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This 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.

Damage is briefly defined as the presence and growth of micro-defects in a material. This study serves to describe the computational implementation of the material damage theory adopted for ductile materials. Thus, pays attention to the computational analysis of the physical behaviour of materials under finite deformations — in particular, the stress-strain behaviour, load-deformation behaviour and location of weak zones. Throughout this study, non-linear continuum mechanics is utilised as the mathematical basis of the constitutive and general finite element framework. In continuum mechanics, there exists no requirement to discretely characterise each microcrack that grows in a material, thus making it possible to provide analysis of the stress and strain response affected by micro-defects using material particles, which are localised collections of many atomic-scale particles. The continuum is thus a sum of its material particles. To complement this description of mechanics, constitutive and phenomenological equations are adopted from the non-linear thermodynamic phenomena of elasticity, plasticity, and damage; the laws of thermodynamics will therefore apply and are shown as such. The proposed material damage model is developed and implemented in the backend of the in-house computational mechanics toolbox SESKA, which uses finite element-based discretisation and approximation techniques. Field and scalar quantities, such as stress and strain, are computed with the use of the return-mapping method. The stress measures utilised are the 2nd Piola-Kirchhoff stress S and the Mandel stress Σ. The Newton-Raphson update scheme is applied in the plasticity evolution equations via the plastic multiplier (denoted λ), which innately controls the evolution of all other inelastic phenomena. Damage is a function of plastic evolution and thus plays a role in the plasticity multiplier calculation. Moreover, this proposed model makes the assumption of full isotropy, all material properties at a material point are the same in tension and compression and the same regardless of the dimension. Finally, several examples are utilised to showcase the model and all the intricacies are presented — the problem setup, boundary condition assignment and multi-layered analysis are detailed in the content of this study and the examples perform well under qualitative scrutiny. These examples include a cantilevered beam model, a simply supported bending model and a plane strain example to evaluate whether the material model achieves qualifiable correlation to expected behaviour and to assess whether the damage-related parameters affect the stress and strain behaviour as expected. In brief conclusion, this paper shows that the model achieves qualifiable correlation and all the material parameters function as expected.

Fracture 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.

This 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.

This thesis is concerned with the initial development of a multiphase material model using the Theory of Porous Media (TPM) for the penetration of intermediary rust product into reinforced concrete subjected to chloride-induced corrosion. Research has shown that although the majority of time-to-cracking service life models for reinforced concrete structures neglect the permeation of rust into the cement paste adjacent to the reinforcement, it is this mechanism that is responsible for discrepancies between experimental data and model results. The model presented may be used to simulate the transport of water and gas through the capillary pores in concrete and the diffusion of iron III chloride within the pore solution. Iron III chloride is a soluble chloride complex formed as an intermediary product during the oxidation reaction at the anode of the corrosion cell. This solute is transported in the pore solution from low oxygen conditions and is oxidized in oxygen-rich conditions resulting in the precipitation of rust in the concrete pores. The Theory of Porous Media has proven proficient for modelling the material behaviour of porous solid bodies saturated with one or more fluids but has yet to be applied to chloride-induced reinforcement corrosion of reinforced concrete. This work outlines the initial efforts of using TPM to model the rust transport process coupled with the poro-elastic material response of reinforced concrete. The latter accounts for the stress build-up due to rust precipitation and volume expansion. The chloride complex is described by a concentration within the liquid phase and is therefore not assigned a unique volume fraction. Precipitation of the rust is not included here as it will be added at a later stage in the development of a more accurate reinforced concrete chloride induced corrosion model. It is intended that the model thus developed may be adapted for other deterioration mechanisms in concrete.

The 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.