Simulation

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• Simulation

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• Experimental
• Provide useful quantitative information
• Are common as they use real system
• Considerable Time and cost usage (repetition!)
• Numerical simulation (Computer Simulation)
• Virtual systems
• To predict the behaviour of a real system
• More flexible in application
• Micro and Macro scale results at any time

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Experimental Simulation

• In-lab experiment that is as much like some real
  situation as possible.
• Small scale equipment
• Example
• ground-based flight (Pesticide application), Dam,
  rainfall and Silo simulators
• behaves as closely as possible to a real one
• still under researcher control

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Experimental Simulation

• Still fairly precise.
• More realistic than in-lab experiment.
• Not a natural setting interaction may not be
  normal.
• Extrapolation of Results may lead to uncertainty
  and ERRORS

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Computer (Numerical) Simulation

• Creating a complete closed system that models
  the operation of the real system without users.
• Example
• Plant growth simulations (Agronomy researchers)
• Engineering Models
• Continuum Models
• Discrete Element Models

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Continuum approach

• The behaviour of a mechanical system can be
  expressed by differential equations
• Mechanical system is divided into Finite elements
• Derived constitutive equations for elements are
  linked together to solve the problem
• Application for Stress and heat analysis
• Finite Element Method (FEM)
• Boundary Element Method (BEM)

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What is FEM?

• Full name Finite Element Method
• General Concepts
• FEM cuts a structure into several elements of the
  structure
• The nodes at the each end of an element are
  reconnected as if nodes were pins that hold
  elements together
• This results in a set of simultaneous algebraic
  equations

• Applications of FEM
• Desire to understand how various elements
  behave with arbitrary shape, loads, and support
  conditions
• Can be contained within a single computer
  program for users to input data such as geometry,
  boundary conditions, and element selection
• Handle complex restraints, which allow
  indeterminate structures to be solved
• Disadvantages of FEM
• FEM obtains only approximate solutions
• Many input data are required

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Discrete Element Method

• Continuum models based on Continuity
• Increases in computer speed
• Calculation of the position of individual
  particles
• DEM Useful for particulate materials
• Grains, Soil , Powder, Fruits
• Solid systems also can be modelled
• Need good Programming skills

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Main steps of DEM

• Particle and environment generation
• Search for contact
• Contact detection between pairs of discrete
  particles
• Calculation of contact force
• Update particle motion due to unbalanced force
• Circulation

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DEM Development

• Appeared in 1979 by Cundall and Strack
• Shape representation
• Circle (2D)
• Sphere (3D)
• Ellipse (2D)
• Ellipsoid (3D)
• Polygon (2 3D)
• Combined Primitives

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DEM Application

• Geomechanics (Soil rock)
• Granular storage flow (Silo)
• Powder Technology
• Fruits and Vegetable (handling)
• Processing Operation ( ball mills)
• Continuous System BUT composed of individual (
  say particles) in Microscopic level ( Asphalt,
  Biomaterials, solid structures)
• Combined DEM FEM

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DEM Limitations

• Matching Real and Model particle shape
• Not for very large spatial domain where millions
  of particles involved
• Need for physical properties
• Running time concern

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Theoretical aspects

• Contact models between contacting bodies
• Contact area
• Contact point
• Contact vector
• Contact Displacement and deformation
• Normal
• Tangetial

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Contact parameters a) for smooth non-spherical,
convex b) circular particles
Normal (?n) and tangential (?st and ?sr)
displacements for two particles in contact due
to (a) relative translation and (b) relative
rotation of the particles.
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Principle of DEM
The DEM procedure for contact force calculations
and updating the dynamic situation of particles
a) Recognising the formation of contact points
due to relative velocities and position of
particles. b) Application of force-displacement
law for each contact point to calculate the
contact force. c) The moment of contact forces
about the particle centroid is calculated and the
resultant force and moment on particle centroid
is determined. d) Application of Newtons second
law of motion to calculate the particle
acceleration and velocity.
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Contact Models
DEM contact models for cohesionless materials a)
the maximum frictional force based on the sum of
spring and dashpot b) the maximum frictional
force calculated only from spring (elastic) force
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Damping

• Contact Damping
• Fdn Cn . n
• Fds Ct . s
• Global Damping (act on Absolute Velocity
  rotation)

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Time step

• In DEM the time step is the time during which
  force is transmitted from one contact point to
  another along the particle boundary.
• The time step should be as large as possible to
  increase the efficiency of simulation and still
  be smaller than the critical time step to justify
  the assumption of constant acceleration within
  each time step and to ensure stability of the
  calculations
• The idea is based on the assumption that the
  selected time step is small enough so that no new
  contacts take place in the current time step
  except those that have already been recognised at
  the beginning of the time step.

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Contact Detection

• the most important step prior to any mechanical
  calculation is determination of which surfaces
  are in contact and the type of contact.
• It is estimated that more than 80 of the
  computational time can be spent on this task.
• In a very simple approach each particle is
  checked against every other particle to determine
  any probable contact.
• The computational time for this simple procedure
  with n particles will be proportional to , which
  is too long if there are hundreds of particles in
  the simulation

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Contact Detection (cont.)

• For densely pack a link list algorithm
• the simulation space is divided into relatively
  large cells
• A separate list of particles for each cell is
  provided, including the particles in the home
  cell and surrounding cells.
• The particles within a cell and its neighbouring
  cells are considered as potential contacting
  bodies.
• Therefore, contact detection for such list would
  be an efficient process regarding time
  consumption

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Contact Detection (cont.)

• For loosely pack a grid search
• Small cells, so that in each cell one particle
  can be occupied
• Contact detection between particles a) Circular
  shape b) Polygonal shape.

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Calculation cycle

• Simulation steps in DEM a) Particle and
  environment generation, b) Contact search and
  detection, c) Calculation of contact force, d)
  update the particle accelerations.

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visualisation