Boundary Element Analysis of Bi-Material Interfaces with Application to Adhesive Dentistry
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Traditional boundary element methods are not well equipped to handle non smooth problems, such as cracks, notches and other singularities. These problems are encountered often when dealing with bi-material interfaces, which are useful for optimizing material properties. A bi-material interface has sharp corners and edges that lead to singularities. For strength analysis, it is necessary to calculate a solution at these singularities. In this thesis, a formulation of the boundary element method has been implemented in the field of dentistry. The formulation is based on a previous work which utilizes a weighted traction-oriented BEM research code written exclusively in terms of bounded quantities. This code has been enhanced to deal with stress singularities in multi-region problems. This research began with convergence analysis to determine that an actual mesh independent solution could be found. This led to solving the dental adhesive problem varying two main variables and establishing the size dependence of the results. The resulting behaviors were modeled as power laws to fully capture the traction behavior at the singularity. The exponents are extremely important to understanding the size dependent nature of the traction solutions and, consequently, the strength of the interface. While holding the interface area constant, the exponents for thickness variation ranged from 0.11 to 0.15 depending on the radius used for both interfaces, with the dentin-adhesive interface consistently 5–10% higher than the resin-adhesive interface. Holding the adhesive thickness constant led to interface area exponents ranging from 0.26 to 0.38 depending on the thickness chosen. Both interfaces provided near identical results, indicating that these curves are not material dependent.