (3)Command Summary (4)RANGE logic

32、(1)RANGE logic (2) Built-in range elements: annulus, circle, line, segment, x, y color, id, radius jset group FISH range elements via user-defined FISH functionHistory logic samples and stores specified model variables during a run built-in variables - e.g., ball position, velocity FISH variables -

33、e.g., detonation pressure history variables can then be plotted versus step number or versus other history variables all history variables are sampled at a single sampling interval - e.g., every 20 stepsPlotting logic Supports interactive viewing and hardcopy Multiple “views” can be defined Each vie

34、w contains a list of “plot-items” Most plot-items are modified by switches color, id, shade, . . .Measurement logic Supports automatic computation of certain quantities over circular/spherical regions (measurement circles or measurement spheres) Measured quantities include: coordination number poros

35、ity sliding fraction stress strain rateFire up the electronic manualTheory & Back., Section 3.4Two Ball CollidingPFC2D 3.1014:49:51 Mon Sep 22 2008View Size: X: -6.650e-001 2.965e+000 Y: -1.693e+000 2.493e+000BallCForce ChainsCompressionTension * All Values ZeroVelocity Maximum = 1.000e+000 Linestyl

36、eSingle Ball FallingPFC2D 3.1021:41:07 Mon Sep 22 2008View Size: X: -1.000e-001 2.100e+000 Y: -5.187e-001 2.019e+000BallVelocity * All Values ZeroWallCForce ChainsCompressionTension * All Values ZeroHistoryx1020 1.0000000 1.0000001 1.0000002 1.0000003 1.0000004 1.0000005 1.0000006 1.0000007 1.000000

37、8 1.0000009 1.0000010 x1020 10 Ball 5 Y-Position Linestyle 1.000e+020 -1.000e+020 Vs. 3 p2_time (FISH Function) 1.000e+020 -1.000e+020Single Ball Sliding Along Convex CornerPFC2D 3.1021:43:15 Mon Sep 22 2008View Size: X: -1.500e-001 3.150e+000 Y: -1.903e+000 1.903e+000BallVelocity * All Values ZeroW

38、allCForce ChainsCompressionTension * All Values ZeroSingle Ball Sliding Into Concave CornerPFC2D 3.1021:45:18 Mon Sep 22 2008View Size: X: -1.500e-001 3.150e+000 Y: -1.553e+000 2.253e+000BallVelocity Maximum = 0.000e+000 Scale to Max = 7.000e-001 LinestyleWallCForce ChainsCompressionTension Maximum

39、= 0.000e+000 Scale to Max = 3.000e+00320 Balls Falling into BoxPFC2D 3.1021:48:37 Mon Sep 22 2008View Size: X: -1.000e-001 2.100e+000 Y: -2.687e-001 2.269e+000BallWallTight Packing of 20 BallsPFC2D 3.10Job Title: Tight pack of 20 balls into 4-sided box (no gravity).View Title: Balls, walls, contact

40、forces, velocities.Step 1461 21:50:42 Mon Sep 22 2008View Size: X: -1.036e-001 2.175e+000 Y: -2.266e-001 2.185e+000BallVelocity Maximum = 2.563e-013 LinestyleWallCForce ChainsCompressionTension Maximum = 2.492e+006Simple Biaxial TestPFC2D 3.10Job Title: Tight pack of 20 balls into 4-sided box (no gr

41、avity).View Title: Evolution of mean contact force & mean unbal. forceStep 2000 21:52:35 Mon Sep 22 2008History 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 x103 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5x106 10 Mean Contact Force Linestyle 1.168e+006 4.513e+006 11 Mean Unbalanced Force Linestyle 0.000e+000

42、 3.895e+006 Vs. Step 1.000e+000 2.000e+003Add Contact or Parallel BondsPFC2D 3.10Job Title: Tight pack of 20 balls into 4-sided box (no gravity).View Title: Balls, walls, contact forces, velocities.Step 2000 21:55:34 Mon Sep 22 2008View Size: X: -1.036e-001 2.175e+000 Y: -2.266e-001 2.185e+000BallVe

43、locity Maximum = 2.317e-013 LinestyleWallCForce ChainsCompressionTension Maximum = 2.492e+006Contact BondsTopic 3: FISH description and tutorialFISH descriptionImplement ball-generation algorithmImplement wall-based servo-controlIntroduce FishTankmaterial genesismaterial testingcompression testing e

44、xampleFISH Description FISH (FLAC-ish) is a built-in programming language for Itasca softwareFISH Description FISH (FLAC-ish) is a built-in programming language for Itasca software functions are entered via a data file and are compiled into a list of instructions stored in the codes memory space var

45、iables are global and are available for monitoring or changing at any time (via the SET command) dynamically typed (integer, float, string, pointer, array) typical uses of FISH include: define a new command define a new range element, history variable or plot item control a series of runs modify the

46、 solution procedure (function is called at every timestep)see next slide for exampleFISH Description Here is a FISH function to delete all particles within a given circle:part of a data filedef make_circle bp = ball_head loop while bp # null next_ball = b_next(bp) dist = sqrt( (b_x(bp) - xcen)2 + (b

47、_y(bp) - ycen)2 ) if dist (rad + b_rad(bp) then ii = b_delete(bp) end_if bp = next_ball end_loopendSET xcen=5.0, ycen=5.0, rad=2.1make_circledefine new functionset parametersuse new functionFISH Description Control Statements DEFINE function body END CASEOF . . . END_CASE IF . . . ELSE . . . END_IF

48、LOOP . . . END_LOOP LOOP WHILE . . . END_LOOP SECTION . . . END_SECTION EXIT and EXIT SECTIONFISH Ref., Sec. 2.3.2FISH Description PFC Linkages FISH variables may be printed or set from the PFC command line via the PRINT & SET commands PFC commands may be executed from within a FISH function by encl

49、osing them within COMMAND . . . END_COMMAND a FISH symbol may be substituted anywhere in a PFC command where a number is expected - e.g., PROPERTY kn = ball_stiff FISH functions may be called from several places within the calculation cycle and when particular events occur during execution via FISHC

50、ALLsFISH Ref., Sec. 2.4FISH Description Predefined Variables and Functions intrinsic functions mathematical & utility functions table functions memory-access functions plotting functions input-output functions PFC-specific functions support and standard functions (e.g., linked-list headers) ball fun

51、ctions contact functions wall (& wall-segment) functions parallel-bond functions measurement-circle functions clump functionsFISH Ref., Sec. 2.5ball_headb_nextb_xb_id (15). . . . .b_nextb_xb_id (14). . . . .b_nextb_xb_id (13). . . . .nullb_nextb_xb_id (12). . . . .Traversing Contacts Around a Ball T

52、raversing Contacts Around a Ball Example 2.11 Controlling a series of PFC2D runs (fishr12.dat)Ball-generation algorithmGenerate a collection of particles of a uniform size distribution with radii in the range that fill a given area, A, at a given porosity, n.minmax,RRCompute:minmax21,2AnRRNRRGENERAT

53、E N balls at half their final size.Compute porosity, , of generated assembly.0nMultiply all ball radii by factor01.1nmnsee 3.8.3 in FISH in PFC2DBall-generation algorithmPFC2D 3.10Job Title: bg: Example of ball-generation procedure11:29:48 Tue Sep 23 2008View Size: X: -9.847e-001 3.985e+000 Y: -2.50

54、0e-001 5.250e+000WallBallCForce ChainsCompressionTension * All Values ZeroPFC2D 3.10Job Title: bg: Example of ball-generation procedure11:30:27 Tue Sep 23 2008View Size: X: -1.004e+000 4.047e+000 Y: -3.342e-001 5.255e+000WallBallCForce ChainsCompressionTension * All Values ZeroBall-generation proces

55、s (bg.dvr)generate the confining wall generate particles at half of their final sizes (no particle overlap)compute current void ratio n0expand the particles by m = sqrt(n/n0)Solve/step to equilibriumPFC2D 3.10Job Title: bg: Example of ball-generation procedureStep 1004 12:06:38 Tue Sep 23 2008View S

56、ize: X: -1.004e+000 4.047e+000 Y: -3.342e-001 5.255e+000WallBallCForce ChainsCompressionTension Maximum = 2.619e+006Simple wall-based servo-controlImplement a wall-servo (bg1.dvr)include operations in bg.dvrmodify velocity of a wall so as to maintain an average of wall stressactivate servo function

57、from FISHCALL, every stepkeep adjusting vertical velocity of the top wall in the process of running the system into equilibrium (servo control)PFC2D 3.10Job Title: bg: Example of ball-generation procedureStep 1000 13:52:28 Tue Sep 23 2008History 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 x103 1.0 1.5 2

58、.0 2.5 3.0 3.5 4.0 4.5x106 100 ws_wstr (FISH Function) Linestyle 5.808e+005 4.705e+006 Vs. Step 1.000e+001 1.000e+003Direct and Indirect Modeling Approaches Rock is a brittle heterogeneous material that exhibits inelastic deformation because of the existence and formation of numerous micro-cracks. U

59、nder increasing load, these micro-cracks coalesce into macro-cracks, or fractures. The approaches for modeling this inelastic deformation and fracture can be classified into two categories, depending on whether damage is represented indirectly via its effect on constitutive relations, or directly by

60、 the formation and tracking of a large number of micro-cracks.Direct and Indirect Modeling ApproachesMost indirect modeling approachesidealize the material as a continuumutilize average measures of material degradation in constitutive relations to represent irreversible micro-structural damagesrelat