# Buckling Analysis of Plain Knitted Fabric Sheets Under Simple Shear in an Arbitrary Direction

**Topics:**Linear elasticity, Continuum mechanics, Elasticity

**Pages:**18 (6145 words)

**Published:**April 4, 2011

Buckling analysis of plain knitted fabric sheets under simple shear in an arbitrary direction Y.T. Zhang

a b

a,*

, C.Y. Liu b, R.X. Du

b

Department of Mechanics, Tianjin University, Tianjin 300072, China Department of Automation and Computer-Aided Engineering, The Chinese University of Hong Kong, Hong Kong, China Received 22 December 2006; received in revised form 12 March 2007 Available online 30 March 2007

Abstract Knitting structures make plain knitted fabric diﬀerent from woven fabric. With the aid of a micro-constitutive model the buckling of a knitted fabric sheet subjected to simple shear in an arbitrary direction is investigated. The large deformation of the fabric sheet in its critical conﬁguration is considered. The theory of stability for ﬁnite deformations is applied to the analysis. All the stress boundary conditions of the knitted fabric sheet are satisﬁed. An equation for determining the buckling direction angle is derived. It is shown that there are two possible buckling modes: a ﬂexural mode and a barreling mode. The buckling conditions for the two modes are also obtained, respectively. A numerical calculation reveals that only the ﬂexural mode can occur, which agrees with experimental observations. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Knitted fabric; Knitting structure; Buckling; Wrinkling; Simple shear

1. Introduction Simulations of draping and buckling/wrinkling of fabric sheet have attracted many researchers’ attention because of their great prospect of application in developing ‘‘Trial Systems of Apparel’’ which can model how clothes would appear on models in fashion shows, see, e.g., Amirbayat and Hearle (1989). The draping and buckling of woven fabric have extensively been studied, see, e.g., Kim (1991), Kang and Yu (1995), Chen and Govindaraj (1995), Zhang and Fu (2000, 2001), Zhang and Xu (2002a,b) and Zhang and Xie (2003). These results have paved the way for the development of a trial system of apparel made of woven fabric. For more details about the recent advances of woven fabric mechanics we refer readers to the review article by Zhang (2003a) and the book by Zhang (2003b). However, very few papers on simulations of draping and buckling/wrinkling of knitted fabric have appeared in the open literature. As knitting structures are more complicated than woven structures, there does not yet exist a suitable constitutive model for describing the mechanical behavior of knitted fabric. Simple tests *

Corresponding author. Tel.: +86 22 27404297; fax: +86 22 87401979. E-mail address: ytzhang@tju.edu.cn (Y.T. Zhang).

0020-7683/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2007.03.020

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demonstrate that the mechanical behavior of knitted fabric is very diﬀerent from that of woven fabric. For example, a plain woven fabric sheet subjected to a tension along warp/weft direction does not buckle (Zhang and Fu, 2001), but a plain knitted fabric sheet under tension along a non-course direction can buckle and the one under tension along a course-direction cannot buckle; see the photos shown of Fig. 1 in Zhang et al. (2004). The knitting structures composed of interlocking loops of yarns make knitted fabric very diﬀerent from woven fabric: the former, for instance, is much ‘‘softer’’, easier to buckle, and hence more suitable for underwear (thus, it is well known that shirts are usually made of woven fabric). In order to characterize its mechanical properties mathematically, a micro-constitutive model for plain knitted fabric has been proposed by Zhang et al. (2004). Based on the model the out-of-plane buckling of knitted fabric sheet subjected to a tension along the wale direction has been predicted successfully, see Zhang et al....

References: Amirbayat, J., Hearle, J.W.S., 1989. The anatomy of buckling of textile fabrics: drape and conformability. Journal of the Textile Institute 26 (1), 51–68. Chen, B.J., Govindaraj, M., 1995. A physically-based model of fabric drape using ﬂexible shell theory. Textile Research Journal 65, 324– 330. Fu, Y.B., Ogden, R.W., 1999. Nonlinear stability analysis of pre-stressed elastic bodies. Continuum Mechanics and Thermodynamics 11, 141–172. Hu, J.L., Zhang, Y.T., 1997. The KES shear test for fabrics. Textile Research Journal 67 (9), 654–664. Kang, T.J., Yu, W.R., 1995. Drape simulation of woven fabric by using the ﬁnite-element method. Journal of the Textile Institute 86, 635– 648. Kim J.H., 1991. Fabric mechanics analysis using large deformation orthotropic shell theory, Ph.D. Thesis. Dept. of Mechanical and Aerospace Engineering, North Carolina State University. Ogden, R.W., 1984. Non-linear Elastic Deformations. Dover Publications, New York. Zhang, Y.T., 2003a. The recent advances in fabric mechanics. Advances in Mechanics 33, 217–226, In Chinese. Zhang, Y.T., 2003b. Modern Fabric Mechanics and the Theory on Stability. Beijing University Press, Beijing, China, In Chinese. Zhang, Y.T., Fu, Y.B., 2000. A micromechanical model of woven fabric and its application to the analysis of buckling under uniaxial tension Part 1: the micromechanical model. International Journal of Engineering Science 38 (17), 1895–1906. Zhang, Y.T., Fu, Y.B., 2001. A micromechanical model of woven fabric and its application to the analysis of buckling under uniaxial tension Part 2: Buckling analysis. International Journal of Engineering Science 39 (1), 1–13. Zhang, Y.T., Xie, Y.X., 2003. Nonlinear micro-mechanical model for plain woven fabric. Acta Mechanica Solida Sinica 16 (2), 110–116. Zhang, Y.T., Xu, J.F., 2002a. Buckling analysis of woven fabric under simple shear along any direction. Textile Research Journal 72 (2), 147–152. Zhang, Y.T., Xu, J.F., 2002b. The buckling analysis of woven fabric subjected to uniaxial tension along any direction. Applied Mathematics and Mechanics 23 (5), 597–605.

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Zhang, Y.T., Li, C.Y., Xu, J.F., 2004. A Micro-mechanical model of knitted fabric in wale direction and the analysis of buckling under tension along wale direction, Part 1: micro-mechanical model. Acta Mechanica Sinica 20 (6), 623–631. Zhang, Y.T., Li, C.Y., Xu, J.F., 2005. A Micro-mechanical model of knitted fabric in wale direction and the analysis of buckling under tension along wale direction, Part 2: buckling analysis. Acta Mechanica Sinica 21 (2), 176–180.

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