### Browsing by Author "Skatulla, Sebastian"

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- ItemRestrictedA tri-phasic continuum model for the numerical analysis of biological tissue proliferation using the Theory of Porous Media. Application to cardiac remodelling in rheumatic heart disease(2019) Mosam, Adam; Skatulla, SebastianThis research is part of an on-going project aimed at describing the mechanotransduction of Rheumatic Heart Disease, in order to study and predict long-term effects of new therapeutic concepts to treat inflammatory heart diseases and ultimately, estimate their effectiveness to prevent heart failure. Attention is given to Rheumatic Heart Disease (RHD) - a valvular heart disease. RHD is a condition which is mostly common amongst poorer regions and mainly affects young people, of which claims approximately 250 000 lives per annum. The Theory of Porous Media (TPM) can represent the proliferative growth and remodelling processes related to RHD within a thermodynamically consistent framework and is additionally advantageous with application to biological tissue due to the ability to couple multiple constituents, such as tissue and blood. The research presented will extend an existing biphasic TPM model for the solid cardiac tissue (solid phase) saturated in a blood and interstitial fluid (liquid phase) [21], to a triphasic model with inclusion of a third nutrient phase. This inclusion is motivated by the reason to constrain the volume of the liquid phase within the system in response to the description of growth, which is modelled through a mass exchange between the solid phase and liquid phase within the biphasic model. Although the nutrient phase acts as a source for growth, the proposed mass supply function used to correlate the deposition of sarcomeres in relation to growth is predominantly mechanically driven and bears no connection to any biochemical constituent, which therefore renders the nutrient phase as a physiologically arbitrary quantity. However, the provision of the nutrient phase is a platform for the inclusion of known constituents which actively contribute towards growth, of which may be explored in future research. The triphasic model is applied to a full cardiac cycle of a left ventricle model, extracted from magnetic resonance imaging (MRI) scans of patients diagnosed with RHD.
- ItemOpen AccessActive contraction of the left ventricle with cardiac tissue modelled as a micromorphic medium(2019) Kamper, Marina; Skatulla, SebastianThe myocardium is composed of interconnected cardiac fibres which are responsible for contraction of the heart chambers. There are several challenges related to computational modelling of cardiac muscle tissue. This is due in part to the anisotropic, non-linear and time-dependent behaviour as well as the complex hierarchical material structure of biological tissues. In general, cardiac tissue is treated as a non-linear elastic and incompressible material. Most computational studies employ the theories of classical continuum mechanics to model the passive response of the myocardium and typically assume the myocardium to be either a transversely isotropic material or an orthotropic material. In this study, instead of a classical continuum formulation, we utilise a micromorphic continuum description for cardiac tissue. The use of a micromorphic model is motivated by the complex microstructure and deformations experienced by cardiac fibres during a heartbeat. The micromorphic theory may be viewed as an extension of the classical continuum theory. Within a micromorphic continuum, continuum particles are endowed with extra degrees of freedom by attaching additional vectors, referred to as directors, to the particles. In this study the directors are chosen such that they represent the deformation experienced by the cardiac fibres. In addition to the passive stresses, the myocardium experiences active stresses as a result of the active tension generated by cardiac fibres. The active tension in the heart is taken to be a function of the sarcomere length, intracellular calcium concentration and the time after the onset of contraction. Experimental studies show that the active behaviour of the myocardium is highly dependent on the tissue arrangement in the heart wall. With a classical continuum description, the sarcomere length is usually defined as a function of the stretch in the initial fibre direction. To allow for a more realistic description of the active behaviour, we define the sarcomere orientation, and consequently also the sarcomere stretch, as a function of the director field. Furthermore, we use the director field to describe the direction in which contraction takes place. The intent of this study is to use a micromorphic continuum formulation and an active-stress model to investigate the behaviour of the left ventricular myocardium during a heartbeat. The simulated results presented here correspond well with typical ventricular mechanics observed in clinical experiments. This work demonstrates the potential of a micromorphic formulation for analysing and better understanding ventricular mechanics.
- ItemOpen AccessAn efficient three-dimensional database driven approach for multi scale homogenization(2019) Jarratt, Nicholas; Skatulla, SebastianThe two-scale homogenization theory, commonly known as the FE2 method, is a well-established technique used to model structures made of heterogeneous materials. Capable of capturing the microscopic effects at the macro level, the FE2 method assigns a representative volume element (RVE) of the materials microstructure at points across the macroscopic sample. This process results in the realization of a fully nested boundary value problem, where macroscopic quantities, required to model the structure, are obtained by homogenizing the RVEs response to macroscopic deformations. A limitation of the FE2 method though is the high computational costs, whereby its reduction has been a topic of much research in recent years. In this research, a two-scale database (TSD) model is presented to address this limitation. Instead of homogenizing the RVEs response to macroscopic deformations, the macroscopic quantities are now approximated using a database of precomputed RVEs. The homogenized results of an RVE are stored in a macroscopic right Cauchy-Green strain space. Discretizing this strain space into a finite set of right Cauchy-Green deformation tensors yields a material database, where the components of each tensor represent the boundary conditions prescribed to the RVE. A continuous approximation of the macroscopic quantities is attained using the Moving Least Squares (MLS) approximation method. Subsequent attention is paid to the implementation of the FE2 method and TSD model, for solving structures made of hyperelastic heterogeneous materials. Both approaches are developed in the in-house simulation software SESKA. A qualitative comparison of results from the FE2 method to those previously published, for a laminated composite beam undergoing material degradation, is presented to verify its implementation. To assess the TSD models performance, an evaluation into the numerical accuracy and computational performance, against the conventional FE2 method, is undertaken. While a significant improvement on computational times was shown, the accuracies in the TSD model were still left to be desired. Various remedies to improve the accuracy of the TSD model are proposed.
- ItemOpen AccessBiological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states(2014) Sack, Kevin; Skatulla, SebastianClassically, the elastic behaviour of cardiac tissue mechanics is modelled using anisotropic strain energy functions capturing the averaged behaviour of its fibrous microstructure. 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 locally the current state of strain [57, 150, 158]. These kinds of approaches, however, are usually of phenomenological nature and do not elucidate on the complex heterogeneous material composition of cardiac tissue characterized by different fibre hierarchies interwoven by collagen, elastin and coronary capillaries [61, 115]. Thus, pathological changes of microstructural constituents, e.g. with regards to the extra cellular matrix, 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 fibre motion relative to the matrix representing the non-local material response due to twisting and bending of fibres. In this sense, a so-called characteristic scaling parameter associated with the micro structure, becomes a material parameters of the formulation. The ability to explicitly account for torsion and bending in the constitutive law gives this approach a natural advantage over classical formulations. Moreover, the additional degrees of freedom in the kinematic description allow for more complex, realistic deformations. The assumed hyperelastic material behaviour of myocardial tissue is represented by a nonlinear strain energy function which includes the contributions linked to the Cosserat fibre continuum and the complementary terms which refer to the extra-cellular matrix. Utilizing the element-free Galerkin method, simulations of the left ventricle undergoing various stages of the cardiac cycle are introduced to investigate ventricular tissue mechanics.
- ItemOpen AccessCharacterisation of phenotypes of inflammation, fibrosis and remodeling in chronic rheumatic heart disease using multiparametric cardiovascular magnetic resonance and autophagy markers(2023) Aremu, Olukayode Olasunkanmi; Ntusi, Ntobeko; Skatulla, SebastianBackground: Rheumatic heart disease (RHD), concomitant to valvular damage, heart failure, arrhythmias and pulmonary hypertension is the major source of cardiovascular morbidity and mortality in the young, predominantly in low- and middle-income countries (LMICs). We investigated the association of valve lesions in RHD with cardiovascular magnetic resonance (CMR) tissue characteristics and autophagy markers, in this study. Methods: Forty-seven (47) patients (42 ± 12.8 years), with advanced RHD, awaiting valve replacement, confirmed on echocardiography, and matched with 30 healthy controls (39 ± 12.1 years), were scanned using a 3T Siemens Magnetom Skyra. CMR parameters were derived from the following acquisitions: cine imaging of the short and long axes, T1 mapping (MOLLI, 5(3)3, estimation of ECV and late gadolinium enhancement (LGE) imaging. For the cellular study, we analysed the immunoexpression of Beclin, LC3, p62, BAX, Bcl-2 and caspase-3 in patients confirmed with RHD and valvular heart disease
- ItemOpen AccessA Computational Fluid Dynamics Model for the Small-Scale Dynamics of Wave, Ice Floe and Interstitial Grease Ice Interaction(2021-04-29) Marquart, Rutger; Bogaers, Alfred; Skatulla, Sebastian; Alberello, Alberto; Toffoli, Alessandro; Schwarz, Carina; Vichi, MarcelloThe marginal ice zone is a highly dynamical region where sea ice and ocean waves interact. Large-scale sea ice models only compute domain-averaged responses. As the majority of the marginal ice zone consists of mobile ice floes surrounded by grease ice, finer-scale modelling is needed to resolve variations of its mechanical properties, wave-induced pressure gradients and drag forces acting on the ice floes. A novel computational fluid dynamics approach is presented that considers the heterogeneous sea ice material composition and accounts for the wave-ice interaction dynamics. Results show, after comparing three realistic sea ice layouts with similar concentration and floe diameter, that the discrepancy between the domain-averaged temporal stress and strain rate evolutions increases for decreasing wave period. Furthermore, strain rate and viscosity are mostly affected by the variability of ice floe shape and diameter.
- ItemOpen AccessComputational modelling of cardiac function and myocardial infarction(2012) MBewu, James; Reddy, B Daya; Skatulla, SebastianCardiovascular disease is a leading cause of death in South Africa. In particular non-fatal myocardial infarction is a key determinant for future cardiac failure due to adverse remodelling and electrophysiological dysfunction. Computational modelling of the electrophysiology and mechanics of the heart can provide useful insights into the causes of cardiac failure and the efficacy of treatments designed to combat myocardial infarction. A computational model of the healthy and infarcted left ventricle of a rat was developed using the eikonal diffusion equation to simulate the electrophysiology; a continuum mechanical model incorporating a passive mechanical model of Usyk to describe the nonlinear, anisotropic and nearly compressible nature of cardiac tissue; and an active stress model of Guccione to model the contraction of cardiac tissue. Boundary conditions modelling the blood pressure on the heart wall were applied to simulate the cardiac cycle.
- ItemOpen AccessComputational modelling of ice floe dynamics in the Antarctic marginal ice zone.(2023) Marquart, Rutger; Skatulla, Sebastian; Machutchon KeithThe contribution of Antarctic sea ice in global climate models requires a more accurately estimation, as a relatively large part, approximately 4% of the Earth's surface in the winter season, is covered by sea ice. Understanding the dynamic and thermodynamic processes of sea ice, results in a better comprehension of sea ice behaviour in the Antarctic marginal ice zone (MIZ) and thus leads to better predictions. Large-scale sea ice models operate at regions of 10-100km2 , describing sea ice in a smeared model approach. However, the highly dynamic sea ice behaviour in the Antarctic MIZ, which is represented by the area where sea ice and ocean waves interact, still eludes reliable prediction. A heterogeneous morphology, consisting of relatively small and mobile ice floes, governed by collisional dynamics and fracture mechanics, requires detailed finer-scale sea ice dynamics models. Therefore, this project focuses on small-scale modelling of sea ice dynamics in the Antarctic MIZ. A more detailed model implies a heterogeneous sea ice material composition, considering separately ice floes and grease ice with their distinct properties. The material behaviour of ice floes is implemented using a Hookean-like flow rule, whereas grease ice is governed by a viscous-plastic material law. The small-scale model assumes that sea ice is isothermal, as only small time windows of less than a minute are considered. As a result, thermodynamic effects, such as sea ice melt and growth, are not taken into account. This work describes key aspects of ice floe collision dynamics in wavy conditions, considering skin drag, the Froude-Krylov force acting at the circumference of ice floes from the wave pressure gradient, and form drag due to the surrounding grease ice deeper into the Antarctic MIZ in a low to medium wave energy regime. Ice floes that interact with each other and the interaction between ice floes and grease ice are analysed. The behaviour of the sea ice rheology of both ice floes and grease ice are studied in realistic sea ice layouts, subjected to different wave properties and grease ice viscosity values. The influence of inertia on the phase shift between the motion of the sea ice cover and the orbital wave velocity of the water layer underneath, is one of the most important aspects in the small-scale model. The phase shift directly affects the interrelation between the sea ice velocity, wave elevation and the ice floe collision dynamics. Additionally, the collision dynamics shows that the ice floe collision pattern in the sea ice domain becomes more random for larger wave periods, due to an increase of the kinetic wave energy. Lastly, strain rates exhibit high localised gradients due to form drag at the interface between ice floes and grease ice, which corresponds to low viscosity values. The small-scale model, demonstrated in this study, shows the general applicability of a detailed continuum framework, contributing to the current research to small-scale atmosphere-ocean physical processes in the Antarctic MIZ. The obtained results provide insights into high resolution behaviour of sea ice on the floe-scale. Furthermore, the newly-developed model can provide for the parametrisation of large-scale models, improving existing global climate models.
- ItemOpen AccessComputational study of compact tension and double torsion test geometries(2014) Goqo, Sicelo Praisgod; Daya, Reddy; Tait, Robert; Becker, Thorsten; Skatulla, SebastianIn the design of many engineering components subjected to cyclic or repetitive loading,fatigue is an ever-present challenge. The engineer often endeavors 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, fatigue threshold, Δҝₜₕ, 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, Δҝₜₕ, is determined experimentally by monitoring growth of a crack (typically in a compact tension ( CT) specimen) and continually reducing cyclic stress levels until the threshold condition is reached. This procedure is very cumbersome and time-consuming, and this project rather considers the design of a fracture mechanics specimen geometry in which there is a decreasing stress in tensity (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.
- ItemOpen AccessDevelopment of a Micromorphic (Multiscale) Material Model aimed at Cardiac Tissue Mechanics(2020) Dollery, Devin; Skatulla, SebastianComputational cardiac mechanics has historically relied on classical continuum models; however, classical models amalgamate the behaviour of a material's micro-constituents, and thus only approximate the macroscopically observable material behaviour as a purely averaged response that originated on micro-structural levels. As such, classical models do not directly and independently address the response of the cardiac tissue (myocardium) components, such as the muscle fibres (myocytes) or the hierarchically organized cytoskeleton. Multiscale continuum models have developed over time to account for some of the micro-architecture of a material, and allow for additional degrees of freedom in the continuum over classical models. The micromorphic continuum [15] is a multiscale model that contains additional degrees of freedom which lend themselves to the description of fibres, referred to as micro-directors. The micromorphic model has great potential to replicate certain characteristics of the myocardium in more detail. Specifically, the micromorphic micro-directors can represent the myocytes, thus allowing for non-affine relative deformations of the myocytes and the extracellular matrix (ECM) of tissue constraining the myocytes, which is not directly possible with classical models. A generalized micromorphic approach of Sansour [73, 74, 75] is explored in this study. Firstly, numerical examples are investigated and several novel proofs are devised to understand the behaviour of the micromorphic model with regards to numerical instabilities, micro-director displacements, and macro-traction vector contributions. An alternative micromorphic model is developed by the author for comparison against Sansour's model regarding the handling of micro-boundary conditions and other numerical artifacts. Secondly, Sansour's model is applied to cardiac modelling, whereby a macro-scale strain measure represents the deformation of the ECM of the tissue, a micro-scale strain measure represents the muscle fibres, and a third strain measure describes of the interaction of both constituents. Separate constitutive equations are developed to give unique stiffness responses to both the ECM and the myocytes. The micromorphic model is calibrated for cardiac tissue, first using triaxial shear experiments [80], and subsequently, to a pressure-volume relationship. The contribution of the micromorphic additional degrees of freedom to the various triaxial shear modes is quantified, and an analytical explanation is provided for differences in contributions. The passive filling phase of the heart cycle is investigated using a patient-specific left ventricle geometry supplied by the Cape Universities Body Imaging Centre (CUBIC) [38].
- ItemOpen AccessFrazil Ice in the Antarctic Marginal Ice Zone(2021-06-10) Paul, Felix; Mielke, Tommy; Schwarz, Carina; Schröder, Jörg; Rampai, Tokoloho; Skatulla, Sebastian; Audh, Riesna R; Hepworth, Ehlke; Vichi, Marcello; Lupascu, Doru CFrazil ice, consisting of loose disc-shaped ice crystals, is the first ice that forms in the annual cycle in the marginal ice zone (MIZ) of the Antarctic. A sufficient number of frazil ice crystals form the surface “grease ice” layer, playing a fundamental role in the freezing processes in the MIZ. As soon as the ocean waves are sufficiently damped by a frazil ice cover, a closed ice cover can form. In this article, we investigate the rheological properties of frazil ice, which has a crucial influence on the growth of sea ice in the MIZ. An in situ test setup for measuring temperature and rheological properties was developed. Frazil ice shows shear thinning flow behavior. The presented measurements enable real-data-founded modelling of the annual ice cycle in the MIZ.
- ItemOpen AccessGrowth, modelling and remodelling of cardiac tissue: a multiphase approach(2017) Hopkins, Gary; Skatulla, SebastianRheumatic heart disease (RHD) is identified as a serious health concern in developing countries, specifically amongst young individuals, accounting for between 250 000 and 1.4 million deaths annually. As such, the attention of this research is initially placed on the importance of the development of a cardiac analysis toolbox with functionality for pathophysiological analysis of the disease. Subsequently, in order to further the understanding of the mechanisms of the disease as linked to cardiomyocyte growth and remodelling of the microstructure, a continuum bi-phasic model applicable to cardiac tissue is formulated based on the theory of porous media (TPM). This makes it possible to account for interactions and contributions of multiple phases of constituent materials, which in computational cardiac modelling are the solid phase - the cardiac tissue - and the liquid phase - blood and interstitial uid. Subsequent attention is paid to the cardiac model development in order to implement a sound base on which to add strain-driven phase transition via a mass supply function proposed within this study. To this end, based on thermodynamical restrictions, constitutive relations are proposed for stress, permeability, seepage velocity, mass supply and interaction forces such as friction. The approach is implemented in the in-house computational cardiac mechanics toolbox SESKA which supports finite element as well as Element- free Galerkin-based approximations. This investigation considers the passive and active non-linear elastic material behaviour of the myocardium of the left ventricle coupled with porous media theory, along with an an additional coupling to the haemodynamics of the circulatory system, facilitating modelling of the full cardiac cycle. As such, an initial cardiac growth and remodelling computer model is developed as an initial step to computational modelling of the adverse effects of RHD and other similar in ammatory heart diseases, with the potential to limit the invasiveness and risk of in-vivo patient studies. A patient specific case study is conducted, making use of cardiovascular magnetic resonance scans taken over a period of two years from a patient affected by RHD to generate realistic 3D computer models, from which information is drawn with regards to the pathophysiological behaviour of the disease.
- ItemOpen AccessLocal maximum entropy approximation-based modelling of the canine heart(2012) Rama, Ritesh Rao; Skatulla, SebastianLocal Maximum Entropy (LME) method is an approximation technique which has been known to have good approximation characteristics. This is due to its non-negative shape functions and the weak Kronecker delta property which allow the solutions to be continuous and smooth as compared to the Moving Least Square method (MLS) which is used in the Element Free Galerkin method (EFG). The method is based on a convex optimisation scheme where a non-linear equation is solved with the help of a Newton algorithm, implemented in an in-house code called SESKA. In this study, the aim is to compare LME and MLS and highlight the differences. Preliminary benchmark tests of LME are found to be very conclusive. The method is able to approximate deformation of a cantilever beam with higher accuracy as compared to MLS. Moreover, its rapid convergence rate, based on a Cook's membrane problem, demonstrated that it requires a relatively coarser mesh to reach the exact solution. With those encouraging results, LME is then applied to a larger non-linear cardiac mechanics problem. That is simulating a healthy and a myocardial infarcted canine left ventricle (LV) during one heart beat. The LV is idealised by a prolate spheroidal ellipsoid. It undergoes expansion during the diastolic phase, addressed by a non-linear passive stress model which incorporates the transversely isotropic properties of the material. The contraction, during the systolic phase, is simulated by Guccione's active stress model. The infarct region is considered to be non-contractile and twice as stiff as the healthy tissue. The material loss, especially during the necrotic phase, is incorporated by the use of a homogenisation approach. Firstly, the loss of the contraction ability of the infarct region counteracts the overall contraction behaviour by a bulging deformation where the occurrence of high stresses are noted. Secondly, with regards to the behaviour of LME, it is found to feature high convergence rate and a decrease in computation time with respect to MLS. However, it is also observed that LME is quite sensitive to the nodal spacing in particular for an unstructured nodal distribution where it produces results that are completely unreliable.
- ItemOpen AccessMaterial parameter identification for modelling the left ventricle in the healthy state(2014) Essack, Mohammed Asaad; Skatulla, SebastianAn idealized truncated ellipsoidal model, was used to simulate a healthy canine left ventricle. Passive behaviour of the myocardium was modelled using the constitutive model of Usyk. In addition, active behaviour of the myocardium was modelled by the active stress law of Guccione. Furthermore, the load faced by the left ventricle in ejecting blood into the arterial system, was modelled with the three element Windkessel model of Westerhof. The model was calibrated to pressure-volume data, which was adaptedfrom the work of Kerckhoffs. The projected Levenberg-Marquardt algorithm was used to identify material parameters. Identification of the anisotropic constants in the model of Usyk proved to be difficult, with the calibration algorithm often converging to parameter values that produced numerical instability. An idealized truncated ellipsoidal model, was used to simulate a healthy canine left ventricle. Passive behaviour of the myocardium was modelled using the constitutive model of Usyk. In addition, active behaviour of the myocardium was modelled by theactive stress law of Guccione. Furthermore, the load faced by the left ventricle in ejecting blood into the arterial system, was modelled with the three element Windkessel model of Westerhof. The model was calibrated to pressure-volume data, which was adapted from the work of Kerckhoffs. The projected Levenberg-Marquardt algorithm was used to identify material parameters. Identification of the anisotropic constants in the model of Usyk proved to be difficult, with the calibration algorithm often converging to parameter values that produced numerical instability. An idealized truncated ellipsoidal model, was used to simulate a healthy canine left ventricle. Passive behaviour of the myocardium was modelled using the constitutive model of Usyk. In addition, active behaviour of the myocardium was modelled by the active stress law of Guccione. Furthermore, the load faced by the left ventricle in ejecting blood into the arterial system, was modelled with the three element Windkessel model of Westerhof. The model was calibrated to pressure-volume data, which was adaptedfrom the work of Kerckhoffs. The projected Levenberg-Marquardt algorithm was used to identify material parameters. Identification of the anisotropic constants in the model of Usyk proved to be difficult, with the calibration algorithm often converging to parameter values that produced numerical instability. An idealized truncated ellipsoidal model, was used to simulate a healthy canine left ventricle. Passive behaviour of the myocardium was modelled using the constitutive model of Usyk. In addition, active behaviour of the myocardium was modelled by the active stress law of Guccione. Furthermore, the load faced by the left ventricle in ejecting blood into the arterial system, was modelled with the three element Windkessel model of Westerhof. The model was calibrated to pressure-volume data, which was adapted from the work of Kerckhoffs. The projected Levenberg-Marquardt algorithm was used to identify material parameters. Identification of the anisotropic constants in the model of Usyk proved to be difficult, with the calibration algorithm often converging to parameter values that produced numerical instability.
- ItemOpen AccessModelling of brine transport mechanisms in Antarctic sea ice(2021) Cook, Andrea; Skatulla, Sebastian; Machutchon, KeithIt is evident that the sea ice cycle, from its formation to its melt, is governed by a complex interaction of the ocean, atmosphere and surrounding continents. Once sea water begins to freeze, physical, biological and chemical processes have implications on the evolution of the sea ice morphology [38]. The distinguishing factor between fresh and sea water ice is brine inclusions that get trapped within the ice pores during freezing. Salt inclusions within frozen ice influence the salinity as well as the physical properties of the sea ice [23]. These brine inclusions form part of a dynamic process within the ice characterized by the movement of brine and phase transition which are the foundation of many of its physical properties [23]. Brine removal subsequently begins to occur due to vertical gravity drainage into the underlying ocean water. This study introduces the application of a biphasic model based on the Theory of Porous Media (TPM) which considers a solid phase for the pore structure of the ice matrix as well as a liquid phase for the brine inclusions, respectively. This work explores the use of the TPM framework towards advancing the description and study of the various desalination mechanisms that are significant in aiding the salt flux into the Southern Ocean. This will foster understanding of brine rejection and how it is linked to the porous microstructure of Antarctic sea ice
- ItemOpen AccessMultiscale modelling and an experimental investigation on size-scale effects in concrete(2010) Braun, Simon; Skatulla, Sebastian; Reddy B DayaClassical continuum mechanics assumes that constitutive parameters are associated with a so-called Representative Volume Element (RVE) and are a statistical average. This concept is based on the presumption that the specimen size is much larger than the size of its constituents, so that the behaviour of a single constituent can be neglected. This presumption does not hold true if the considered problem domain is smaller than the RVE. The size of material constituents in relation to the dimension of the specimen can then not be considered negligible and the interaction between the constituents needs to be addressed. In this context, so-called generalised continuum formulations have proven to provide a remedy.
- ItemOpen AccessPermeability of winter and spring first-year ice in the Antarctic marginal ice zone(2022) Lin, Xuefeng; Skatulla, SebastianThis study was part of the 2019 Southern oCean seAsonal Experiment (SCALE) Winter and Spring Cruise of the South African icebreaker SA Agulhas II. First-year spring and winter sea ice were sampled from the Antarctic marginal ice zone. Consolidated pack ice was collected during both cruises, while pancake ice floes and brash ice floes were collected during Winter and Spring Cruise, respectively. The ice cores analyses of temperature, salinity, and texture were subsequently performed during the Spring and Winter Cruise, and an additional falling head permeability test was conducted during the Spring Cruise. The brine volume is determined empirically from sea ice temperature and bulk salinity. The ice permeability is then calculated from the porosity-permeability relation. The mean permeability of spring pack ice is 2.6 × 10−11 ± 3.67 × 10−11 m2 , marginally higher than the winter pack ice with a mean permeability of 1.1×10−11±2.3×10−11 m2 . Comparing the permeability values of spring and winter consolidated pack ice shows a continuous increase in permeability with seasonal progressions and a rise in ice temperature. The falling head permeability test using kerosene has been made in-house by Hasham Taujoo to determine the in situ sea ice permeability during the Spring Cruise. The experimentally determined permeability values of spring consolidated pack ice were consistent with the above-stated permeability data. However, the permeability values of spring brash ice floes (1.4 × 10−11 ± 2.12 × 10−11 m2 ) determined from porositypermeability relation deviate from field observations due to the presence of large holes and cracks on the ice samples.
- ItemOpen AccessPhase field modeling of dynamic brittle fracture at finite strains(2019) Omatuku, Emmanuel Ngongo; Skatulla, SebastianFracture is the total or partial separation of an initially intact body through the propagation of one or several cracks. Computational methods for fracture mechanics are becoming increasingly important in dealing with the nucleation and propagation of these cracks. One method is the phase field approach, which approximates sharp crack discontinuities with a continuous scalar field, the so-called phase field. The latter represents the smooth transition between the intact and broken material phases. The evolution of the phase field due to external loads describes the fracture process. An original length scale is used to govern the diffusive approximation of sharp cracks. This method further employs a degradation function to account for the loss of the material stiffness during fracture by linking the phase field to the body’s bulk energy. To prevent the development of unrealistic crack patterns and interpenetration of crack faces under compression, this study uses the anisotropic split of the bulk energy, as proposed by Amor et al. [5], to model the different fracture behavior in tension, shear and compression. This research is part of a larger project aimed at the modeling of Antarctic sea ice dynamics. One aspect of this project is the modeling of the gradual break-up of the consolidated ice during spring. As a first step, this study reviews a phase field model used for dynamic brittle fracture at finite strains. Subsequently, this model is implemented into the in-house finite element software SESKA to solve the benchmark tension and shear tests on a single-edge notched block. The implementation adopts the so-called monolithic scheme, which computes the displacement and phase field solutions simultaneously, with a Newmark time integration scheme. The results of the solved problems demonstrate the capabilities of the implemented dynamic phase field model to capture the nucleation and propagation of cracks. They further confirm that the choice of length-scale and mesh size influences the solutions. In this regard, a small value of the length-scale converges to the sharp crack topology and yields a larger stress value. On the other hand, a large length-scale parameter combined with a too coarse mesh size can yield unrealistic results.
- ItemOpen AccessProper orthogonal decomposition with interpolation-based real-time modelling of the heart(2017) Rama, Ritesh Rao; Skatulla, Sebastian; Reddy, DayaSeveral studies have been carried out recently with the aim of achieving cardiac modelling of the whole heart for a full heartbeat. However, within the context of the Galerkin method, those simulations require high computational demand, ranging from 16 - 200 CPUs, and long calculation time, lasting from 1 h - 50 h. To solve this problem, this research proposes to make use of a Reduced Order Method (ROM) called the Proper Orthogonal Decomposition with Interpolation method (PODI) to achieve real-time modelling with an adequate level of solution accuracy. The idea behind this method is to first construct a database of pre-computed full-scale solutions using the Element-free Galerkin method (EFG) and then project a selected subset of these solutions to a low dimensional space. Using the Moving Least Square method (MLS), an interpolation is carried out for the problem-at-hand, before the resulting coefficients are projected back to the original high dimensional solution space. The aim of this project is to tackle real-time modelling of a patient-specific heart for a full heartbeat in different stages, namely: modelling (i) the diastolic filling with variations of material properties, (ii) the isovolumetric contraction (IVC), ejection and isovolumetric relation (IVR) with arbitrary time evolutions, and (iii) variations in heart anatomy. For the diastolic filling, computations are carried out on a bi-ventricle model (BV) to investigate the performance and accuracy for varying the material parameters. The PODI calculations of the LV are completed within 14 s on a normal desktop machine with a relative L₂-error norm of 6x10⁻³. These calculations are about 2050 times faster than EFG, with each displacement step generated at a calculation frequency of 1074 Hz. An error sensitivity analysis is consequently carried out to find the most sensitive parameter and optimum dataset to be selected for the PODI calculation. In the second phase of the research, a so-called "time standardisation scheme" is adopted to model a full heartbeat cycle. This is due to the simulation of the IVC, ejection, and IVR phases being carried out using a displacement-driven calculation method which does not use uniform simulation steps across datasets. Generated results are accurate, with the PODI calculations being 2200 faster than EFG. The PODI method is, in the third phase of this work, extended to deal with arbitrary heart meshes by developing a method called "Degrees of freedom standardisation" (DOFS). DOFS consists of using a template mesh over which all dataset result fields are projected. Once the result fields are standardised, they are consequently used for the PODI calculation, before the PODI solution is projected back to the mesh of the problem-at-hand. The first template mesh to be considered is a cube mesh. However, it is found to produce results with high errors and non-physical behaviour. The second template mesh used is a heart template. In this case, a preprocessing step is required where a non-rigid transformation based on the coherent point drift method is used to transform all dataset hearts onto the heart template. The heart template approach generated a PODI solution of higher accuracy at a relatively low computational time. Following these encouraging results, a final investigation is carried out where the PODI method is coupled with a computationally expensive gradient-based optimisation method called the Levenberg- Marquardt (PODI-LVM) method. It is then compared against the full-scale simulation one where the EFG is used with the Levenberg-Marquardt method (EFG-LVM). In this case, the PODI-LVM simulations are 1025 times faster than the EFG-LVM, while its error is less than 1%. It is also observed that since the PODI database is built using EFG simulations, the PODI-LVM behaves similarly to the EFG-LVM one.
- ItemOpen AccessA Proper Orthogonal Decomposition-based inverse material parameter optimization method with applications to cardiac mechanics(2016) Moodley, Kamlin; Skatulla, SebastianWe are currently witnessing the advent of a revolutionary new tool for biomedical research. Complex mathematical models of "living cells" are being arranged into representative tissue assemblies and utilized to produce models of integrated tissue and organ function. This enables more sophisticated simulation tools that allows for greater insight into disease and guide the development of modern therapies. The development of realistic computer models of mechanical behaviour for soft biological tissues, such as cardiac tissue, is dependent on the formulation of appropriate constitutive laws and accurate identification of their material parameters. The main focus of this contribution is to investigate a Proper Orthogonal Decomposition with Interpolation (PODI) based method for inverse material parameter optimization in the field of cardiac mechanics. Material parameters are calibrated for a left ventricular and bi-ventricular human heart model during the diastolic filling phase. The calibration method combines a MATLAB-based Levenberg Marquardt algorithm with the in-house PODIbased software ORION. The calibration results are then compared against the full-order solution which is obtained using an in-house code based on the element-free Galerkin method, which is assumed to be the exact solution. The results obtained from this novel calibration method demonstrate that PODI provides the means to drastically reduce computation time but at the same time maintain a similar level of accuracy as provided by the conventional approach.