Direct stress–strain representation for coated woven fabrics B.N. Bridgens, P.D. Gosling * School of Civil Engineering and Geosciences, University of Newcastle-upon-tyne, Newcastle-upon-tyne, NE1 7RU, UK Arup, 13 Fitzroy Street, London W1T 4BQ, UK Received 5 December 2002; accepted 26 July 2003 Available online 3 August 2004 Abstract An understanding of the complex behaviour of coated woven fabrics is vital for the design of state-of-the-art fabric structures. Fabric behaviour is typically defined using elastic constants based on plane stress assumptions. This paper considers two new methods of representing fabric response: (i) use of spline functions to define response surfaces, (ii) use of stress–strain mean and difference functions (proposed by Day [IASS symposium proceedings: shells, membranes and space frames 2 (1986) 17]. Both techniques provide direct correlation between stresses and strains, eliminating the assumption of plane stress. Extensive biaxial fabric testing is proposed to assess the validity of these approaches and extend their use. Ó 2004 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved. Keywords: Coated woven fabrics; Lightweight structures; Material models; Response surface; Biaxial behaviour; Splines; Non-linear 1. Introduction Coated woven fabrics are used in a wide range of structural applications to provide lightweight, architec- turally striking solutions. The design of fabric structures is complicated by the complex response of coated woven fabrics to biaxial loads in the plane of the fabric. A bet- ter understanding of the behaviour of architectural fab- rics may significantly reduce levels of uncertainty in the design process and enable more ambitious architectural forms to be generated. There are two principal types of coated woven fabric: glass fibre fabric with a PTFE (polytetrafluoroethylene) coating and polyester fabric with a PVC (poly vinyl chloride) coating. Both fabrics are composed of an open weave mesh of orthogonal yarns with a coating which encloses the mesh on both sides. The characteristics of the two fabrics are different, but the underlying defor- mation mechanisms are very similar. Fabric structures resist environmental loads as tensile stresses in the plane of the fabric. Under biaxial tensile loading the behaviour of coated woven fabrics is highly non-linear [1–3]. Geo- metric non-linearity occurs in the yarns (due to the com- plex twisted fibre structure) and in the finished fabric (interaction of orthogonal warp and weft yarns under biaxial in-plane stress leads to fundamental non-lineari- ties, compounded by the effect of the coating). Material non-linearity is evident in the load–extension character- istics of both the yarn fibres and the fabric coating. The material response is also time-dependent and hysteretic 0045-7949/$ - see front matter Ó 2004 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2003.07.005 * Corresponding author. Address. School of Civil Engineer- ing and Geosciences, University of Newcastle-upon-tyne, Newcastle-upon-tyne, NE1 7RU, UK. Tel.: +44 191 222 6422; fax: +44 191 222 6502. E-mail address: p.d.gosling@ncl.ac.uk (P.D. Gosling). Computers and Structures 82 (2004) 1913–1927 www.elsevier.com/locate/compstruc