A modelling framework for composites containing 3D reinforcement Fredrik Stig, Stefan Hallström ⇑ Royal Institute of Technology (KTH), Dept. of Aeronautical and Vehicle Engineering, SE-100 44 Stockholm, Sweden article info Article history: Available online 17 March 2012 Keywords: 3D weave Textile composite Elastic properties FEM abstract Composite materials reinforced with three-dimensionally (3D) woven carbon fibre textiles are investi- gated and the challenge and the driver for the work is to generate numerical models to predict the mechanical behaviour of these composites. The result of the final modelling stage is near authentic finite element (FE) models of representative volume elements (RVEs) of the composites. They are created by using only a small number of input parameters, such as the size of the RVE, the number of yarns and their mutual interlacing, and the yarn crimp. The FE models may then be utilised for various purposes but are here used to derive homogenised elastic mechanical properties of 3D reinforced composite materials. The correlation between the models and experiments is good, both in terms of details in the architecture and mechanical properties. There are however some deviations that could be explained by the models being more regular than the real material. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The emerging textile technique facilitating three-dimensional (3D) weaving is now receiving great interest, particularly from the aerospace industry, for its potential utilisation in structural composites. It involves cross-directional shedding and picking, enabling net shape production of 3D textile profiles with great flex- ibility in cross-sectional shape. 3D weaving with carbon fibres has successfully been used to produce reinforcement preforms for subsequent resin infusion into composite beams. There are many potential advantages with this novel weaving technique, such as,  possibility to weave complex 3D shapes directly to net shape in a single production step  virtually no scrap material being generated  huge flexibility in shape, textile architecture and yarn content and  an inherent 3D, orthogonal orientation of interlaced yarns. 3D textiles are characterised by complex internal geometry which is sometimes difficult to model accurately. According to Larve et al. [1], the complex internal geometry is the reason for the lack of ‘‘robust and widely accepted methodology for their design and analysis’’. For this material class to be more widely used and accepted, new and better analysis tools are needed [2]. Simulations are important for several reasons. They provide cost-effective ways to perform parameter studies of mechanical properties and their relation to the reinforcement type and compo- sition. There are also properties, such as the out-of-plane stiffness and strength, that are difficult to extract experimentally, where simulations of representative volume elements (RVEs) could offer routes for predictions [3]. According to Chapman and Whitcomb [4] small changes in the strand architecture can have a substantial effect on the local stress predictions but also on the predicted moduli. In this work ‘strand’ is used for a region occupied by an infiltrated fibre bundle, as op- posed to regions containing pure matrix, in between the strands. They further state that strands with high waviness are more sensi- tive to variations in strand architecture than strands that exhibit low waviness. This illustrates the importance of accurately repre- senting and predicting the internal geometry within modelling frameworks, especially for materials containing 3D textile reinforcements. There are a number of different approaches to analyse the RVE of 3D textile reinforced composites and their mechanical properties. The most common approaches can be categorised into mosaic mod- els based on classical laminate theory (CLT) [5], analytical models where the stiffness matrix is transformed for each sub-element and homogenised [6,7], and finite element (FE) models [8]. The geometry description in the analytical models may be discretised in different ways, one example being use of so called voxels or 3D cells [9]. Sheng and Hoa [10] state that the FE approach seems to be more accurate than other methods, and acknowledge the dif- ficulties of defining the fabric geometry for a complex 3D-textile preform. They further state that ‘‘a generalised volumetric approach is not yet feasible’’. Much effort has been spent on creating frameworks for the modelling of composites in general but also for modelling 3D 0263-8223/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2012.03.009 ⇑ Corresponding author. E-mail address: stefanha@kth.se (S. Hallström). Composite Structures 94 (2012) 2895–2901 Contents lists available at SciVerse ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct