Locking in simulation of composite reinforcement deformations. Analysis and treatment

The locking phenomenon that occurs in some finite element simulations of textile composite reinforcement deformation is analysed for different meshes in the case of the bias extension test. The inability of the fully integrated four node element to represent tension free motion for any mesh is highlighted. It is shown that the use of one point quadrature quadrilateral elements is a possible solution to this locking phenomenon. In order to avoid spurious singular modes, a specific stabilisation procedure is proposed. It is based on a Γ-projection method. It only acts on the non-constant part of the in-plane shear strains. Based on the underintegrated element, this approach is numerically efficient. It is shown that locking is eliminated.