Continuum-mechanical modelling of kink-band formation in fibre-reinforced composites

A kink is a singular surface across which the displacement is continuous but the deformation gradient and the fibre direction suffer a discontinuity. A kink band is a highly deformed or even damaged region bounded by two kinks. The objective of modelling kink-band formation, within the framework of finite elasticity theory, is to find a suitable strain– energy function, guided by results from a finite number of simple experiments, that can be used to predict what have been observed and what might be possible under other loading conditions. In this paper, we explain a theoretical basis for choosing such strain–energy functions. More precisely, for a given strain–energy function that allows formation of kinks and a given deformation field, we characterize all possible deformation fields that can join the given deformation field through a kink and explain a procedure that can be used to assess the stability properties of any kink solution that is mathematically possible. In contrast with most previous studies in the engineering community where, for instance, the kink orientation angle is undetermined, the present theory completely determines the kink propagation stress, the kink orientation angle and the fibre direction within the kink band.