Generalised homogenisation procedures for granular and layered materials

Research output: ThesisDoctoral Thesis

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Abstract

[Truncated] Engineering materials are generally non-homogeneous, yet standard continua for the description of such materials are admissible, provided that the size of the non-homogeneities is much smaller than the characteristic length of the deformation pattern. If this is not the case, the classical continuum approach has to be abandoned in favour of explicit description of individual non-homogeneities. Alternatively, one can extend the range of applicability of the continuum concept by including additional variables or degrees of freedom, or one applies non-local theories in which the constitutive equations are expressed by integral operators. The development, application and discussion of such theories are the subject of this thesis. The theories are applied to two classes of materials, namely granular and layer materials.

The strategy for developing the theories is as follows. The discrete nature of granular materials is reflected in finite-difference equations that can be homogenised in two ways. The simplest approach is to replace the finite differences by the corresponding Taylor expansions. This will lead to Cosserat continuum theories. A more sophisticated strategy is to homogenise the equations by the discrete Fourier transform. The result is a Kunin-type non-local theory. Both Cosserat and Kunin theories have been around for quite a while. What have not been provided so far are significant applications for these theories. This is where the main contribution of this thesis lies. It is demonstrated in a systematic way that granular and layer materials are manifestations of Cosserat theories on different level of sophistication.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • The University of Western Australia
DOIs
Publication statusUnpublished - 2002

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