Constitutive model development for granular and porous materials and modelling of particulate processes Csaba Sinka ics4@le.ac.uk Department of Engineering Mechanics of Materials Group Geophysics modelling meeting Leicester 27 May 2015
Area of research Relevance to geophysical modelling Discrete Element Modelling (DEM) coupled with Computational Fluid Mechanics (CFD) and Population Balance Modelling (PBM) Constitutive model development for granular and porous materials and implementation into finite element codes (FEA). Features: Large deformation with state evolution Coupled problems (stress, temperature, diffusion, fluid flow, chemical reaction) Swelling (polymers) Fracture and damage Currently main supervisor of 8 PhD projects The DEM-CFD-PBM models are used for: dense and dilute powder flow modelling in air particulate materials handling and processing relevant to volcano eruptions, avalanches and pyroclastic flows The continuum models are similar to constitutive models used in rock and soil mechanics: Cam-Clay, Mohr-Coulomb, Drucker-Prager cap Relevant to groundwater flow, oil well stimulation and reservoir modelling, coalbed methane, CO 2 sequestration, mudslides, etc. http://climate.blog.co.uk/2009/12/18/45-global-dimming-7596401/ Accessed 06/06/2015 http://www.kgs.ku.edu/publications/pic/pic32.html Accessed 06/06/2015
A numerical investigation into particle interactions and transformations using coupled DEM-CFD-PBM modelling PhD student: Hasan Elmsahli Computational Fluid Dynamics (CFD) OpenFOAM Discrete Element Method (DEM) LIGGGHTS Population Balance Modelling (PBM) DEM computes the particles motions and interactions CFD solver calculates the volume fraction and momentum exchange Start Transfer drag force data into DEM solver Agglomeration and particles breakage New collision and particles properties Update the state of the system PBM predicts the new particles size distribution
Modelling of solid-solid and air-solid interactions for particulate handling and processing PhD student: Abdulrahman Alharbi Normal contact force (KN) Normal contact force (KN) 0 43 76 105 132 157 182 206 229 252 274 Programming DEM Start Validation of contact laws against the Hertz analytical solution Create boundary Generate particles (radius, mass, initial positions, orientations and velocities) n o Calculate external forces, incl. gravity Contact? yes Calculate contact forces F net = F 1 + F 2 + F 3 + F 4 + F 5 +.. F 1 = Gravity F 2 = Contact law (Hertz, JKR, DMT) F 3 = Friction force F 4 = Drag force F 5 = Other forces can be included Loop 12 10 8 6 4 2 0 force-time curve numerical solution(matlab) analytical solution 0 10 20 30 40 Time (µsec) 12 10 8 6 4 2 0 force-displacment curve numerical solution( matlab) analytical solution Normal contact displacment (µm) Integrate the equation of motion to calculate the new positions, velocities and orientations (Newton's second law ) DEM analysis of spheronisation (using open source DEM software) Time increment: t = t + dt
Powder flow in air and vacuum PhD student: Reza Baserinia Dimensional model development for powder flow initiation and flow rate Linear shoe-die system with pressure measurement in the die Powder container Loading funnel Powder conditioning device Vacuum chamber Critical orifice diameter measurement Effect of shoe velocity and air pressure in the die on mass of powder introduced is investigated m ρ b D 2 L = c H D a v s P ρ b g 1.5 D 1.5 n Shoe Pressure transducer ports Die Punch Effect of vacuum pressure on flow rate through orifices of different size is studied m ρ b g 0.5 = c P D2.5 ρ b gd n The effect of air pressure conditions on flow initiation from an arching state is investigated. P ρ b gd = c H D n Lab scale rotary powder feeder into controlled low pressure environment Exit diameters 5, 10 and 15 mm Paddle shapes * c and n are empirical material constants
Constitutive model development, implementation and application to pharmaceutical tablet compaction Powder in Tablet out Rotary tablet press Tablet geometry Pressing sequence State after die fill Tablet strength Constitutive Model Temperature Finite Element Analysis of tablet compaction Solving equations: Equilibrium Compatibility Constitutive Bilayer tablets Friction Applications Tool design
Stress, MPa Numerical constitutive laws for powder compaction PhD student: Lida Che Primary particle properties + Packing arrangement (X-ray CT reconstruction) + Multi-particle finite element analysis (MPFEM) = Numerical constitutive law 120 100 Experiment 80 MPFEM 60 40 20 0 750 950 1150 1350 1550 Density, kg m -3
Understanding densification and crack propagation in pharmaceutical tablet manufacturing PhD student: Peter Polak F w Empirical data set 1 Criterion 1 t t Criterion 3 Criterion 2 From: Shang C., Sinka I.C. and Pan J., 2013. Modelling of the break force of tablets under diametrical compression. International Journal of Pharmaceutics. Vol. 445, Issues 1 2, pp. 99-107. Empirical data set 2
Influence of contact strength between particles on the constitutive law for powder compaction PhD student: Muhanad Al-Sabbagh Particle Properties Size, Shape, Material Interaction Properties Friction, Adhesion Contact Constitutive Law Compaction Constitutive Law (Includes Explicitly the Contact Constitutive Law) Implementation into FEM 1.5 1 0.5 0 Σ/P y -0.5-1 -1.5-2 -1 0 1 2 Σm/P y Case Studies (Isostatic Compaction and Closed-die Compaction) Yield surfaces using a cohesion parameter using the Fleck model (Fleck N. 1995. On the cold compaction of powders. Journal of the Mechanics and Physics of Solids 43, 1409-1431) Σ deviatoric stress Σ m mean stress P Y macroscopic yield pressure
Swelling and disintegration of multi-component polymeric structures PhD student: Amnani Binti Shamjuddin Drug Rubbery region Glassy core region S1 S2 *S1 Glassy/Rubbery interface *S2 Polymer/Solvent interface S2 S1 S1 Swelling - controlled release drug delivery 1. Glassy hydrogel 2. Swollen hydrogel 3. Diminished 4. Drug in glassy core hydrogel region is completely dissolved This figure was adapted from Hsieh, M. H., & Faculty, E. (2012). PhD Thesis. Mathematical modelling of controlled drug release from polymer microspheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems. Queensland University of Technology. Unswollen disintegrant particles Swollen disintegrant particles Stress concentrated area Large deformation Diffusion Reaction/degradation Disintegration - immediate release system Dry dosage form Hydrated dosage form 1. 2. 3. 4. Weakened structure Disintegrating dosage form This figure was adapted from Omidian, H., & Park, K. (2008). Swelling agents and devices in oral drug delivery. Journal of Drug Delivery Science and Technology, 18(2), 83 93.