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• W1520561570 abstract "Composite materials are already widely used in engineering structures, especially in the aeronautical, and, indeed, the aerospace industries where their high specific strength and stiffness make them ideally suited to realise lower mass components. However, a major weakness of these laminated materials is that they are prone to delamination at both the interface bet ween the plies (interlaminar) and within plies (intralaminar), which hinders reliable prediction of thei r durability in service. It is therefore of primary importance to devise reliable experimental and numerical techniques to study and predict the behaviour of existing materials as well as engineer new damage tolerant composites capable of sustaining the increasingly demanding conditions in which they are used. Advanced composites are composed of stiff elastic fibres bonded together by a toughened epoxy matrix, t o form a lamina; numerous lamina are then bonded together to form a laminate. At the first level of simpl ification, each layer (i.e. lamina) can be considered as a linear, elastic, orthotropic material. In o rder to predict the intralaminar failure in such lamina, it is important to be able to accurately simulate cra ck behaviour and propagation. To achieve this, methods exist in the literature however, many approaches suffer a number of drawbacks, such as mesh sensitivity and the requirement for a-priori knowledge of where the delamination will occur, and so not suited to intralaminar delamination prediction.To allevi ate these difficulties, partition of unity methods (PUM) [1] were introduced. In the PU framework, arbitrary functions are added to the standard polynomial finite element (FE) space in order to improve the approxi mation power of the resulting numerical method. In particular, the extended finite element method (X FEM) [2] allows simulation of crack propagation without remeshing by introducing two classes of enrichment functions:discontinuous enrichment to capture the displacement jump through the crack faces and near-tip asymptotic enrichment to capture the stress singularity at the crack tip in linear elastic fra cture mechanics (LEFM). In this paper, a new tool based on the extended finite element method (XFEM) [2] wh ich allows to simulate the growth of arbitrary cracks in orthotropic materials is devised, anal ysed and evaluated. The extended finite element method works by enriching the sta ndard FEM basis through a local partition of unity. The standard FE displacement approximation equation is given by u h (x) = ∑ ieI Ni(x)ui (1) where: uh(x) is an approximation for the displacement field, Ni(x) are the element shape functions and ui are the nodal displacements. In XFEM, the displacement field is augmented by discontinuous enrichment functions to give the displacement approximation as Ni(x)ui +∑ jeJ Nj(x)Ψ(x)a j (2) where Nj(x)are the element shape functions associated with the nodal subset j, Ψ(x) are the enrichment functions and a j are the additional degrees of freedom associated with the enrichment. The enrichment functions Ψ(x) are decided based upon an analytical solution of the problem. For crack modelling the most commonly used enrichment functions are the heavyside step function or split enrichment function which is often used to enrich the midsection of a crack. In order to model the crack tip singularity, the" @default.
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• W1520561570 date "2010-01-01" @default.
• W1520561570 modified "2023-09-27" @default.
• W1520561570 title "Enriched finite elements (xfem) for multi-crack growth simulations in orthotropic materials" @default.
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