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Title: Computational strategies for multiscale analysis of material behaviour
Author: Partovi, Maziar
Awarding Body: Swansea University
Current Institution: Swansea University
Date of Award: 2007
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The main objective of this thesis is the computational implementation and assessment of multi-scale constitutive modelling strategies based on the volume averaging of the strain and stress tensors over a representative volume element (RVE) under infinitesimal strains assumption. The computational procedure is based on the finite element discretisation at both macro- and microscopic levels. Four classes of multi-scale constitutive models are considered, corresponding to: the Taylor, the linear boundary displacement, the periodic boundary displacement fluctuations and the uniform boundary traction assumptions. The corresponding finite element formulation is described in detail including the derivation of the homogenised tangent moduli which are crucial for the use of the Newton-Raphson method in the iterative solution of non-linear macro-scale problems. The code developed possesses a recursive hierarchical structure. Under this scheme the main equilibrium procedure, operating on the macroscopic level, calls itself each time it requires to evaluate the material behaviour by homogenisation of microstructure. A comprehensive set of numerical examples is presented. Application of the multiscale methodology to materials with linear elastic microscopic constituents is considered first. The effect of the fibre orientation in the micro-cell and anisotropy of the RVE on the homogenised material properties are also discussed. Existing analytical methods are used to benchmark the numerical results. The effect of the topology of cavities on the homogenised material properties and the overall yield surface under different boundary conditions are also studied in the context of elasto-plastic material models. Finally, a materially non-linear fully coupled two-scale boundary value problem is solved numerically, demonstrating the suitability of the developed framework to large scale computations. The present research shows that the adopted multi-scale methodology provides an effective tool for the constitutive modelling of heterogeneous materials in the linear and non-linear range.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available