Browsing by Author "Reddy, Batmanathan D."
Now showing 1 - 2 of 2
Results Per Page
Sort Options
- ItemOpen AccessNumerical investigation of theories of strain-gradient plasticity(2018) Mhlongo, Nothando Precious; Reddy, Batmanathan D.In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. This theory is based on that originally developed by Gurtin and Anand, and includes both dissipative and energetic contributions. A detailed numerical study is based on the problem of simple shear of a homogeneous and a non-homogeneous block. Combinations of micro-hard and micro-free boundary conditions are used. The elastic gap, that is, elastic behaviour following a change in the plastic regime from micro-free to micro-hard boundary conditions, is clearly evident. A second phenomenon studied is that of strengthening and hardening with increase in dissipative and energetic length scales, respectively. For the purely dissipative theory, it has been shown that the flow relation in terms of Cauchy stress is necessarily global in terms of the dissipation function. This relation cannot be inverted in closed form to obtain a relation in terms of a global yield function. Approximations to the yield function are proposed using a maximisation relation, and these predictions of yield are compared with actual yield determined numerically.
- ItemOpen AccessNumerical modelling of the Oldroyd-B fluid(2019) Vundla, Nkosilathi; Reddy, Batmanathan D.The purpose of this thesis is to develop a 3D finite element model of the Oldroyd-B fluid for use in a complex geometry. The model is developed in deal.ii, which is a C++ finite element library. In addition to the standard finite element approach for the momentum equation, the discontinuous Galerkin method is used for the constitutive relation of the fluid model, with the extra stress as the unknown variable. The model developed is verified by using the symmetric “flow over a cylinder” benchmark problem. The effect of using piecewise-constant discontinuous and bilinear discontinuous elements for the extra stress field is investigated. The the results of the scheme are compared to those found in literature. The model is implemented in the solution of a complex problem of blood flow in an arteriovenous fistula, using geometry acquired from MRI data. A resistance boundary condition is used for the outlets. The flow profiles obtained from using both the Newtonian and Oldroyd-B fluids are validated against velocity encoded MRI and also compared to Fluid-Structure Interaction results for Newtonian fluids, from the literature. The effect of using a viscoelastic fluid on the flow profile and wall shear stresses are investigated. The results from this work show that using a viscoelastic fluid, rather than a Newtonian fluid, provides additional details regarding the wall shear stress in the arteriovenous fistula.