A numerical approach for the failure analysis of textile composites

The paper presents a numerical approach to evaluate the mechanical behaviour up to failure of textile composites and the validation of the method against experiments. The main assumption is the periodic distribution of the reinforcements in the composite. This allows us to exploit the theoretical concepts of the homogenization theory for periodic media. The model is based on two levels of homogenization. The first level concerns the warp and weft yarns considered as unidirectional fibre reinforced composites with a fibre volume fraction equal to the packing density. Their mechanical properties are obtained by numerical analyses of a representative volume. The second homogenization level is applied at a representative volume of the textile composite that is modelled by means of a three-dimensional finite elements. The assumed material periodicity is taken into account imposing kinematic boundary conditions. According to this procedure, the parameters necessary to describe the problem are limited to the geometry of the reinforcement and to the mechanical properties of the components (matrix and fibres). The macroscopic behaviour up to failure is investigated assuming a Tsai-Hill like failure domain for the homogenized reinforcements. The progressive damage of the yarns is followed by a procedure involving the stiffness matrix elements degradation when the stress state in the current elements satisfies the assumed failure criterion. The elements of the stiffness matrix to be reduced depend on the failure mechanism of the yarns