Abstract
Finite element (FE) simulation plays a crucial role in the analysis of the mechanical behaviour of structural elements built with complex microstructure composite materials. In order to define microstructural details, finite element analysis (FEA) often leads to the need for unstructured meshes and large numbers of finite elements. This fact frequently makes it impossible to perform numerical analyses on the mechanical behaviour of such structural components, due to the large amounts of required memory and CPU time. In this particular context, homogenisation methodologies lead to significant computational benefits.
One of these homogenisation methods is the asymptotic expansion homogenisation (AEH). Following this approach, overall material properties can be derived from the mechanical behaviour of selected microscale representative volumes, also known as representative unit-cells (RUC). Nevertheless, unit-cell based models require the control of several parameters. Additionally, the unstructured tetrahedral finite element meshes frequently required by the complexity of RUC involve the control of specific periodic boundary conditions.
This work shows the mathematical formulation and implementation details of a dedicated three-dimensional FEA platform developed by the authors, which enables the modelling of the elastic behaviour of structural components built from composite materials. Automatic representative unit-cell generation procedures are also developed with control over relevant geometrical parameters. Additionally, in order to enforce the periodicity of boundary conditions, specific algorithms for the association of degrees of freedom are implemented.
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Oliveira, J.A., Pinho-da-Cruz, J., Teixeira-Dias, F. (2008). Prediction of Mechanical Properties of Composite Materials by Asymptotic Expansion Homogenisation. In: Mechanical Response of Composites. Computational Methods in Applied Sciences, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8584-0_11
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DOI: https://doi.org/10.1007/978-1-4020-8584-0_11
Publisher Name: Springer, Dordrecht
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