Material-tissue interfacial phenomena: Challenges in mathematical modeling

Abstract The dentin–adhesive (d-a) interface is critical to the success of composite tooth restoration. The durability behavior of this narrow interface is affected by the complex biochemomechanical environment that the interface experiences. From the viewpoint of composition and structure, the interface is highly heterogeneous irrespective of the scale of observation. Moreover, the characteristics of this interface evolves with time as it is subjected to time- and rate-dependent loading. All these features offer challenges not only for the laboratory analytical techniques but also for mathematical modeling. This chapter elucidates some of these challenges and offers directions to how mathematical modeling can be applied to understand the d-a interface mechanical behavior.