Predictions of local stress heterogeneities within fibre-reinforced laminated plates

Abstract

Most plate models in use are hypothesis-based, which struggle to resolve the internal stress distribution resulted from plate microstructural heterogeneities, making the strength prediction of such plates still a challenging issue nowadays. To this end, exemplified by fibre-reinforced laminates, the asymptotic behaviour of three-dimensional full-resolution models of microstructural plates is studied. Without containing any phenomenological parameters but merely the information about the isotropic constituting materials and the microstructural geometry, the derived (leading-order) asymptotic plate model is able, not only to reproduce the quantities indexing the homogenised properties of a microstructural plate, such as its stiffness coefficients and vibration modes, but also to predict the locally heterogeneous stress distribution. For fibre-reinforced laminates, the internal stress distribution can be calculated in a semi-analytical manner, and the relative error in stress prediction is shown to be lower than 8.5% for an arbitrarily oriented laminate bearing a slenderness of 0.08. The predictability of the introduced asymptotic plate model is also demonstrated over methods based on the concept of representative volume.