Modelling interface problems within strain gradient elasticity framework

In classical continuum mechanics, the interface problems are well established: a two-phase body, a solid undergoing a chemical reaction, contact problems, etc. In this talk, we discuss some of these problem formulations within the context of generalized continuum theory, namely strain gradient elasticity (SGE). In the latter, the elasticity-related length scales parameter is introduced to reflect the microstructural (or substructural in the case of so-called architectured metamaterials) effects at the continuum level, which allows a much more reliable prediction of material behaviour.

Two types of interface problems are covered in this talk. The first one is a coupled mechano-diffusion problem in the framework of SGE and Cahn-Hilliard diffusion models. Such a coupled model can be used for the simulation of diffusion-based coarsening in solder alloys where the microstructure may have a significant contribution to the process of phase separation. Phase evolution and interface kinetics are then simulated using a smooth interface model. The second part of the talk is devoted to contact problems within SGE theory. For both these examples, weak formulations are derived, and numerical results obtained using isogeometric analysis are shown.

Venue: Fulton G20