Buckling analysis of plain knitted fabric sheets under simple shear in an arbitrary direction Y.T. Zhang
, C.Y. Liu b, R.X. Du
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 *
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0020-7683/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2007.03.020
Y.T. Zhang et al. / International Journal of Solids and Structures 44 (2007) 7049–7060
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....