Abstract
The macroscopic material behaviour of novel textile-reinforced composites is defined by its constituents (micro-level) and the design of the textile reinforcement (meso-level). Consequently, a multi-scale approach to the prediction of the material behaviour is necessary because only in this vein the adaptability of the textile reinforcement can be used to develop materials whose features can be adjusted precisely to certain applications.
Due to the difference in size between the macroscopic component and the fine-scale material structure a direct modelling of the reinforcement in a structural analysis is not reasonable.
Therefore, a decoupled computational homogenization procedure is applied. Based on a representative volume element (RVE) of the reinforcing architecture effective material properties C̄ ijkl for a macroscopically homogeneous continuum are computed. These properties are used to characterize the effective linear elastic material behaviour of the composite in a structural analysis and allow for efficient component analysis and design.
In the process of generating numerical models for RVE of textile-reinforced composites the extended finite element method (X-FEM) is applied and an automated modelling procedure is developed. The computed effective stiffness values are compared to experimental data from ultrasonic and standard tensile tests.
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References
Belytschko T, Mo ës N, Usui S, Parimi C (2001) Arbitrary discontinuities in finite elements. Int J Numer Meth Eng 50:993-1013
Daux C, Mo ës N, Dolbow J et al (2000) Arbitrary branched and intersecting cracks with the extended finite element method. Int J Numer Meth Eng 48:1741-1760
Fagerstr öm M, Larsson R (2006) Theory and numerics for finite deformation fracture modelling using strong discontinuities. Int J Numer Meth Eng 66:911-948
Gravouil A, Mo ës N, Belytschko T (2002) Non-planar 3D crack growth by the extended finite element and level sets - Part I: mechanical model. Int J Numer Meth Eng 53:2549-2568
Gravouil A, Mo ës N, Belytschko T (2002) Non-planar 3D crack growth by the extended finite element and level sets - Part II: level set update. Int J Numer Meth Eng 53:2569-2586
Haasemann G, K ästner M, Ulbricht V (2006) Multi-Scale modelling and simulation of textile-reinforced materials. CMC 3:131-146
Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11:357-372
Hufenbach W, B öhm R, Langkamp A, Kroll L, Ritschel T (2006) Ultrasonic evaluation of anisotropic damage in textile multi-axial reinforced thermoplastic composites made from hybrid yarns. Mech Compos Mater 42:221-234
K ästner M, Ulbricht V (2006) Homogenization of fibre-reinforced composites using X-FEM. Proc Appl Math Mech 6:489-490
Lukkassen D, Persson LE, Wall P (1995) Some engineering and mathematical aspects on the homogenization method. Compos Eng 5:519-531
11. Melenk JM, Babuška I (1996) The partition of unity finite element method: basic theory and applications. Research Report
Mo ës N, Cloirec M, Cartraud P, Remacle J (2003) A computational approach to handle complex microstructure geometries. Comput Methods Appl Mech Eng 192:3163-3177
Mo ës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Meth Eng 46:131-150
14.Sanchez-Palencia E, Zaoui E (1987) Homogenization techniques for composite media. Lecture Notes in Physics 272. Springer, Berlin
Stazi L, Budyn E, Chessa J, Belytschko T (2003) An extended finite element method with higher-order elements for curved cracks. Comput Mech 31:38-48
Sukumar N, Chopp D, Mo ës N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite element method. Comput Methods Appl Mech Eng 190:6183-6200
Sukumar N, Huang ZY, Pr évost J, Suo Z (2004) Partition of unity enrichment for bimaterial interface cracks. Int J Numer Meth Eng 59:1075-1102
Sukumar N, Mo ës N, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modelling. Int J Numer Meth Eng 48:1549-1570
Zi G, Belytschko T (2003) New crack-tip elements for XFEM and applications to cohesive cracks. Int J Numer Meth Eng 57:2221-2240
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Kästner, M., Haasemann, G., Brummund, J., Ulbricht, V. (2008). Computation of Effective Stiffness Properties for Textile-Reinforced Composites Using X-FEM. In: Mechanical Response of Composites. Computational Methods in Applied Sciences, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8584-0_13
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DOI: https://doi.org/10.1007/978-1-4020-8584-0_13
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