The deformation and failure properties of granular soils largely affect the stability of upper structures built on or in such soils. Owing to its discrete nature as well as the randomness of particle shape and inter-particle connectivity, the internal structure of a granular material usually exhibits a certain level of anisotropy. In addition, the microstructure of a granular material evolves following certain patterns, which are influenced by the initial fabric, void ratio, stress level, as well as the stress or deformation history. It has been a major challenge to properly describe the deformation of anisotropic granular materials in constitutive models especially when the materials are subjected to cyclic loading. The existing constitutive models usually have limited capabilities in describing the behaviour of granular materials subjected to repeated loading with principal stress rotation. How to quantify the microstructure change and how to consider the changing microstructure in constitutive models have been two missing links for building a comprehensive model framework. This research aimed at developing a constitutive model that can properly describe the deformation of granular soils under repeated multi-directional loading. To achieve this goal, a systematic study was performed, including a comprehensive experimental study and a theoretical development of a stress-strain model with proper consideration of the influence of fabric. The developed model was verified with experimental results and then implemented into a finite element code to solve boundary-valued problems. In the first part of this study, a comprehensive experimental study was carried out to investigate the behaviours of granular materials under both monotonic and cyclic loading to investigate the influence of the intermediate principal stress and the major principal stress direction on soil responses. The results of monotonic loading tests showed that both the strength and dilatancy of sand decreased notably with an increase of either the intermediate principal stress or the inclination angle of the major principal stress direction relative to the major principal fabric direction. The stress states at failure from the tests suggested that the benchmarked Matsuoka-Nakai and Lade-Duncan failure criteria are only valid under certain conditions. From the cyclic loading tests, it was observed that, in addition to the increased intermediate principal stress, varied cyclic loading direction caused a significant increase in accumulative volumetric compaction. To consider the microstructural dependencies of granular materials, a more general mathematical formulation of stress-dilatancy was developed based on the assumption of the existence of a critical state fabric surface that is expressed as a function of the invariants of the fabric tensor. This assumption was also used to establish the fabric evolution law. The implementation of the resulting stress-dilatancy formulation and the fabric evolution law in elasto-plasticity theory produced interesting modelling results consistent with experimental observations with respect to the microstructural aspects of granular materials. The developed constitutive model was further extended to cyclic loading within the framework of hypo-plasticity with kinematic hardening. The model was capable of describing the behaviour of sand subjected cyclic loading under various conditions including the variation of loading directions. Finally, the constitutive model was implemented into a commercial software package ABAQUS via the subroutine UMAT. The capacity of the proposed stress-strain model in solving boundary value problems was examined. Six series of elements tests were designed to examine the proposed model under different initial void ratios, degrees of anisotropy, loading directions, and stress paths. Furthermore, a series of simulations were performed for the settlement of footing on sands with different bedding plane orientations. Results from the simulations were found to be consistent with experimental observations. / Thesis / Doctor of Philosophy (PhD)

The behaviour of sands during loading has been studied in great detail. However, little work has been devoted to understanding the response of sands in unloading. Drained triaxial tests indicate that, contrary to the expected elastic behaviour, sand often exhibit contractive behaviour when unloaded. Undrained cyclic simple shear tests show that the increase in pore water pressure generated during the unloading cycle often exceeds that generated during loading. The tendency to contract upon unloading is important in engineering practice as an increase in pore water pressure during earthquake loading could result in liquefaction. This research contributes to filling the gap in our understanding of soil behaviour in unloading and subsequent reloading. The approach followed includes both theoretical investigation and numerical implementation of experimental observations of stress dilatancy in unload-reload loops. The theoretical investigation is done at the micromechanical level. The numerical approach is developed from observations from drained triaxial compression tests. The numerical implementation of yield in unloading uses NorSand — a hardening plasticity model based on the critical state theory, and extends upon previous understanding. The proposed model is calibrated to Erksak sand and then used to predict the load-unload-reload behaviour of Fraser River sand. The trends predicted from the theoretical and numerical approaches match the experimental observations closely. Shear strength is not highly affected by unload-reload loops. Conversely, volumetric changes as a result of unloading-reloading are dramatic. Volumetric strains in unloading depend on the last value of stress ratio (q/p’) in the previous loading. It appears that major changes in particles arrangement occur once peak stress ratio is exceeded. The developed unload-reload model requires three additional input parameters, which were correlated to the monotonic parameters, to represent hardening in unloading and reloading and the effect of induced fabric changes on stress dilatancy. The calibrated model gave accurate predictions for the results of triaxial tests with load-unload-reload cycles on Fraser River sand.

The behaviour of sands during loading has been studied in great detail. However, little work has been devoted to understanding the response of sands in unloading. Drained triaxial tests indicate that, contrary to the expected elastic behaviour, sand often exhibit contractive behaviour when unloaded. Undrained cyclic simple shear tests show that the increase in pore water pressure generated during the unloading cycle often exceeds that generated during loading. The tendency to contract upon unloading is important in engineering practice as an increase in pore water pressure during earthquake loading could result in liquefaction. This research contributes to filling the gap in our understanding of soil behaviour in unloading and subsequent reloading. The approach followed includes both theoretical investigation and numerical implementation of experimental observations of stress dilatancy in unload-reload loops. The theoretical investigation is done at the micromechanical level. The numerical approach is developed from observations from drained triaxial compression tests. The numerical implementation of yield in unloading uses NorSand — a hardening plasticity model based on the critical state theory, and extends upon previous understanding. The proposed model is calibrated to Erksak sand and then used to predict the load-unload-reload behaviour of Fraser River sand. The trends predicted from the theoretical and numerical approaches match the experimental observations closely. Shear strength is not highly affected by unload-reload loops. Conversely, volumetric changes as a result of unloading-reloading are dramatic. Volumetric strains in unloading depend on the last value of stress ratio (q/p’) in the previous loading. It appears that major changes in particles arrangement occur once peak stress ratio is exceeded. The developed unload-reload model requires three additional input parameters, which were correlated to the monotonic parameters, to represent hardening in unloading and reloading and the effect of induced fabric changes on stress dilatancy. The calibrated model gave accurate predictions for the results of triaxial tests with load-unload-reload cycles on Fraser River sand.

Within the aerospace industry, the reduction of costs associated with operation, manufacture and development of gas turbine engines is a primary objective. Component and assembly design optimisations can satisfy weight reductions which correspond to operational and manufacturing cost reductions. Development cost can be reduced by implementing additional numerical validation stages as an alternative to experimental validation alone. Therefore, the overarching purpose of this research is the development of a computationally efficient constitutive modelling tool, which predicts the macroscopic deformation and failure of fan system components and assemblies during dynamic and highly non-linear thermo-mechanical loading. At the macroscopic scale a series of physical deformation and failure phenomena have been identified from the literature which are necessary for accurate representation of the dynamic behaviour of Ti-6Al-4V. Across the surveyed literature these capabilities have not been implemented together within a single constitutive framework prior to the commencement of this research. Experimental support provides validation data for the subsequent constitutive modelling activities, whilst also demonstrating the importance of strain-rate sensitivity, tension-compression asymmetry and anisotropic behaviour associated with texture orientation in Ti-6Al-4V. Numerical studies were also conducted to develop a robust procedure for rapid assimilation of uni-axial experimental data within constitutive benchmarking models, for development purposes. Further parametric studies of sub-component plate impact benchmarks revealed several limitations within the commercially available solutions. These limitations are related to mesh sensitivity and damage evolution. A technique has been proposed which couples damage evolution and imposes a directional length-scale. This provides enhanced mesh insensitivity and damage evolution rate control. However, a single damage evolution mechanism was demonstrated to be insufficient when representing shear damage mechanisms in uni-axial and multi-axial loading regimes. Therefore, an additional damage mechanism has been developed and coupled with the mesh sensitivity and localisation technique. The resulting cumulative and competitive damage evolution and localisation capabilities reflect the localisation characteristics observed in the literature. The variability of alloy manufacture and the subsequent macroscopically observed behaviour remain a limitation within an isotropic framework. This has motivated the development of both asymmetric and anisotropic formulations, integrated within the newly proposed multi-mode damage localisation framework. The ability of the newly implemented non-isotropic framework successfully provides both asymmetric yielding and hardening capabilities and anisotropic evolution. These developments have been demonstrated against experimentally obtained results for validation and calibration purposes. Together these capabilities allow for accurate representation of a wide range of macroscopically observable phenomena based upon micro mechanical mechanisms.

The behaviour of sands during loading has been studied in great detail. However, little work has been devoted to understanding the response of sands in unloading. Drained triaxial tests indicate that, contrary to the expected elastic behaviour, sand often exhibit contractive behaviour when unloaded. Undrained cyclic simple shear tests show that the increase in pore water pressure generated during the unloading cycle often exceeds that generated during loading. The tendency to contract upon unloading is important in engineering practice as an increase in pore water pressure during earthquake loading could result in liquefaction. This research contributes to filling the gap in our understanding of soil behaviour in unloading and subsequent reloading. The approach followed includes both theoretical investigation and numerical implementation of experimental observations of stress dilatancy in unload-reload loops. The theoretical investigation is done at the micromechanical level. The numerical approach is developed from observations from drained triaxial compression tests. The numerical implementation of yield in unloading uses NorSand — a hardening plasticity model based on the critical state theory, and extends upon previous understanding. The proposed model is calibrated to Erksak sand and then used to predict the load-unload-reload behaviour of Fraser River sand. The trends predicted from the theoretical and numerical approaches match the experimental observations closely. Shear strength is not highly affected by unload-reload loops. Conversely, volumetric changes as a result of unloading-reloading are dramatic. Volumetric strains in unloading depend on the last value of stress ratio (q/p’) in the previous loading. It appears that major changes in particles arrangement occur once peak stress ratio is exceeded. The developed unload-reload model requires three additional input parameters, which were correlated to the monotonic parameters, to represent hardening in unloading and reloading and the effect of induced fabric changes on stress dilatancy. The calibrated model gave accurate predictions for the results of triaxial tests with load-unload-reload cycles on Fraser River sand. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Yes / A multi-element constitutive model for a lactide-based shape memory polymer has been developed that represents loading to large tensile deformations, stress relaxation and stress recovery at 60, 65 and 70°C. The model consists of parallel Maxwell arms each comprising neo-Hookean and Eyring elements. Guiu-Pratt analysis of the stress relaxation curves yields Eyring parameters. When these parameters are used to define the Eyring process in a single Maxwell arm, the resulting model yields at too low a stress, but gives good predictions for longer times. Stress dip tests show a very stiff response on unloading by a small strain decrement. This would create an unrealistically high stress on loading to large strain if it were modelled by an elastic element. Instead it is modelled by an Eyring process operating via a flow rule that introduces strain hardening after yield. When this process is incorporated into a second parallel Maxwell arm, there results a model that fully represents both stress relaxation and stress dip tests at 60°C. At higher temperatures a third arm is required for valid predictions.

Recent experiences from the Darfield and Canterbury, New Zealand earthquakes have shown that the soft soil condition of saturated liquefiable sand has a profound effect on seismic response of buildings, bridges and other lifeline infrastructure. For detailed evaluation of seismic response three dimensional integrated analysis comprising structure, foundation and soil is required; such an integrated analysis is referred to as Soil Foundation Structure Interaction (SFSI) in literatures. SFSI is a three-dimensional problem because of three primary reasons: first, foundation systems are three-dimensional in form and geometry; second, ground motions are three-dimensional, producing complex multiaxial stresses in soils, foundations and structure; and third, soils in particular are sensitive to complex stress because of heterogeneity of soils leading to a highly anisotropic constitutive behaviour. In literatures the majority of seismic response analyses are limited to plane strain configuration because of lack of adequate constitutive models both for soils and structures, and computational limitation. Such two-dimensional analyses do not represent a complete view of the problem for the three reasons noted above. In this context, the present research aims to develop a three-dimensional mathematical formulation of an existing plane-strain elasto-plastic constitutive model of sand developed by Cubrinovski and Ishihara (1998b). This model has been specially formulated to simulate liquefaction behaviour of sand under ground motion induced earthquake loading, and has been well-validated and widely implemented in verifcation of shake table and centrifuge tests, as well as conventional ground response analysis and evaluation of case histories. The approach adopted herein is based entirely on the mathematical theory of plasticity and utilises some unique features of the bounding surface plasticity formalised by Dafalias (1986). The principal constitutive parameters, equations, assumptions and empiricism of the existing plane-strain model are adopted in their exact form in the three-dimensional version. Therefore, the original two-dimensional model can be considered as a true subset of the three-dimensional form; the original model can be retrieved when the tensorial quantities of the three dimensional version are reduced to that of the plane-strain configuration. Anisotropic Drucker-Prager type failure surface has been adopted for the three-dimensional version to accommodate triaxial stress path. Accordingly, a new mixed hardening rule based on Mroz’s approach of homogeneous surfaces (Mroz, 1967) has been introduced for the virgin loading surface. The three-dimensional version is validated against experimental data for cyclic torsional and triaxial stress paths.

The effects of lime treatment on the mechanical properties of soils are usually not accounted for in the design of geotechnical structures. As a result the potential of lime treatment has not been fully exploited. In this thesis, a comprehensive experimental program has been carried out to identity the key features of the mechanical behaviour of structured materials. The chemical modifications arising from lime treatment were quantified using thermal analysis methods. From these results a non-linear chemo-mechanical coupling was established between the concentration of cementitious compounds and the yield stress. Using these results, a new formulation to model the degradation of the structure at yield has been developed and implemented in a constitutive model for structured materials. This new model, developed in the framework of the Modified Cam Clay model, requires a limited number of additional parameters that all have a physical meaning and can all be determined from a single isotropic compression test. The model has proven to be successful in reproducing the key features of structured materials and for the modelling of the mechanical behaviour of lime treated specimens under various stress paths. Due to similarities in behaviour, it is shown that the formulation is also suitable for naturally structured soils. To account for a structured material in the design of geotechnical structures, a fully functional finite element program for elasto-plastic problems was developed including the pre- and post-processing of the results. A thorough validation has confirmed the good implementation of the finite element method and its suitability for the modelling of complex geometries involving structured materials.

The purpose of this work was to develop a practical method for constitutive modelling of polyethylene, based on a phenomenological approach, which can be applied for structural analysis. Polyethylene (PE) is increasingly used as a structural material, for example in pipes installed by trenchless methods where relatively low stiffness of PE reduces the required installation forces, chemical inertness makes it applicable for corrosive environments, and adequate strength allows to use it for sewer, gas and water lines. Polyethylene exhibits time-dependent constitutive behaviour, which is also dependent on the applied stress level resulting in nonlinear stress-strain relationships. Nonlinear viscoelastic theory has been well established and a variety of modelling approaches have been derived from it. In order to be able to realistically utilize the nonlinear modelling approaches in design, a simple method is needed for finding the constitutive formulation for a specific polyethylene type. In this study, time-dependent constitutive relationships for polymers are investigated for polyethylene materials. Creep tests on seven polyethylene materials were conducted and the experimental results indicate strong nonlinear viscoelasticity in the material responses. Creep tests on seven materials were conducted for 24 hours for modelling purposes. However, creep tests up to fourteen days were performed on one material to study long-term creep behaviour. Multiple-stepped creep tests were also investigated. Constant rate (load and strain rate) tensile tests were conducted on two of the seven polyethylene materials. A practical approach to nonlinear viscoelastic modelling utilizing both multi-Kelvin element theory and power law functions to model creep compliance is presented. Creep tests are used to determine material parameters and models are generated for four different polyethylene materials. The corroboration of the models is achieved by comparisons with the results of different tensile creep tests, with one dimensional step loading test results and with test results from load and displacement rate loading.

The purpose of this work was to develop a practical method for constitutive modelling of polyethylene, based on a phenomenological approach, which can be applied for structural analysis. Polyethylene (PE) is increasingly used as a structural material, for example in pipes installed by trenchless methods where relatively low stiffness of PE reduces the required installation forces, chemical inertness makes it applicable for corrosive environments, and adequate strength allows to use it for sewer, gas and water lines. Polyethylene exhibits time-dependent constitutive behaviour, which is also dependent on the applied stress level resulting in nonlinear stress-strain relationships. Nonlinear viscoelastic theory has been well established and a variety of modelling approaches have been derived from it. In order to be able to realistically utilize the nonlinear modelling approaches in design, a simple method is needed for finding the constitutive formulation for a specific polyethylene type. In this study, time-dependent constitutive relationships for polymers are investigated for polyethylene materials. Creep tests on seven polyethylene materials were conducted and the experimental results indicate strong nonlinear viscoelasticity in the material responses. Creep tests on seven materials were conducted for 24 hours for modelling purposes. However, creep tests up to fourteen days were performed on one material to study long-term creep behaviour. Multiple-stepped creep tests were also investigated. Constant rate (load and strain rate) tensile tests were conducted on two of the seven polyethylene materials. A practical approach to nonlinear viscoelastic modelling utilizing both multi-Kelvin element theory and power law functions to model creep compliance is presented. Creep tests are used to determine material parameters and models are generated for four different polyethylene materials. The corroboration of the models is achieved by comparisons with the results of different tensile creep tests, with one dimensional step loading test results and with test results from load and displacement rate loading.