Variational multiscale approach to enforce perfect bond in multiple-point constraint applications when forming composite beams

Abstract

Composite laminates that consist of two or more layers find widespread applications in a variety of engineering structures. In the computational modelling of composite laminates, the layers can be stacked together and connected conveniently at the nodes by using multiple-point constraints (MPCs). However, this type of modelling leads to weakening of the kinematic constraint conditions imposed by the bond between the juxtaposed layers and as a consequence, MPCs application at the nodes produces behaviour that is softer than the perfectly bonded composite beam behaviour. The work herein shows that when kinematic conditions for composite action are weakly imposed in the variational form, they can be enforced in the point-wise sense by proper selection of the interpolation field or otherwise reinforced by using variational multiscale approach without modifying the kinematic model. The originality of the approach presented herein is in the interpretation of the MPCs application as the solution in a superfluously extended space because of the weakening in the kinematic constraints. It is shown that the perfect bond between the composite beam layers can be recovered by excluding the identified fine-scale effect from the solution of the multiple point constraint application. The convergence characteristic of the finite element formulation is also improved by using the variational multi-scale approach. It is also shown that the fine-scale effects can be represented by using extra fictitious elements and springs, which offers a direct correction technique in modelling of composite beams that is especially useful when access to the numerical procedure is limited.