Modeling of Progressive Damage in the Adhesive Bond Layers of Actuated Plates

Abstract

This article discusses finite element modeling of progressive damage in the adhesive bond layers of actuated plates and investigates the reduction in actuation capacity caused by the damaged bond layers. The primary challenge posed by this class of problems stems from the vast range of geometric scales that are represented, with the thickness of the adhesive layer representing the smallest scale, the overall thickness of the actuated plate representing the intermediate scale, and the in-plane dimensions of the plate representing the largest scale. In multiscale problems, the overall efficiency of the numerical methodology is of paramount importance, thus model development is guided by the need to obtain a sufficiently accurate solution at an acceptable computational expense. In this study, this goal is achieved through the use of a hierarchical, displacement-based, 2-D finite element model that includes the first-order shear deformation (FSD) model, Type I layerwise models (LW1) and Type II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C0 continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C0 continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the individual material ply or, in the case of layerwise models, by the individual numerical layer. The results clearly demonstrate that the resulting model can efficiently simulate progressive damage in the adhesive layers. For rectangular actuator patches, the adhesive damage is highest near the corners of the actuator and is driven primarily by local concentrations in the transverse normal and transverse shear stresses. In contrast to previous studies that have shown that the inclusion of discrete layer transverse normal stress does not significantly influence the predicted global deformations, the present study shows that the transverse normal stress has a very significant effect in the initiation and progression of localized damage in the adhesive layers.