High order analysis of debonding failure of orthodontic brackets

The paper investigates the initiation and evolution of debonding failure in orthodontic brackets. The latter forms a layered structure consisting of the tooth, an adhesive layer, the bracket, and the inter-laminar interface. The layered structure is prone to debonding, which critically impairs the therapeutic process. The purpose of this study is to develop a quantitative model to analyze the nonlinear and potentially unstable debonding failure in the layered structure. The model integrates the concepts of the high-order theory with nonlinear cohesive interfaces and rigid body displacement field of the bonded bracket. Numerical methods, based on a specially tailored finite element formulation and the arc-length continuation method, trace the full nonlinear response path and characterize its stability. The analysis is validated through comparison with experiments documented in the literature. The principal results quantify the unstable nature of debonding failure and identify factors influencing the instability. The analysis highlights the influence of the rich stress and displacement field in the adhesive layer on failure progression. This is achieved by exploring the coupled role of shear and tensile stresses in the bond layer and the coupling of slip and separation across the interfaces, which jointly form the shear-peel effect, even under globally tangential loading. The major conclusions designate the innovative modeling approach as a tool for the investigation of the interfacial failure mechanism and a steppingstone towards modeling additional features of the layered structure, including curved surfaces, the impact of the surface conditions, and the uncertainty associated with the bonding practice.