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Research

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

Details of activities during 2015 follow. Also given are details of student involvement and interactions with outside collaborators.

A: COMPUTATIONAL SOLID, STRUCTURAL AND PARTICULATE MECHANICS

Activities in this broad area were devoted to continuing theoretical and computational work on crystal and strain-gradient plasticity, including thermoelastic-plastic modelling of friction stir welding. Other topics, details of which follow, include continuum modelling of surfaces and interfaces, shell theories, strain-induced crystallization in polymers, and experimental studies of bovine bone mechanics. The topic of crack initiation in low-cycle fatigue has been studied using a phase field approach. A new topic is that of ice mechanics with reference to the Antarctic ice shelf.
 

STRAIN GRADIENT PLASTICITY
BD Reddy, F Ebobisse, AT McBride  

Collaborators:
S Bargmann (Technische Universität Hamburg-Harburg)
ME Gurtin (Carnegie-Mellon University)
P Neff (Universität Duisberg-Essen)
P Steinmann (Friedrich-Alexander-Universität Erlangen-Nürnberg)
A Javili (Stanford University)
T Böhlke (Karlsruhe Institute of Technology)

Student graduated:  
D Gottschalk (PhD) (Leibniz Universität Hannover)

Student:
E Bayerschen (Karlsruhe Institute of Technology)

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 introduced. Current work is devoted to problems ?of single and polycrystal plasticity. A focus of work has been on the purely dissipative theory, with a view to investigating and understanding its behaviour under conditions of non-proportional loading. Another area of research involves modelling the influence of the grain boundary on the overall response of a polycrystal.
There has also been work on the development and implementation of solution algorithms for the thermal problem.

Publications:

Anand, Gurtin and Reddy (2015)
McBride, Bargmann and Reddy (2015)
Bayerschen, McBride, Reddy and Böhlke (in press)
Gottschalk, McBride, Reddy, Javili, Wriggers and Hirschberger (in press)
McBride, Gottschalk, Reddy, Wriggers and Javili (in press)
Gurtin and Reddy (in review)
Ebobisse, Neff and Reddy (in review)

CONTINUUM MODELLING OF SURFACES AND INTERFACES
AT McBride, BD Reddy

Collaborators:
S Bargmann (Technische Universität Hamburg-Harburg)
A Javili (Stanford University)  
P Steinmann (Friedrich-Alexander Universität Erlangen-Nürnberg)

Student:
J Wilmers (Technische Universität Hamburg-Harburg)
 
This work focuses on the problem of an elastic bulk encased by an energetic elastic surface. The primary application of the
theory is to nano-scale structures where, due to the termination of interatomic bonds on the surface, the surface can exhibit
fundamentally different behaviour to the bulk.  An  important  aspect  of  the  work  is  coupling  the  mechanical  response  with  thermal  effects  to  obtain  more  realistic  interface models. The calibration of the continuum model is done using atomistic simulations. Recent  contributions  have  been  on  the  description  of  surface  elasticity  using  a  curvilinear-coordinate-based  
finite element methodology and the implementation of the finite element approximation within the open-source library deal. II.

Publications:
Javili, Chatzigeorgiou, McBride, Steinmann, and Linder (2015)
Wilmers, McBride, Bargmann (in review)

SHELL THEORIES WITH SCALE EFFECTS AND HIGHER ORDER GRADIENTS OR FREE ROTATIONS
S Skatulla

Collaborator:
C Sansour (University of Nottingham, UK)

Based on a generalized continuum framework developed by Sansour (1998) strain gradient and micropolar formulations are derived which are suitable to address scale effects of structures where one dimension is very small (e.g. thin films, nano tubes etc.).

Whereas a previous strain gradient approach by Sansour and Skatulla (2009) considered the fully three-dimensional setting, this new approach proposes a shell theory which aims to run computations of thin structures more efficiently and to include scale effects.

Both theories feature a generalized deformation description, new strain and stress measures. As consequence of these new quantities corresponding generalized variational principles are formulated. The approaches are completed by Dirichlet boundary conditions for the displacement field and its derivatives or the rotation field. As numerical frame a moving least squares-based meshfree method is chosen which provides the necessary C1 continuity for the strain gradient approach.

Publications:
Skatulla, Sansour, and Hjiaj (2015)
Skatulla and Sansour (in review)

NUMERICAL MODELS FOR STRAIN-INDUCED CRYSTALLIZATION IN POLYMERS
BD Reddy

Student:
EB Ismail (PhD)

In polymer science, there exists a large family of thermoplastic materials that are present in either amorphous or crystalline solid phases at working temperatures. During unperturbed cooling from the liquid ``melt’’ phase, the amorphous solid phase is usually achieved. A transition from the amorphous to the crystalline phase can occur, however, as a result of strain-induced crystallization. This occurs when the material is deformed at temperatures exceeding the glass transition temperature. In this temperature range the material is still solid, but crystals may grow in the direction of applied stresses.
The amorphous material is often modelled as isotropic and viscoelastic, with flow rules defining part the displacement response to applied loading. The crystalline phase is typically anisotropic and elastic. Crystallization occurs progressively, and a mixture of amorphous and crystalline phases is common.
Several approaches exist for modelling the crystallization process mathematically. The approach followed introduces internal coordinates that are linked to the deformation of the material and relate to preferred orientations and configurations. By tracking strain relative to both the reference and preferred configurations, as well as the crystallization fraction, it is possible to swap phenomenologically the macroscopic behaviour of crystallizing systems. Such models have typically been limited to simple geometric configurations and loading states, where the mathematics remains analytically tractable. This project aims to develop finite element models within this framework, and associated algorithms that are sufficiently robust for use in applications.

FINITE ELEMENT SIMULATION OF FATIGUE CRACK INITIATION IN SURFACE PRESETRESSED TURBINE BLADES
BD Reddy, AT McBride

Collaborators:
T Becker (University of Stellenbosch)
L De Lorenzis (Technische Universität Braunschweig)

Student: H White (MSc Eng)

In the design of mechanical components reliability of the component and its dynamic strength are often a key factor for many industries and applications. Finding this dynamic strength is often subject to many “real-world” factors?that cause deviations from laboratory test conditions. One such factor is the residual stress distribution in a component that is a result of processes such as: welding, shot-peening and forging. These stresses may be beneficial or detrimental to the component’s fatigue/fracture performance.

In structures where reliability is key components designed for long fatigue life (high cycle fatigue) will spend the bulk of their life in the crack initiation phase. In this regime, factors causing deviations from ideal conditions have a significant effect on fatigue life estimates.

Over the last few decades, finite element analyses have become widely used as a way of reducing testing and prototyping costs for machine design companies. Additionally, new techniques such as xFEM and cohesive zone approaches have been developed to model more accurately crack behaviour. This study aims to incorporate the two factors of residual stresses and crack initiation in a computational model that simulates low-cycle fatigue, to predict their effects. Finite element methods incorporating approaches such as continuum damage mechanics for crack initiation and phase field modelling for crack growth without a predefined path are being investigated to this end.

NUMERICAL SIMULATION OF FRICTION WELDING PROCESSES
BD Reddy, AT McBride

Collaborator: D Hattingh (Nelson Mandela Metropolitan University)

Student: M Hamed (PhD)

Friction welding is a family of solid state joining processes where friction is used to generate the necessary welding heat. These processes are used in various important applications where other joining methods are infeasible or produce inferior results. Numerical simulation of friction welding processes can be a useful tool in their deployment in new applications by aiding with selection of welding parameters and with requirement specification for friction welding equipment. In addition, data from friction welds tests can be combined with numerical simulation to analyse material behaviour at the high temperature and deformation rate ranges characteristic of these processes.

In this project, simulation of friction welding processes is carried out through finite-element analysis of a large-strain coupled thermo-viscoplasticity model with friction contact. To address the extremely large deformations undergone by the material at the thermo-mechanically affected zone during these processes, an arbitrary-Lagrangian-Eulerian procedure is being implemented into the solver. Additional variables will be incorporated in the model to study the interaction between process parameters and relevant macro- and microscopic material properties.


MODELLING OF SEASONAL CHANGES IN THE ANTARCTIC ICE-SHELF
S Skatulla

Collaborators:
K MacHutchon, Coastal Marine Technology
M Vichi (Dept. of Oceanography, UCT)

Student:
E Ngongo (MSc)

The Antarctic sea-ice has a significant impact on global climate. The seasonal variations in the occurrence of sea-ice control the exchange between air and sea and consequently influence atmospheric and oceanic circulation. It is therefore important to understand how sea and air temperatures, together with the wave dynamics of the ocean, impact on the morphology of the ice.

For this purpose, as a first step, a continuum mechanical model must be developed which is able to describe the thermodynamics of the ice when subjected to mechanical and thermal loading. In particular, the phase transition of the sea water from frozen to liquid stage, and vice versa, must be included in a suitable multiphase model. As a second step, the model will be calibrated and verified from sea-ice cores which are artificially created in laboratory environment and as obtained at expeditions to the Antarctica facilitated by the Department of Oceanography at UCT.

 

B: NUMERICAL ANALYSIS AND ALGORITHMS

The area of research includes mathematical analyses of finite element and other approximation methods, as well as of associated algorithms. Topics that received attention during 2015 included work on Discontinuous Galerkin and Virtual Element formulations, operator-splitting methods applied to problems in generalized thermoelasticity, solution schemes for fluid-structure interaction problems, and time integrators for deterministic and stochastic systems.

DEVELOPMENT, ANALYSIS AND IMPLEMENTATION OF NEW FINITE ELEMENTS
BD Reddy, AT McBride

Collaborators:
P Wriggers (Leibniz Universität Hannover),
C Carstensen (Humboldt Universität, Berlin)

Student:
F Rasolofoson (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.

The focus has been to undertake detailed analyses and to generate novel approaches, largely within the context?of mixed and discontinuous Galerkin formulations. Current work is concerned with the extension of earlier investigations to the use of Discontinuous Galerkin (DG) for problems of nonlinear elasticity, with a view to developing uniformly convergent (locking-free) formulations.

An investigation (with C Carstensen and M Schedensack, Berlin) has been carried out of construction and analysis of finite element methods for the Bingham flow problem, which is characterized by a variational inequality. New results on optimal-order convergence for mixed and nonconforming formulations have been obtained.
A new area of study (with P Wriggers) focuses on the virtual element method, a recently developed variant of the finite element method which is able to accommodate arbitrary polygonal elements. Applications to contact and to nonlinear problems are of particular interest.


Publications:
Carstensen, Reddy and Schedensack (in press)
Chama and Reddy (in review)
Grieshaber, McBride, and Reddy (2015, in review)

OPERATOR-SPLITTING METHODS FOR COUPLED PROBLEMS
BD Reddy, AT McBride

Student:
MF Wakeni (PhD)

This project is concerned with the development and analysis of efficient and stable operator-splitting methods for solving coupled problems, in the context of the finite element method. The full problem is decomposed into two sub-problems where each one satisfies the same dissipation condition as the original problem. Each of these sub-problems?is discretized appropriately to obtain a stable time- stepping algorithm. Finally, the two algorithms are combined at each time step to obtain a stable algorithm for the whole problem. The emphasis is on nonlinear problems, with the intention of extending some approaches that have been successfully developed for linear problems to the nonlinear regime.

The model problem is that of thermoelasticity, with particular attention to the generalized hyperbolic model of heat conduction that incorporates the second sound effect. When coupled with the equations for elastic behaviour, a fully hyperbolic problem is obtained. Current work is concerned with the?analysis and implementation of operator-splitting methods for the linear and nonlinear problems and comparison of these with monolithic approaches. The space-time discontinuous Galerkin method has been shown to be effective at accurately capturing the various waves that propagate through the system.

Publications:
Wakeni, Reddy and McBride (in review (2))

EFFICIENT AND ROBUST PARTITIONED SOLUTION SCHEMES FOR FLUID-STRUCTURE INTERACTIONS
BD Reddy, T Franz

Collaborator:
S Kok (University of Pretoria)

Student graduated:
A Bogaers (PhD)

This work is concerned with the development of strongly coupled partitioned fluid-structure interaction (FSI) solvers. The methods analysed are primarily geared towards the solution of incompressible transient FSI problems, which facilitate the use of black-box sub-domain solvers.

Radial basis function (RBF) interpolation is introduced for interface information transfer. The primary aim?is to demonstrate that the widely used conservative formulation is a zero-order method, and that the consistent formulation converges within the limit of mesh refinement.

A multi-vector update quasi-Newton (MVQN) method for implicit coupling?of black-box partitioned solvers has been developed. This scheme provides near Newton-like convergence behaviour. Further developments include the use of artificial compressibility in combination with the MVQN method. The analysis of the coupled environment is extended?to treat steady state FSI, FSI with free surfaces, and an FSI problem with solid-body contact.

Publications:
Bogaers, Kok, Reddy, Franz (2015, in review)    

STABLE TIME INTEGRATORS FOR DETERMINISTIC AND STOCHASTIC SYSTEMS
A Tambue (also African Institute for Mathematical Sciences (AIMS)), BD Reddy

Student:
E Kossi (MSc)

Postdoctoral researcher:
F Kalala Mutombo

Current work is concerned with investigating the efficiency of exponential integrators and Rosenbrock-type methods in the context of parallel algorithms to solve large, highly nonlinear problems in porous media.  Dr F Kalala is working on multiphase phase flow with deal.ii. The space discretization is performed using continuous and discontinuous Galerkin methods, while the time discretization is performed using Rosenbrock methods. The Masters project is concerned with exponential integrators and Rosenbrock-type for differential algebraic equations with application on flow and transport in porous media.

Rigorous convergence proofs in space and time are provided, where the space discretization is performed using the finite element method or finite volume method.

Due to current significant applications of fractional derivatives, current numerical techniques for PDEs are being extended to fractional PDEs, with applications in biology.

Further work is concerned with the development of new stable time integrators for nonlinear stochastic differential equations.   Indeed current numerical techniques for stochastic systems usually assume that the nonlinear terms are globally Lipschitz, which is quite restricted in many applications as such functions are mostly one-sided globally Lipschitz or locally Lipschitz.
Here the aim is to build some numerical techniques which are convergent (strong convergence and weak convergence) for such nonlinear functions. Applications will be in uncertainty quantification in porous media flow and in finance.

Publications:
Tambue (in press)
Mvogo, Tambue, Ben-Bolie, and Kofane (in press)

 

C:    BIOMECHANICS

Work continues on a range of topics in cardiovascular biomechanics: in particular, on the mechanics of myocardial infarction, tissue mechanics of rheumatic heart disease, and on patient-specific simulation of the heart. There have also been studies directed towards the design of implants such as stented aortic valves, and scaffolds for soft tissue generation. Other work has been devoted to topics in orthopaedic mechanics such as bone remodelling during shoulder arthroplasty, and experiments on the behaviour of bovine bone at high strain rates.

BIOTHERMOMECHANICS OF SKIN
AT McBride

Collaborators:
S Bargmann (Technische Universität Hamburg-Harburg),
G Limbert (University of Southampton)

Student:
D Pond (MSc)

This project is concerned with the computational modeling of human skin. The first area of research is predicting the response of skin when subjected to thermal loads commonly used in medical treatment and therapy.  The second is the development of a model that accounts for both chronological and UV-induced ageing.

Publication:
McBride, Bargmann and Pond (in review)

BEHAVIOUR OF BOVINE CORTICAL BONE AT HIGH STRAIN RATES
EB Ismail, T Cloete

Biological materials are complex materials, typified by interaction between various types of fluid and solid and exhibit complex rheological and deformation behaviours. In addition to complexities relating to anisotropy, finite deformations, and various brittle and non-brittle failure mechanisms, biological materials are typically highly rate sensitive. This is due, in part, to the dominance associated with different load distribution mechanisms at various rates and size scales.

Material testing has, to date, been performed quasi-statically, or at high strain rates, but data for behaviour at intermediate rates (10s-1 – 100s-1) are lacking due to experimental difficulties, particularly for constant strain rates. As a result, material models that capture the behaviour of biological materials in this regime are seldom found. The need for experimental data and suitable material models at these rates is evident, considering that most locomotion and other biological activities, as well the majority of damage inducing loading, occurs at these rates.

Recent experimental techniques developed at the Blast, Impact and Survivability Unit (BISRU) have allowed testing of materials, including biological materials, at these rates. On-going collaboration with this group is focused on the development of material models for biological materials at intermediate strain rates. At present, work relating to the dynamic behaviour of bovine cortical bone is in press, or has been recently published, and modelling of further materials is underway.

Further activities in impact dynamics are lead by Professor GN Nurick, who in 2003 established the Blast Impact and Survivability Research Unit (BISRU) at UCT. Research activities that fall under the auspices of BISRU are reported separately (see also http://www.bisru.uct.ac.za).

Publications:
Cloete, Paul, and Ismail (in review)

CELL MECHANICS AND MECHANOBIOLOGY
T Franz

Collaborators:
N Davies, L Dubuis (Cardiovascular Research Unit, UCT)
A Gefen (Tel Aviv)

Student:
R Ahmed (PhD)

Mechanobiology is an emerging field that focuses on the way in which physical forces and changes in cell or tissue mechanics contribute to development, physiology, and disease. A major challenge is understanding mechanotransduction, the molecular mechanism by which cells sense and respond to mechanical signals. The lack of mechanistic understanding of these processes is one of the primary foci of this field, which, as a consequence, has enormous potential to (1) bring critical new insights into physiological function and aetiology of disease and (2) lead to multiple innovations in the coming years, both for biomedicine and biotechnology. Elucidating the relationship between mechanical environment and biological response offers a prime target for halting some disease mechanisms, initiating remodelling for engineered tissues, potentially differentiating stem cells, and clarifying how these transduced mechanical signals differ throughout our lifetime. While medicine has typically looked for the genetic basis of disease, first advances in mechanobiology suggest that changes in cell mechanics, extracellular matrix structure, or mechanotransduction may contribute to the development of many diseases, including heart failure, cancer, atherosclerosis, osteoporosis, and asthma. Insights into the mechanical basis of tissue regulation may also lead to development of improved medical devices, biomaterials, and engineered tissues.

The research has focused on computational mechanics of single cells and sub-cellular components. Tissue regeneration is based on the function and differentiation of cells. For a long time research on cell differentiation and tissue regeneration focused mainly on the biochemical stimulus of cells. The important role of the physical environment on signalling, differentiation and function of cells has been recognised only recently. As a consequence, scaffold-based tissue regeneration evolved empirically, without a clear deduction of principles required for a rational design approach. This project focusses at the mechanical interactions of single cells in controlled physical environments using computational modelling and complementary experimental methods.

MYOCARDIAL INFARCTION AND HEART FAILURE
T Franz

Collaborators:
N Davies (Cardiovascular Research Unit, UCT)
L Dubuis
M Ngoepe (Human Biology, UCT)

Student graduated:
MS Sirry (PhD)

Students:
F Masithulela (PhD), K Sack (PhD)


Cardiovascular diseases (CVD) will become the leading cause of death by 2020, superceding 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. 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 a dramatic increase in CVD incidences in Africa in the future, in the younger population in particular, 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. The 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 research is the development and utilisation of computational models to study the biomechanics of myocardial infarction (MI) and emerging MI therapies based on bio-material injection into the infarct.

Publications:
Davies, Dubuis, Franz, Kadner, Meintjies, Saleh, Spottiswoode, Zilla (2015)
Davies, Goetsch, Ngoepe, Franz, Lecour (in press)
Sack, Baillargeon, Acevedo-Bolton, Genet, Rebeleo, Kuhl, Klein, Weiselthaler, Franz, Guccione (in review)
Sack, Davies, Guccione, Franz (in review)
Sirry, Davies, Kadner, Dubuis, Saleh, eintjies, Spottiswoode, Zilla, Franz (2015)
Wise, Davies, Sirry, Kortsmit, Dubuis, Chai, Baaijens, Franz (in review)

MICRO-STRUCTURE MOTIVATED TISSUE MECHANICS OF RHEUMATIC HEART DISEASE
S Skatulla

Collaborators:
J Hussan (University of Auckland)
T Ricken (TU Dortmund)
J Schröder (University of Duisburg-Essen)
N Ntusi and E Meintjes (Dept. of Radiology, UCT)
P Zilla (Dept. of Cardiothoracic Surgery, UCT)

Students:
G Hopkins (MSc Eng)
N Jarratt (MSc Eng)
D Dollery (MSc Eng)

Classically, the elastic behaviour of cardiac tissue mechanics is modelled using anisotropic strain energy functions capturing the averaged behaviour of its fibrous micro-structure. The strain energy function can be derived via representation theorems for anisotropic functions where a suitable nonlinear strain tensor, e.g. the Green strain tensor, describes the current state of strain locally. These approaches are usually of a phenomenological nature and do not elucidate on the complex heterogeneous material composition of cardiac tissue. Thus, pathological changes of micro-structural constituents, e.g. with regards to the extra cellular matrix (ECM), and their implications on the macroscopically observable material behaviour cannot be directly investigated.

In this research the fibrous characteristics of the myocardium are modelled by one-dimensional Cosserat continua. This additionally allows for the inclusion of non-local effects due to the heterogeneous material composition at smaller scales. Specifically, the non-local material response is linked to higher-order deformation modes associated with twisting and bending of an assembly of muscle fibres arising, for example, from fibre dispersion within a representative volume element (RVE). In this sense, a scaling parameter characteristic for the tissue's underlying micro-structure, becomes a material parameter of the formulation. The ability to implicitly account for scale-dependent torsion and bending effects in the constitutive law gives this approach a natural advantage over classical formulations. The assumed hyperelastic material behaviour of myocardial tissue is represented by a nonlinear strain energy function which includes contributions linked to the Cosserat-fibre continuum and complementary terms which refer to the ECM.

The framework is embedded in the in-house code SESKA to facilitate large scale heart simulations to investigate ventricular tissue mechanics.

Publications:
Sack, Skatulla, and Sansour (2015)

SCAFFOLDS FOR VASCULAR SOFT TISSUE REGENERATION
T Franz

Collaborators:
D Bezuidenhout
N Davies (Cardiovascular Research Unit, UCT)
G Limbert (Southampton)

Students: H Krynauw (PhD)

The long-term success of tissue-engineered vascular grafts comprised of synthetic materials depends largely on the host response. Porosity is a key factor for mitigation of foreign body response and inflammation. Poor clinical outcomes observed with small and medium-calibre synthetic grafts are mainly attributed to ongoing thrombogenicity and anastomotic intimal hyperplasia. The overall research is informed by the challenges in structural and fluid mechanics in the development of elastomeric vascular scaffolds comprising a blood barrier component and a structural reinforcement, which allows for regeneration of viable, endothelialised tissue in contrast to clinically used ePTFE and Dacron grafts.

One project has been focusing on the characterization and constitutive modelling of the time-dependent mechanical properties of degradable electro-spun scaffolds during degradation. To provide structural integrity of the regenerating blood vessel, the loss in mechanical strength of the scaffolds needs to be proportional to the regenerating vascular tissue. The study involves the manufacture of hydrolytically degradable porous polymeric scaffolds by electro-spinning. These scaffolds are then subjected to in-vitro degradation. Mechanical characterization of the scaffolds is conducted at various time points during the degradation process.

Publications:
Voorneveld, Oosthuysen, Franz, Zilla and Bezuidenhout (in review)
Human, Franz, Dobner, Ilsley, Black, Wolf, Bezuidenhout, Moodley, Zilla (in review)

CARDIOVASCULAR MAGNETIC RESONANCE IMAGING AND COMPUTATIONAL MODELLING
T Franz, BD Reddy, AT McBride

Collaborators:
D Kahn (Department of Surgery, UCT)
EM Meintjes (Human Biology, UCT)
M Markl (Northwestern University)
B Spottiswoode (Siemens Medical Solutions USA)

Students:
A de Villiers (PhD)
W Guess (MSc Eng)
S Jermy (MSc Med)
J Downs (MMed)

On a systemic level, insight into the complex interactions of function and flow of the interconnected vascular compartments is still scarce. The research aims at improving the detailed understanding of hemodynamics and vascular mechanics in arterio-venous shunting and organ transplants.

Arterio-venous shunts are studied in the form of haemodialysis access grafts and fistulas while organ transplants will focus on renal and liver replacements. The objective of this project is the development and optimisation of advanced magnetic resonance (MR)
imaging technologies and computational models towards improved understanding of the hemodynamics and vascular mechanics of arterio-venous shunts (e.g. in haemodialysis access grafts) and organ transplants. Flow-sensitive 4D (time-resolved 3-D) MR imaging and analysis methods will be optimised to obtain comprehensive clinical data. These data facilitate the development of detailed realistic computational models.

REAL-TIME AND PATIENT-SPECIFIC SIMULATION OF THE HEART
S Skatulla

Collaborators:
BD Reddy
C Sansour (University of Nottingham, UK)

Students:
RR Rama (PhD)
K Moodley (MSc Eng)

Computational cardiac mechanics is emerging as a rapidly expanding area of research bringing together multidisciplinary research centred on understanding the electrophysiological and mechanical behaviour of the heart at scales ranging from cell to tissue and organ levels. Principles of continuum mechanics are key in creating a realistic multi-scale model of the heart. They allow the description of the directly observable behaviour of the heart by incorporating on, micro level, its complex heterogeneous and anisotropic structure, as well as the coupling mechanisms between mechanical fields on the one hand and chemical and electrical fields on the other. Computational models therefore help to quantify the mechanical environment in health, injury, disease, as well as to identify mechanosensitive responses and their mechanisms. This leads to advances in therapeutic and diagnostic procedures.

In contrast to existing computational models, we want to feed our cardiac mechanics models with realistic patient-specific material properties from magnetic resonance imaging (MRI). This high accuracy with regards to material properties can only be exploited if the geometric model of the heart features a similar degree of accuracy. The increase in geometry and material detail, however, is matched by an exponential increase in computing time such that it inevitably results in massive supercomputer simulations.

The novelty of our approach is to pair unparalleled accuracy with fast computing time such that it is usable on a normal computer and provides instant real-time feedback. This will be achieved by a special model reduction technique, the Proper Orthogonal Decomposition with Interpolation (PODI) method. The approach will open a new dimension for heart diagnostics and provide medical researchers, as well as practitioners, with a computational toolbox enabling them to gain in-depth understanding of the mechanical, electro-physiological and molecular processes and coupled mechanisms which aids in the development of new therapy concepts for heart disease.

Publications:
Rama Skatulla and Sansour (in review)

MECHANICAL ASSESSMENT OF STENTED AORTIC VALVES
BD Reddy

Collaborator: H Appa (Strait Access Technologies)

Industrial sponsor:  Strait Access Technologies

Student: M Shirzadi (MSc Eng)

The aortic valve which allows for the uni-directional flow of blood from the left ventricle of the heart to the ascending aorta is prone to several type of valvular disease. Due to high risks associated with open heart surgery, a minimally invasive valve replacement procedure has been developed over the last decade to reduce the risks of this procedure. Transcatheter Aortic Valve Implantation (TAVI) is the method in which a stented prosthetic valve is deployed within the native diseased aortic valve. An accurate simulation of the biomechanical interaction of the stent, aortic root and partially functional leaflets is?critical for predicting and avoiding post procedural complications such as tissue tearing, valve migration and failure and impairment of coronary flow. Work on this project has been concerned with the development of a finite element model of a commercially produced stent and a patient-specific aortic root, to study the effects of pressure loading on the valve, and to assess the mechanical interaction of the stent and the aortic root.

AT McBride

Collaborators:
S Roche (Department of Orthopaedics, UCT)
S Sivarasu (Division of Biomedical Engineering, UCT)

Student:
H Liedtke (MSc)

Reverse total shoulder arthroplasty is a procedure for the treatment of gleno-humeral joint disease among patients with severe rotator cuff deficiency. The medial head of the humerus is removed and a replaced by a cup-shaped implant. A hemispherical implant (the glenosphere) is then attached to the glenoid. The procedure is widely used, but several complications can occur. These include scapula notching, and instability of the glenosphere due to loosening of the fixating screws. The hypothesised cause of the instability is bone remodelling due to the significant changes in the loading on the scapula. Remodelling is the process whereby bone undergoes changes in geometry, density, and constitutive response in order to optimize its structure to the loading environment.

The objective of this collaborative project is to better understand the post-operative loading environment and the subsequent remodelling process using advanced computational modelling. Numerical methods, such as the finite element method, are required to solve the mathematical relations that describe the problem approximately on realistic three-dimensional geometries.

 

D     FLUID DYNAMICS

Activities in fluid dynamics have to a large extent been driven by industrially motivated problems. These include work on the optimal design of turbine baldest mitigate aerodynamic losses, the rheology of particulate suspensions, the determination of effect of system pressure on leakage in water distribution systems, and the use of nanofluids in solar heating systems. Work continues on various topics devoted to the study of liquid polymers and other viscoelastic fluids.

OPTIMAL DESIGN OF TURBINE BLADES
CJ Meyer, BD Reddy

Industrial sponsors: CSIR         

Students: S Selvaraju (PhD), J Bergh (PhD), E Joubert (MSc Eng)

This project concerns the mitigation of the aerodynamic losses associated with the highly three-dimensional (secondary) flows which develop in turbine blade passages. This is important because even relatively small increases in component efficiencies can be shown to have a proportionally larger effect on overall engine thermal efficiency and performance. Recently, non-axisymmetric contouring of the hub and shroud endwalls turbine blade passages have been shown to be an effective method for reducing the strength of the secondary flows. The current investigation employs a surrogate-based optimization (SBO) algorithm coupled to a commercial CFD code to design various sets of blade / contour combinations using a selection of objective functions previously used in industry specifically for this purpose. In addition to the numerical design phase, physical testing of each set of contours will be conducted in a low speed, 1 ½ stage research turbine in order to validate the numerical predictions associated with each design and ultimately determine the relative efficacy of each objective function as a basis for the design of endwall contours within the industrial design process.  

Publication:
Bergh & Snedden (2015)

MODELLING AND ANALYSIS OF THE FLOW OF COMPLEX FLUIDS
T Chinyoka

Collaborators:
OD Makinde (Stellenbosch University)
LG Leal, ME Helgeson (University of California, Santa Barbara)
IE Ireka (Fraunhofer Institute for Industrial Mathematics, Germany)

Students: JG Abuga (PhD), ZS Nyandeni (MSc), FNZ Rahantamialisoa (MSc)

Student graduated:
IE Ireka (PhD)

Current work is concerned with the mathematical modelling, analysis and (computational) solution of flows of complex (non-Newtonian) fluids under various conditions. Of interest are non-isothermal processes and flow inhomogeneities in polymeric (viscoelastic) flows with applications in engineering and biological systems.

Publications:
Chinyoka and Makinde (2015a)
Chinyoka and Makinde (2015b)
Ireka and Chinyoka (2015)
Ireka et al. (2015)

RHEOLOGY OF PARTICULATE SUSPENSIONS
DA Deglon, CJ Meyer

Student graduated: 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. A combination of CFD for the fluid and DEM (discrete element method) for the particles is used to model the suspension. Simulations are compared to experimental data for phyllosilicate mineral suspensions, characterized by a wide range of shape and surface charge distribution.

Publications:
Dabic, Deglon and Meyer (in press)

EFFECT OF SYSTEM PRESSURE ON LEAKAGE FROM WATER DISTRIBUTION SYSTEMS
JE van Zyl, BD Reddy

Collaborators: CRI Clayton (University of Southampton)

Students Graduated: E Ssozi (MSc)

Leakage from water distribution systems is becoming a serious problem world wide as systems age and water resources are placed under increasing strain.  Field and laboratory tests over the past decade have shown that leakage from distribution systems are often substantially more sensitive to changes in pressure that conventional theoretical models predict.  Research has shown that this is mainly due to leak areas varying with pressure (in addition to changes in leakage velocity), but that other factors may also play a role.  The aim of this project is to investigate the various mechanisms involved in the pressure-leakage response.  Currently the project is investigating viscoelastic deformation in plastic pipes and the soil-leak interaction.

Publications:
Ssozi, Reddy and van Zyl (in press)

NANOFLUID DYNAMICS AND SOLAR ENERGY
M MacDevette, BD Reddy

Student: G Gakingo (MSc Eng)

A recent development in renewable energy is that of the direct absorption solar collector (DASC) which absorbs solar energy directly within the working fluid. The project investigates making these DASCs more efficient. This is done by replacing the working fluid with a nanofluid (fluid with suspended nano-sized particles) as even with very low concentrations of nanoparticles these fluids have been shown to have greatly enhanced heat transfer properties. The objective of the project is to develop and analyse mathematical models of DASCs with the purpose of improving their design and efficiency and ultimately ensuring that this clean and renewable energy source can be efficiently exploited. Two equations are integral in describing the problem mathematically; the radiative transfer equation accounts for the attenuation of solar radiation through the depth of the collector and the heat equation describes the distribution of heat in the collector.  For non-steady regimes this is further coupled with the Navier-Stokes equations to account for the flow of the nanofluid. Both analytical and numerical methods are used in solving the one-dimensional model. This provides a good approximation to the two-dimensional model which is solved numerically. The results from the models are then used to assess the performance of the DASC. In power generation applications high operating temperatures and maximum energy absorption are favourable. The performance of the DASCs are therefore represented in terms of Carnot numbers and total solar energy absorption.

Publications:
MacDevette and Reddy (2015)

MODELLING BLOOD FLOWS AS VISCOELASTIC FLUIDS
BD Reddy

Student: N Vundla (MSc Eng)

Current work in this area is concerned with models of viscoelastic fluids arising in biomedical applications. Of interest are Oldroyd-B models of viscoelastic fluids for use in modeling of blood flow. The basis for computations is a Discontinuous Galerkin approach which is well suited to dealing with complications arising from the hyperbolic nature of the equations for the extra stress. The aim is to apply the model to blood flows in patient-specific vessel geometries.

 

E PARTICULATE FLOW CHARACTERIZATION IN INDUSTRIAL AND BIOLOGICAL SYSTEMS
I Govender, AT McBride

Collaborators:
GB Tupper (Physics),
AN Mainza (Chemical Engineering)

Students: D Blakemore (MSc), T Povall (PhD)
Granular Flow Modelling combines the inherent frictional nature of particles with their distinctly fluid-like structure. We focus on two classes of flows: (i) confined flows and (ii) free surface flows. Tumbling mills, chutes, and avalanches are examples of free surface flows while cyclonic separators and stirred mills fall into the class of confined flows. Given the high concentration of solids in industrial flows, the granular flow approximation is unique in its ability to capture the solid-solid interactions within a Navier-Stokes-like framework, typical of fluid flow. The physically valid dissipative mechanisms associated with granular material allows for more realistic quantification of abrasion and attrition in comminution processes while accurately capturing important flow features like free surface shape and velocity field profiles.

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 nonuniform packing of rock and steel balls, form the channels through which the viscous slurry flows. A multi-pronged approach employing noninvasive 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 non-linear 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 PEPT laboratory is situated at the national iThemba Laboratory for Accelerator Based Sciences at Faure, near Cape Town. 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.