Research Activities
Research activities in CERECAM are organised into a number of research programmes which range from those of a fundamental nature to projects having a direct link to industrial and other applications.
The research activities are arranged into six broad groupings:
A. Computational solid, structural and particulate mechanics
B. Numerical analysis and partial differential equations
C. Biomechanics
D. Fluid dynamics
E. Particulate flow characterization in industrial and biological systems
F. Computational electromagnetics
Details of activities during 2011 follow.
A. Computational solid, structural and particulate mechanics
Strain gradient plasticity
Team members: BD Reddy (project leader), F Ebobisse, AT McBride
Collaborators: S Bargmann (Technische Universität Dortmund), ME Gurtin (Carnegie-Mellon University), P Neff (Technische Universität Darmstadt), C Wieners (Karlsruhe Institute of Technology), BI Wohlmuth (Technische Universität München)
Students: N Richardson (MSc, in progress)
The constitutive relations of classical plasticity do not possess a natural length scale, and are therefore unable to account for size effects.
Gradient theories represent a popular and well-established extension in which physically relevant length scales are able to be introduced.
Current work is devoted to problems of single- and polycrystal plasticity.
One focus has been on the development of variational formulations, where the role of particular choices of defect energy and of dissipation functions has been investigated.
Computational work has been concerned with the development and implementation of finite element approximations for viscoplastic crystal problems involving large deformations, and in which both energetic and dissipative microstresses are present.
Both single crystals and ensembles of crystal grains are considered.
A further area of activity has been in the analysis and implementation of semi-smooth Newton approximations for the problem of rate-independent single-crystal plasticity.
Analysis of heterogeneous deformation and size-scale effects in micro- and nano-scale structures
Team members: S Skatulla (project leader), BD Reddy
Collaborators: C Sansour (University of Nottingham)
Classical theories of deformation do not provide the means to describe non-locality and size-scale effects of small structures which can be readily observed in experiments.
In particular, scale effects are relevant when the specimen or structures dimensions themselves are on the micron and submicron scale but also when it comes to high strain concentrations as in the case of localised shear bands or at crack tips etc.
In this context so-called generalized continuum formulations have been proven to provide remedy as they allow for the incorporation of internal length scale parameters which reflect the micro- structural influence to the macroscopic material response.
In this project a generalized continuum framework is adopted which introduces additional degrees of freedom which constitute a so-called micromorphic deformation.
Based on this generalized deformation description new strain and stress measures are defined which lead to the formulation of a corresponding generalized variational principle.
The theory aims to study the physical characteristics and mechanical performance of size dependent deformation of nano-laminate metallic structures, composite nano-wires, thin films and nano-particulate composites, for use in micromechanical systems, microelectronics, and medical devices.
Modelling of natural fibre-reinforced composites
Team members: BD Reddy, AT McBride
Collaborators: HC Bowles (FEAS)
Students graduated: H Morrissey (MSc (Eng))
The aim of this project is to model the behaviour of natural fibre-reinforced composites, and to use these models in simulations of structural components.
The project is in collaboration with the Council for Scientific and Industrial Research (CSIR) and forms part of an overarching project Natfibio: Development of a natural fibre/bio-composite cabin interior component, sponsored jointly by Airbus, the Department of Science and Technology, and the Advanced Manufacturing Technology Strategy.
The objective is to design composites for use as interior components in aircraft.
A multiscale methodology has been adopted.
Current work is concerned with the identification of a suitable representative volume element, using information such as scanning electron microscope images of the non-woven fibres.
The model will be validated using experimental data obtained by the CSIR.
As a route toward increasing the recyclability of interior componentry in aeroplanes, natural fibres are being introduced as reinforcement in composite materials.
The aim in this paper is to develop and implement numerically a model of the natural fibre-reinforced composite, within a linear-elastic, small-strain context.
Challenges include the identification of a suitable representative volume element and the choice of appropriate boundary conditions at the micro-scale.
The methodology is tested on multiple samples and, as such, a statistical analysis is used to analyse the results, which show relatively smooth histograms and believable trends with increasing fibre-volume fraction.
Impact dynamics
Team members: GN Nurick (project leader), T Cloete
Activities in this area are concerned with the understanding of the physics and mechanics of material properties at high strain rates in order to develop constitutive equations for implementation in predictive analyses.
Currently this work centres around both experimental and analytical techniques and is focused on structures subjected to blast loads, crashworthiness and comminution.
Applications of this research are in the industrial field where vessels are operated at large pressures, in scenarios where there is a threat of a blast as a result of a fire, in design of passenger and cargo vehicles, and in the mining industry.
Activities in impact dynamics are lead by Professor GN Nurick, who in 2003 established the Blast Impact and Survivability Research Unit (BISRU) at UCT.
There is a close relationship between CERECAM and BISRU, and Professor Nurick and Mr Cloete remain associate members of CERECAM.
Research activities that fall under the auspices of BISRU are reported separately (see also
www.bisru.uct.ac.za).
Fracture mechanics
Project leader: R B Tait (project leader), S Skatulla
Students: K Rosie (MSc (Eng)), S Goqo (MSc)
In the design of many engineering components subjected to cyclic or repetitive loading, fatigue is an ever-present challenge.
The engineer often endeavours to design the structural or component system in such a way that the cyclic stresses are below a particular fatigue limit, or in fracture mechanics terms, at stress levels below threshold. In the Paris formulation, the fatigue threshold may be regarded as that value of cyclic stress intensity below which fatigue crack growth does not occur.
For a particular material and environment this threshold value is determined experimentally by monitoring growth of a crack (typically in a compact tension specimen) and continually reducing cyclic stress levels until the threshold condition is reached.
Alternatively, a fracture mechanics specimen can be designed in which there is a decreasing stress intensity (with crack length) that facilitates determination of the threshold value simply at constant applied cyclic amplitude, and the crack length at which fatigue crack growth arrests.
Numerical methods provide a useful and cost-effective way to design such a specimen for easy experimental work and assist in the fatigue design of components and structures.
Numerical analysis can be used to overcome the cost and the amount of time spent on experimental work.
Such analysis is implemented here, where a very promising specimen has been designed using the conventional and extended finite element methods.
The dynamical modelling of fracture propagation results using XFEM allows further understanding of design and assessment of this particular specimen.
Experimental testing is soon to be undertaken, to assess and vindicate the fatigue performance.
Ice sheet modeling and data assimilation
Team members: JV Johnson (project leader), BD Reddy
Current work is concerned with the development of an ice sheet model capable of combining the best available observations with detailed physical descriptions of the ice.
Once observations have been 'assimilated', the model can be used to assess the impact of climate change on the ice sheet's stability.
Ultimately, the purpose of models like this is to determine the amount of sea level change that ice sheets will produce.
Breakage and wear within comminution devices
Team members: A Mainza (project leader), I Govender
Collaborators: M Powell (University of Queensland)
The objective of the comminution process is to reduce the size of ore by several orders of magnitude so that downstream operation can liberate the valuable minerals.
This process is generally performed by crushers or mills and is notoriously inefficient and hard to optimise.
The purpose of this project is to use numerical tools, such as the discrete element method, to determine the energy that the comminution devices transfer to the ore and from that attempt to predict breakage.
The wear of the comminution device is also modelled.
Experimental testing is performed in order to characterise the breakage process.
B. Numerical analysis and partial differential equations
Development, analysis and implementation of new finite elements
Team members: BD Reddy (project leader)
Collaborators: BP Lamichhane (Australian National University), AT McBride (Universität Erlangen-Nuernberg)
Students: A Chama (PhD), B Grieshaber (PhD)
Research in this area has been directed towards the development, analysis and implementation of new low-order finite elements that are simple but stable and efficient, particularly in situations involving small parameters such as those that arise in situations of near incompressibility, and for thin domains in which one or more dimensions are much smaller than the others.
The focus has been first to undertake detailed analyses and to generate novel approaches, largely within the context of mixed and discontinuous Galerkin formulations.
Earlier work, which was based on the use of low-order quadrilaterals, has been extended to broader families of elements.
Stokes-stable pairs are an essential feature of the three-field theory, and well-known examples of these pairs have been used as the base on which to build a wide range of stable elements for three-field formulations.
Related work has been carried out on the discontinuous Galerkin method, where the aim has been to generate new families of elements by exploiting features of the mixed formulation.
Work has also continued on smoothed particle hydrodynamics (SPH), with a view to gaining a better understanding of the convergence properties of SPH interpolations.
Piezoelectric viscoelastic materials with frictional contact
Team members: OP Layeni (project leader)
This project is concerned with the question of solvability of piezoelectric viscoelastic materials in dynamic and quasi-static frictional (bi or) uni-lateral contact.
Consistent with this is the study of existence of solutions to certain types of evolution variational inequalities or differential inclusions, under certain assumptions on the constitutive and 'friction' operators.
The existence of traveling wave(s) generated from these possibly non-smooth mechanical systems is being studied.
Further, we determine the conditions under which, if possible, these present with global bifurcation.
Moving boundary problems
Team members: OP Layeni (project leader)
Collaborators: JV Johnson, A Adegoke (Obafemi Awolowo University, Ile-Ife, Nigeria)
This investigation involves the development of new simple and highly accurate semi-analytical heat integral balance methods for the solution of moving boundary problems, especially multi-phase Stefan problems.
Consequently, the development and qualitative properties of novel finite difference schemes for moving boundary problems are being examined.
Efficient shock-capturing schemes for equations of fluid dynamics
Team members: AR Appadu (project leader), BD Reddy
In computational fluid dynamics, many problems involve shocks.
When used to solve these problems, high order schemes give rise to non-physical oscillations while first-order schemes being dissipative cause damping, close to these regions of sharp gradients. Several numerical algorithms have been developed to obtain better shock-capturing methods like composite methods, artificial viscosity added to a high order method, Weighted Essentially Non Oscillatory methods and high order methods adapted with limiters.
The shock capturing property of a numerical scheme depends on the physical parameters of the method, for instance the cfl number.
An optimization technique has been developed which enables better control over the grade and balance of oscillation and dissipation to optimize parameters for a given numerical method.
Based on numerical experiments carried out in 1-D, 2-D and 3-D, it has been shown that the technique is efficient.
Future work involves the use of this technique in the construction of high-order schemes with low dispersive and low dissipative properties, especially suited for computational aeroacoustics applications, numerical seismic modeling and mathematical morphology.
C. Biomechanics
Myocardial infarction and heart failure
Team member: T Franz (project leader), BD Reddy, S Skatulla
Collaborators: N Davies, J Kortsmit (Cardiovascular Research Unit, UCT)
Students: MS Sirry (PhD), F Masithulela (PhD), R Miller (MSc(Med)), D Dollery (BSc(Eng)), G Abed (BSc(Eng))
Cardiovascular diseases (CVD) will become the leading cause of death by 2020 superseding infectious diseases such as HIV, TB, and Malaria.
The risk of CVD has been reported to increase with the improvement of economic wealth and social environment, in particular in Africa.
A higher risk for acute myocardial infarction, the leading causes of Congestive Heart Failure, has been reported in the black African group in Sub-Saharan Africa due to an increased level of hypertension.
Similarly, the American Heart Association expects in the near future a dramatic increase in CVD incidences in Africa, in particular in the younger population, in conjunction with the emergence of a new epidemic of obesity, diabetes and uncontrolled hypertension.
Up to one third of infarct patients develop heart failure making myocardial infarct the most common cause of heart failure. T
he fact that 30-40% of patients die from heart failure within the first year after diagnosis, even with optimal modern treatment, indicates the urgent need for alternative therapies.
The aim of this collaborative research project, which is sponsored by the national Centre for High Performance Computing, is the development and utilisation of high performance computing (HPC) tools to study the biomechanics of myocardial infarction (MI) and emerging MI therapies based on bio-material injection into the infarct.
The presented problem is highly complex, including the representation of the architecture of cardiac soft tissue with dispersed biomaterial at micro if not nano scale, the highly non-linear elastic myocardial mechanics, and the electro-sensitivity of the myocardial muscle.
Comprehensive treatment exceeds conventional computing resources in terms of problem size and complexity of the developed codes to capture the physical phenomena with sufficient accuracy.
HPC will form an imperative platform for this research towards the advancement of MI therapies and prevention of heart failure.
Arterio-venous Access for Haemodialysis
Team member: T Franz (project leader), BD Reddy,
Collaborators: C Meyer (University of Stellenbosch), D Kahn (Department of Surgery, UCT), B Spottiswoode (Department of Human Biology, UCT)
Students: W Guess (BSc(Eng)), MN Ngoepe
Hemodialysis requires the creation of an arterio-venous (AV) vascular access in patients with end-stage kidney disease.
Such access, connecting an artery to a vein for example at the elbow, is one of the most radical inventions on the vascular system.
The arterio-venous connection results in a flow rate increase of 5-10 times the normal values of flow, including higher pressure and flow in the vein.
The AV connection can be established either with a fistula, directly anastomosing artery and vein, or with a graft (typically synthetic).
Unfortunately, more than half of the AV grafts fail and require surgical reconstruction within three years.
The majority of these graft failures are caused by a narrowing of the anastomoses, i.e. junctions between graft and artery and vein, respectively, and of the vein downstream of the graft.
Because the use of AV grafts for hemodialysis access is expected to rise, there is significant interest in finding treatments that prevent or reduce these problems.
The objective of this research is the numerical investigation of fluid dynamics and structural deformation in anastomotic regions of an arterio-venous access graft towards the assessment of anastomotic configuration.
Numerical models (FEM and CFD) are used to represent the peri-anastomotic regions of an arterio-venous access graft.
The blood flow through the anastomotic region during haemodialysis is simulated.
Developing and applying a customized fluid-structure interaction (FSI) algorithm will capture the interactions between the blood flow and the graft structure.
The comparison of flow fields, wall shear stresses, and structural mechanics for various anastomotic geometries will provide data for assessment and optimization of anastomotic geometries.
Biomechanics of the upper airway
Team members: BD Reddy (project leader), I Govender
Collaborator: Y Saman
Students: J-P Pelteret (PhD)
Work in this area is concerned with the use of modelling and computational tech niques to develop a better understanding of the mechanisms of obstructive sleep apnea.
The initial phase of this work has involved the development of a model for the nonlinear anisotropic behaviour of the tongue, which comprises a number of muscle groups, as well as of other relevant soft tissues.
The tongue model takes account of neural activation.
Further work will entail the simulation of fluid structure interaction involving the tongue and soft palate, and upper airway flow.
Experimental studies in the form of PEPT investigations are being carried out by I Govender (see project
E.
below).
Computational palaeontology
Team members: S Jasinoski (project leader), BD Reddy
Collaborators: A Chinsamy-Turan (Zoology, UCT), TS Kemp (Oxford)
Computational mechanics is used to assist in understanding the jaw mechanics and skull function in cynodonts, an extinct group of mammal-like reptiles that are considered to be the ancestors of mammals.
The cranial function of three evolutionary grades of cynodonts is being investigated using the finite element method.
The skull bones and teeth of Thrinaxodon have been meticulously reconstructed from microCT scans.
Of interest are strain distributions within the skull during simulated feeding activities. We are also investigating how sutures (joints between the skull bones) affect the magnitude and distribution of strain.
Profs Chinsamy-Turan and Kemp provide background palaeontological information, including muscle reconstructions and qualitative functional comparisons.
D. Fluid dynamics
The research in this area includes theoretical, computational, and experimental studies of problems involving fluid flows of industrial or environmental importance.
Unless otherwise stated, computational studies have made use of the proprietary code FLUENT.
Aerodynamics, combustion and free-surface flows
Team members: AT Sayers
Collaborators: C Meyer (University of Stellenbosch)
Industrial sponsors: Denel Aviation, SASOL Advanced Fuels Laboratory
Students: J Long (MSc (Eng)), A Thiart (MSc (Eng))
Research in this area is concerned with industrial aerodynamic problems that occur in the transport industry (flows around bluff bodies such as commercial vehicles), defence (high Mach number separating flows in missile and aircraft aerodynamics, determination of aerodynamic coefficients for wings operating in ground effect), building and architecture (wind loading), the leisure industry (sports equipment manufacture and design), and industrial applications (aircooled heat exchangers, combustion in in-cylinder flows, cavitation in fuel injectors).
The vast majority of computational investigations have been accompanied by extensive experimental studies, much of these in wind tunnels.
Further studies on internal flows have included low-Reynolds number flows in gas turbine compressors and turbine disc cavities.
The main aim has been the formulation of numerical strategies with which to accurately resolve the flow fields through compressor blade cascades as well as the flow and temperature fields within turbine disc cavities.
Work is in progress on a 3D CFD model of the intake process of the engine used to measure the octane rating of various gasoline fuel blends.
Emphasis is on the effect of fuel evaporation on end-gas temperature, which is a huge contributing factor to engine knock.
Further work is devoted to the use of CFD as a tool in the design of gas turbine combustion chambers.
Combustion modelling relies heavily on capturing turbulence effects accurately.
This leads to the close coupling of two of the most poorlyunderstood processes in a single simulation.
Work in progress concerns the calibration of a cold flow model, before proceeding to modelling of the combustion process in the same test rig.
Multi-phase reactive and mixing flows in complex geometries
Team members: DA Deglon (project leader), AE Lewis, CJ Meyer
Sponsors: Anglo Platinum, Murrin Murrin: Minara Resources (Australia)
Students: H Appa (PhD), D Olivier (MSc (Eng)), N Paradza (MSc (Eng)), J Long (MSc (Eng))
Problems of this nature occur widely in the chemical process industry (stirred tank reactors, fluidised bed reactors), the bioprocessing industry (fermenters), and the mining industry (flotation cells, crystallisers, metal precipitation).
These problems generally involve a reactor of fairly complex geometry in which a multiphase mixture - generally non-Newtonian - of solids, liquids and gases is reacting, either chemically or through the transfer of heat and mass.
Flow is generally turbulent.
The projects in this section have focussed on computational aspects of flotation, leaching, precipitation and crystallisation, which are important to the chemical process industry, the mining industry and the environmental field.
All have been accompanied by extensive experimental investigation.
The first problem concerns the modelling of flotation cells, which are agitated multi- phase reactors with complex geometries.
The second problem concerns the modelling of hydrodynamics of leaching and precipitation reactors in the minerals processing industry.
Temperature-dependent flows of non-Newtonian fluids
Members: T Chinyoka (project leader)
Collaborators: OD Makinde (CPUT)
Students: S Abueldahab (PhD)
Current work being led by T Chinyoka is concerned with the mathematical modelling and computational solution of temperature dependent flows of non-Newtonian fluids.
Of interest are nonisothermal processes in polymer (viscoelastic) systems with applications in engineering (food industry, lubrication, heat exchangers) and biological systems (blood flow).
Recent activity includes the development of efficient computational methods of solution of the highly nonlinear coupled systems as well as comparative studies of the response to thermal loading of elastic versus inelastic fluids in flows of industrial interest.
Stability of flows of viscoelastic fluids
Members: BD Reddy
Collaborators: JK Djoko (University of Pretoria), JMW Munganga (University of South Africa)
Students: HBH Mohamed (PhD)
Current work in this area is concerned with models of viscoelastic fluids arising in biomedical applications, and in industry. Of current interest are thermomechanical models which incorporate shearthinning as well as multiple reference states.
These are applicable to the modeling of blood, and of melt phases of polymer fibre spinning processes.
Key questions concern existence of solutions, and stability with respect to relevant definitions of energy.
Similar questions are being addressed in the context of flows of fibre suspensions.
Related work is concerned with the stability of flows of generalized Oldroyd-B fluids, in which conditions for stability, depending on the variable viscosity of the fluid, are obtained.
Rheology of particulate suspensions
Members: DA Deglon
Collaborators: D Khismatullin (Tulane University)
Students: E Smuts (PhD)
Work, in this area is concerned with modelling the rheology of a general particulate suspension within a rheometer.
With this model, the effects of parameters such as particle shape and charge distribution are examined.
Simulations are compared to experimental data for phyllosilicate mineral suspensions, characterised by wide range of shape and surface charge distribution.
E. Particulate flow characterization in industrial and biological systems
Member: I Govender
Collaborators: A Buffler (Physics, UCT), SM Wheaton (Physics, UCT), AN Mainza (CMR, UCT)
Students:L Bbosa (PhD), A Morrison (mSc), M Hromnik (MSc), D Kallon (MSc) K Sichalwe (MSc), N Mangensana (MSc), S Bremner (PhD), T Pathmathas (PhD), M Richter (Post-doc)
Industrial systems such as tumbling mills are typified by rotational and axial flows of rock, steel balls and slurry.
The tortuous, porous network created by the non-uniform packing of rock and steel balls form the channels through which the viscous slurry flows.
A multi-pronged approach employing non-invasive nuclear techniques (PEPT, X-ray) and computational modelling (DEM, CFD, SPH) has formed the key ingredients for mechanistic modelling of such industrial systems.
Biological processes such as breathing are characterised by nonlinear deformation of the tissue and musculature in the human upper airway.
PEPT and X-ray imaging are employed to elucidate the mechanisms responsible for conditions such as obstructive sleep apnoea.
The associated airflow that provides the stimulus for the final deformation is also tracked experimentally using PEPT. These measurements complement coupled FEM-CFD modelling of the upper airway.
The world's second positron emission particle tracking facility, PEPT Cape Town, was officially opened on 4 August 2009.
The new laboratory is situated at the iThemba LABS national cyclotron centre near Faure, Cape Town, and was set up by Dr Indresan Govender and Assoc Prof Andy Buffler.
PEPT is a technique for the tracking of a single tracer particle within the field of view of a PET camera (typically used in medical imaging), and provides a means for the characterisation and visualisation of flow within a range of contexts, including aggressive industrial systems such as tumbling mills, flotation cells and powder mixers.
The establishment of the new PEPT laboratory was significantly advanced by the donation by Imperial College London of the ECAD 'EXACT3D' PET camera which features 27 648 individual detector elements.
F. Computational electromagnetics
Electro-mechanical coupling of electro-active polymers
Member: S Skatulla
Collaborators: C. Sansour, A. Arockiarajan
In recent years, functional or active materials have played an increasingly important role for the design of advanced and smart structures as well as intelligent and micro-electromechanical systems (MEMS).
Amongst these kinds of smart materials are smart hydrogels, ferroelectric polymers, piezoelectric poly- mers, electrostatic polymers, ionic polymer-metal composites and conducting polymers which are collectively known as dielectric elastomers or electroactive polymers (EAP).
EAP have been discovered to be very useful, because, in contrast to piezoelectric ceramics, they are less critical with regard to deformability and formability.
EAP are highly compliant and typically require low actuation voltage to show high strain output on the order of hundred of percent, but are nearly incompressible.
The properties of EAP have been intensively studied in experiments and various models have been developed based on the general nonlinear electro-elasticity equations to capture their behaviour in specific applications.
This work seeks to address nonlinear electro-mechanical coupling on a very fundamental manner.
That is to formulate a continuum mechanical approach which links electric and deformation field on kinematics level rather on constitutive level.
As the theory is kept very general, it is applicable to a high diversity of electro-mechanical coupling problems.
Eddy currents
Member: BD Reddy
Collaborators: A Wilkinson (Electrical Engineering, UCT), Mintek
Students: L Adams (MSc (Eng))
The aim of this work, which forms the basis of the Masters thesis by L Adams, is to develop a finite element code using curlconforming elements, the numerical solution of eddy current problems.
The work is linked to experimental investigations in Electrical Engineering.
