Internal wrinkling instabilities in layered media

Abstract

The large deformation Cosserat continuum model presented shows the potential of capturing internal buckling instabilities within layered media at a fraction of the computational cost when compared with conventional modelling methods. A homogenized elasto-plastic Cosserat tensor is derived for periodic arrangements of orthotropic elastic layers separated by weak interfaces that exhibit a modified Mohr–Coulomb friction law. Focus is given to the physical interpretation of the Cosserat deformation measures, the derivation of the Cosserat elastic tensor and implementation of the model using the finite element method. The resulting formulation is validated for three simplified loading scenarios: a cantilever, internal buckling and simple shear of a multilayered beam. Finally, the model is applied to a new application to capture the formation of wrinkling defects during the manufacturing of composite laminates. The results show good agreement with observed manufacturing defects, demonstrating the clear potential for application of the Cosserat model within composite process modelling and other layered material applications.