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Type: Thesis
Title: A Mechanism-based Approach to Constitutive Modelling of Quasi-Brittle Geomaterials with and without Fibre Reinforcement
Author: Le, Linh Anh
Issue Date: 2019
School/Discipline: School of Civil, Environmental and Mining Engineering
Abstract: The formation and development of localisation bands and/or cracks have been experimentally identified as the key failure mechanism governing responses of quasi-brittle geomaterials like concrete, sandstones and soft rocks. In fact, key features of the material behaviour, including Lode-angle dependence, size effect and brittle-ductile transition can be considered as consequences stemming from the localised failure mechanism in several loading conditions. For geomaterials with fibre reinforcement (i.e., fibre reinforced concrete), even though adding short fibres into the material significantly changes its mechanical characteristics and performances, the development of cracks and localisation bands remains the central mechanism driving the material responses. In this case, the bridging effect caused by fibres across cracks, together with the material cohesive-frictional resistance, refrains cracks from further developing and forces the material to form more cracks throughout the structure to dissipate the given energy. This prolongs the coalescence of diffuse micro/meso-cracks to form a macro-crack and considerably improve the material strength and ductility. Classical continuum models, in principle, can capture the overall responses of the material with stress-strain relationships formulated from experimental observations at the macroscopic level. However, the material behaviour in these models is homogenous throughout the whole element domain, leading to an incorrect dependence of dissipated energy and specimen responses on the discretisation resolution. This is because they fail to capture the difference of deformation and behaviour between the localisation zone and its surrounding bulk material. As a result, with the presence of crack/localisation band, the definition of averaged quantities such as overall stress and strain is not adequate to describe the volume element and using them for analysing post-localisation behaviour of quasi-brittle geomaterials is inappropriate, if not totally incorrect. Consequently, classical approaches that ignore the strong heterogeneity induced by the localisation of deformation suffer from mesh convergence issues in Boundary Value Problems (BVPs) analysis. In this research, the localised failure mechanism is employed as the basis to develop a continuum-based constitutive model for quasi-brittle geomaterials with and without fibre reinforcement. The cracks/localisation bands are explicitly included as an intrinsic part of the model with its own behaviour in conjunction with the responses of the surrounding bulk material. This allows an additional constitutive relationship, together with its internal variables, to be defined inside the localisation band to describe its microstructural changes under the course of loading. The material inelastic behaviour and important features such as brittle-ductile transition, Lode-angle dependence, size effect and hydrostatic pressure dependence can thus be correctly captured in association with observable failure patterns at constitutive level. The model, constructed in this manner, is also capable of featuring multiple localisation bands/cracks inside the constitutive equations to account for any change of loading path and avoid unphysical stress-locking naturally. In addition, for modelling quasi-brittle geomaterials with fibre reinforcement, the incorporation of cracks within the constitutive model enables the inclusion of separate models describing the fibre bridging effect and material cohesive-frictional resistance. As a result, the interactions between these two components and their contributions to the stress transfer across a crack are naturally captured for different types of fibres and their volume contents. The transition from hardening to softening, corresponding to the change from diffuse cracking phase to localised failure can also be reflected as a consequence. Furthermore, owing to the explicit inclusion of cracks in the model, the resulting constitutive behaviour automatically scales with the discretisation resolution and the results are thus mesh-independent when solving BVPs, without requiring any additional regularisation. Model validations against experimental data show that the proposed model is simple yet effective in capturing the localised failure of quasi-brittle geomaterials with and without fibre reinforcement at both constitutive and structural levels. The model is proven to be reliable and computationally inexpensive, with a few model parameters which can be identified and calibrated in a consistent and physically meaningful manner. The proposed model can thus be applied straightforwardly for the analysis and design of solids/structures made of rocks or concrete, with or without fibre reinforcements.
Advisor: Nguyen, Giang D.
Dissertation Note: Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 2019
Keywords: Constitutive modelling
quasi-brittle geomaterials
localised failure
fibre reinforced concrete
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