Browsing by Author "Mitchell, Greg"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Open Access
    The application of the homogenisation method to the numerical modelling of cancellous bone
    (1995) Conway, Damian John; Mitchell, Greg; Spirakis, Thanos
    This thesis reports on an investigation into the viability of developing idealised numerical models of cancellous bone in order to make reasonable predictions about its macro- and microstructural mechanical behaviour using the homogenisation method. In total joint replacement, cancellous bone (the soft porous bone which lies below the articular surfaces at weight-bearing joints) provides the medium for the transfer of loads from the artificial component, or prosthesis to the hard, outer cortical bone. Although total joint replacement is usually a successful operation - providing relief from pain and often considerably improved joint function - loosening of the metal components remains a major obstacle to the long-term success of these operations. In the ongoing work to develop joints which are less susceptible to loosening, it has become necessary to study the micromechanics of cancellous bone in order to predict its response to the changing stress environments brought about by the inserted prostheses. Biomechanical engineers have used finite element analysis extensively in the analysis of reconstructed joints. However, owing to the prohibitively high computational costs associated with the microstructural modelling of cancellous bone, it is generally modelled simply as a homogeneous, isotropic material. It is not possible to accurately predict the mechanical response of cancellous bone to various implant conditions under this simplistic modelling assumption. Thus, alternative methods are being sought which will allow for more realistic modelling of cancellous bone. The homogenisation method is one such alternative. This method makes it possible to uncouple the analysis of some problem involving a composite material into an apparent global analysis and a local microstructural analysis. The apparent material properties of the periodically repeating composite microstructure are calculated, taking into account the structural heterogeneities of the composite. These properties are then used in the global analysis where the composite is treated as a continuum. The apparent global-level results are subsequently postprocessed to obtain the microstructural behaviour in any local regions of interest. The main aim of this research project was to investigate the applicability of the homogenisation method to the modelling of cancellous bone. The first part of this work involved an extensive literature study on the architecture and micromechanics of cancellous bone to investigate whether cancellous bone can indeed be modelled as an idealised composite material with a periodically repeating microstructure. The outcome of this investigation revealed that the structure and behaviour of cancellous bone is highly variable - depending on the patient, anatomic location and the level of density. However, certain regions of cancellous bone do have typical repeating architectures which have a major influence on the apparent mechanical behaviour of the bone. Thus it has been concluded that these specific regions of cancellous bone can be modelled by idealised structures, provided the observed microstructures and predominant deformations modes are well characterised in the models.
  • Thumbnail Image
    Item
    Open Access
    Time intergration schemes for rate dependent elasto-plastic constitutive equations
    (1997) Hulley, Derek; Mitchell, Greg
    The purpose of this thesis is to set out the results of an investigation into the commonly used methods of performing material update calculations within the framework of the Finite Element Method, as well as an investigation into possible new methods of performing the material update procedures within the context of a rate dependent plastic material obeying the Von Mises yield condition. Material update procedures which have been used and analysed frequently are the Generalised Midpoint Algorithm, including the Midpoint Method, the Trapezoidal Rule and the Backward Euler Method with Radial Return. Each method displays its own advantages when applied to different input parameters (being material properties, initial stresses and strains, and increments in time and strain).
  • Thumbnail Image
    Item
    Open Access
    A yield function to simulate earing in the deep drawing of aluminium
    (1996) Thomas, Gary David; Mitchell, Greg
    Deep drawing of metal sheeting is a commercially significant manufacturing process and as with all metal forming processes is subject to geometric defects. One defect of particular concern, termed earing, is characterised by an uneven edge to the drawn article. This work covers the implementation of a suitable constitutive model in a general purpose finite element code ABAQUS Version 5.4 to simulate this earing phenomenon in aluminium can body stock. Earing is caused by plastic anisotropy of the blank material and anisotropy induced during the drawing process. It is the result of crystallographic textures or preferred grain orientations that develop during the sheet rolling process. In polycrystalline materials it may be modelled via either crystallographic texture models or phenomenological yield surface models. Crystallographic models have the advantage over phenomenological ones in that they are able to describe both initial and evolving anisotropy. However, they are very demanding in terms of computational power and are reported to over predict the plastic strain ratios in anisotropic materials. A phenomenological yield surface model proposed by Karafillis and Boyce was consequently selected as a suitable constitutive model to investigate the earing phenomenon. This model can describe the elasto-plastic behaviour of both isotropic and anisotropic three dimensional polycrystalline materials. It is a pressure independent yield surface which is convex in stress space and assumes an associated flow rule. It was implemented in ABAQUS as a FORTRAN 77 User-Material Subroutine. An Euler Backward integration scheme was adopted and a consistent tangent modulus used. Four axisymmetric cupping operations were simulated: two with the model's parameters set to represent the aluminium alloy under consideration and two to investigate the effect of the yield surface on earing. For comparison purposes, a fifth case was run using the Hill (1948) anisotropic material model.