ABSTRACT
This chapter introduces a researcher/student to the utility of Finite element method in solving selected problems related to mechanics of materials problems at the nanoscale. In the context of nanoscale materials, structures and defects studied include voids, cracks, dislocations, twins, interfaces, precipitates, and epitaxial systems. Mesh size and order of the mesh refinement have to be carried out to make sure that the results are meshing invariant. A fine uniform mesh costs in terms of the computation time, but in the nanoscale, often one can get away with this kind of meshing, as the number of nodes may still be small in number. The importance of eigenstrains in the mechanics of solids can be comprehended from the fact that Professor Toshio Mura starts his book on “micromechanics of defects in solids,” with the theory of eigenstrains. A dislocation in a semi-infinite domain feels a force toward a free surface, called the image force.
