Tension locking in finite-element analyses of textile composite reinforcement deformation

Abstract

The mechanical behaviour of textile composite reinforcements is characterised by a tensile stiffness in the two fibre directions, which is very large in comparison with the in-plane shear rigidity. The in-plane deformations of these materials are mainly due to the shear angle between warp and weft yarns. The finite-element analysis of these deformations leads to locking phenomena if the mesh is not aligned with the fibre directions. In this case the calculation gives spurious tensions in the fibres that make the analysis inaccurate. In the present paper, this phenomenon is highlighted and analysed in the case of the four-node finite element. In particular, a two-element example shows the impossibility of obtaining solutions without tensile strains for unaligned meshes. A solution to this tension locking is proposed for the four-node quadrilateral. It is based on a one-point quadrature and a specific stabilisation reduced to non-constant in-plane shear strains.