Volume 9, Issue 4, 2000

Geometrical Non-Linearity of Textile Composites in Large Deformation

T. C. Lim^{1, 2}, M. Zako³, S. Sakata³, S. Ramakrishna¹

¹Department of Mechanical and Production Engineering, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260.

²High Performance Concrete Research Laboratory, Faculty of Engineering, The National University of Singapore, EW2, 1 Engineering Drive 3, Singapore 117576.

³Department of Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan.

(Received 3/00 ; accepted 7/00)

ABSTRACT

In considering small deformation of solids, it is common to assume linear elasticity. Where large deformation is concerned, material non-linearity – whether hyper elasticity, strain hardening, etc – must be considered. In large deformation of textile composites, overall material non-linearity consists of (a) constituent material non-linearity, and (b) geometrical non-linearity due to strain-deformation relation. This paper firstly proposes a finite element procedure for obtaining the stiffness matrix of a representative volume element. The procedure involved is simple due to an effective decoupling methodology. Secondly, co-ordinate updating of the FE mesh is performed to allow readjustment to the fibre bundle elements in the RVE. This enables the process of fabric realignment to be theoretically mimicked to consider the influence of fibre bundle reorganisation on the overall stiffness of the textile composite – hence geometrical non-linearity.