On the Initial Stages of the Densification and Lithification of Sediments

Peer reviewed

On the Initial Stages of the Densification and Lithification of Sediments

Peer reviewed

Microstructural-based approach to the interpretation of clays and transitional soils behaviour

Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2016.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Feasibility of agent-based modelling of articular cartilage including a conceptual representation of its structure

Articular cartilage is a complex structure with an architecture in which fluid-swollen proteoglycans constrained within a 3D network of collagen fibrils. Because of the complexity of the cartilage structure, the relationship between its mechanical behaviours at the macroscale level and its components at the micro-scale level are not completely understood. The research objective in this thesis is to create a new model of articular cartilage that can be used to simulate and obtain insight into the micro-macro-interaction and mechanisms underlying its mechanical responses during physiological function. The new model of articular cartilage has two characteristics, namely: i) not use fibre-reinforced composite material idealization ii) Provide a framework for that it does probing the micro mechanism of the fluid-solid interaction underlying the deformation of articular cartilage using simple rules of repartition instead of constitutive / physical laws and intuitive curve-fitting. Even though there are various microstructural and mechanical behaviours that can be studied, the scope of this thesis is limited to osmotic pressure formation and distribution and their influence on cartilage fluid diffusion and percolation, which in turn governs the deformation of the compression-loaded tissue. The study can be divided into two stages. In the first stage, the distributions and concentrations of proteoglycans, collagen and water were investigated using histological protocols. Based on this, the structure of cartilage was conceptualised as microscopic osmotic units that consist of these constituents that were distributed according to histological results. These units were repeated three-dimensionally to form the structural model of articular cartilage. In the second stage, cellular automata were incorporated into the resulting matrix (lattice) to simulate the osmotic pressure of the fluid and the movement of water within and out of the matrix; following the osmotic pressure gradient in accordance with the chosen rule of repartition of the pressure. The outcome of this study is the new model of articular cartilage that can be used to simulate and study the micromechanical behaviours of cartilage under different conditions of health and loading. These behaviours are illuminated at the microscale level using the socalled neighbourhood rules developed in the thesis in accordance with the typical requirements of cellular automata modelling. Using these rules and relevant Boundary Conditions to simulate pressure distribution and related fluid motion produced significant results that provided the following insight into the relationships between osmotic pressure gradient and associated fluid micromovement, and the deformation of the matrix. For example, it could be concluded that: 1. It is possible to model articular cartilage with the agent-based model of cellular automata and the Margolus neighbourhood rule. 2. The concept of 3D inter connected osmotic units is a viable structural model for the extracellular matrix of articular cartilage. 3. Different rules of osmotic pressure advection lead to different patterns of deformation in the cartilage matrix, enabling an insight into how this micromechanism influences macromechanical deformation. 4. When features such as transition coefficient were changed, permeability (representing change) is altered due to the change in concentrations of collagen, proteoglycans (i.e. degenerative conditions), the deformation process is impacted. 5. The boundary conditions also influence the relationship between osmotic pressure gradient and fluid movement at the micro-scale level. The outcomes are important to cartilage research since we can use these to study the microscale damage in the cartilage matrix. From this, we are able to monitor related diseases and their progression leading to potential insight into drug-cartilage interaction for treatment. This innovative model is an incremental progress on attempts at creating further computational modelling approaches to cartilage research and other fluid-saturated tissues and material systems.

Modelling the failure of thin layered mortar joints in masonry

This paper deals with the failure of high adhesive, low compressive strength, thin layered polymer mortar joints in masonry through a contact modelling in finite element framework. Failure due to combined shear, tensile and compressive stresses are considered through a constitutive damaging contact model that incorporates traction–separation as a function of displacement discontinuity. The modelling method is verified using single and multiple contact analyses of thin mortar layered masonry specimens under shear, tensile and compressive stresses and their combinations. Using this verified method, the failure of thin mortar layered masonry under a range of shear to tension ratios and shear to compression ratios has been examined. Finally, this model is applied to thin bed masonry wallettes for their behaviour under biaxial tension–tension and compression–tension loadings perpendicular and parallel to the bed joints.

Hyperelastic constitutive relationship for the strain-rate dependent behavior of shoulder and other joint cartilages

Non-linear finite deformations of articular cartilages under physiological loading conditions can be attributed to hyperelastic behavior. This paper contains experimental results of indentation tests in finite deformation and proposes an empirical based new generalized hyperelastic constitutive model to account for strain-rate dependency for humeral head cartilage tissues. The generalized model is based on existing hyperelastic constitutive relationships that are extensively used to represent biological tissues in biomechanical literature. The experimental results were obtained for three loading velocities, corresponding to low (1x10-3 s-1), moderate and high strain-rates (1x10-1 s-1), which represent physiological loading rates that are experienced in daily activities such as lifting, holding objects and sporting activities. Hyperelastic material parameters were identified by non linear curve fitting procedure. Analysis demonstrated that the material behavior of cartilage can be effectively decoupled into strain-rate independent(elastic) and dependent parts. Further, experiments conducted using different indenters indicated that the parameters obtained are significantly affected by the indenter size, potentially due to structural inhomogeneity of the tissue. The hyperelastic constitutive model developed in this paper opens a new avenue for the exploration of material properties of cartilage tissues.

Characterisation of head-hardened rail steel in terms of cyclic plasticity response and microstructure for improved material modelling

Stress- and strain-controlled tests of heat treated high-strength rail steel (Australian Standard AS1085.1) have been performed in order to improve the characterisation of the said material׳s ratcheting and fatigue wear behaviour. The hardness of the rail head material has also been studied and it has been found that hardness reduces considerably below four-millimetres from the rail top surface. Historically, researchers have used test coupons with circular cross-sections to conduct cyclic load tests. Such test coupons, typically five-millimetres in gauge diameter and ten‐millimetres in grip diameter, are usually taken from the rail head sample. When there is considerable variation of material properties over the cross-section it becomes likely that localised properties of the rail material will be missed. In another case from the literature, disks 47 mm in diameter for a twin-disk rolling contact test machine were obtained directly from the rail sample and used to validate ratcheting and rolling contact fatigue wear models. The question arises: How accurate are such tests, especially when large material property gradients exist? In this research paper, the effects of rail sampling location on the ratcheting behaviour of AS1085.1 rail steel were investigated using rectangular-shaped specimens obtained at four different depths to observe their respective cyclic plasticity behaviour. The microstructural features of the test coupons were also analysed, especially the pearlite inter-lamellar spacing which showed strong correlation with both hardness and cyclic plasticity behaviour of the material. This work ultimately provides new data and testing methodology to aid the selection of valid parameters for material constitutive models to better understand rail surface ratcheting and wear.

On numerical implementation of an isotropic elastic-viscoplastic constitutive model for bulk metallic glasses

An efficient algorithm within the finite deformation framework is developed for finite element implementation of a recently proposed isotropic, Mohr-Coulomb type material model, which captures the elastic-viscoplastic, pressure sensitive and plastically dilatant response of bulk metallic glasses. The constitutive equations are first reformulated and implemented using an implicit numerical integration procedure based on the backward Euler method. The resulting system of nonlinear algebraic equations is solved by the Newton-Raphson procedure. This is achieved by developing the principal space return mapping technique for the present model which involves simultaneous shearing and dilatation on multiple potential slip systems. The complete stress update algorithm is presented and the expressions for viscoplastic consistent tangent moduli are derived. The stress update scheme and the viscoplastic consistent tangent are implemented in the commercial finite element code ABAQUS/Standard. The accuracy and performance of the numerical implementation are verified by considering several benchmark examples, which includes a simulation of multiple shear bands in a 3D prismatic bar under uniaxial compression.

Finite element modelling of the sismic behaviour of water front structures

Water front structures have suffered significant damage in many of the recent earthquakes. These include gravity type quay walls, vertically composite walls, cantilever retaining walls, anchored bulkheads and similar structures. One of the primary causes for the poor performance of these classes of structures is the liquefaction of the foundation soil and in some instances liquefaction of the backfill soil. The liquefaction of the soil in-front of the quay wall tends to cause large lateral displacements and rotation of the wall. Often such gravity walls are placed on rubble mound deposited onto the sea bed.This paper presents finite element analyses of such a problem in which strength degradation of the foundation soil and the backfill material will be modelled using PZ mark III constitutive model. The performance of the wall in terms of its lateral displacement, vertical settlement and/or the rotation suffered by the wall will be presented. In addition, the contours of the horizontal and vertical effective stresses and the excess pore pressure ratio will be presented at different time instants together with hyrdraulic gradients. Immediately after the earthquake, the hydraulic gradients indicate migration of pore water into the region below the wall, suggesting further softening of the foundation soil below the wall.

An efficient approach of modelling the flexural cracking behaviour of un-notched plain concrete prisms subject to monotonic and cyclic loading

In the field of vibration-based damage detection of concrete structures efficient damage models are needed to better understand changes in the vibration properties of cracked structures. These models should quantitatively replicate the damage mechanisms in concrete and easily be used as damage detection tools. In this paper, the flexural cracking behaviour of plain concrete prisms subject to monotonic and cyclic loading regimes under displacement control is tested experimentally and modelled numerically. Four-point bending tests on simply supported un-notched prisms are conducted, where the cracking process is monitored using a digital image correlation system. A numerical model, with a single crack at midspan, is presented where the cracked zone is modelled using the fictitious crack approach and parts outside that zone are treated in a linear-elastic manner. The model considers crack initiation, growth and closure by adopting cyclic constitutive laws. A multi-variate Newton-Raphson iterative solver is used to solve the non-linear equations to ensure equilibrium and compatibility at the interface of the cracked zone. The numerical results agree well with the experiments for both loading scenarios. The model shows good predictions of the degradation of stiffness with increasing load. It also approximates the crack-mouth-opening-displacement when compared with the experimental data of the digital image correlation system. The model is found to be computationally efficient as it runs full analysis for cyclic loading in less than 2. min, and it can therefore be used within the damage detection process. © 2013 Elsevier Ltd.