An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites

In a nanostructured material, the interface-to- volume ratio is so high that the interface energy, which is usually negligible with respect to the bulk energy in solid mechanics, can no longer be neglected. The interfaces in a number of nanomaterials can be appropriately characterized by the coherent interface model. According to the latter, the displacement vector field is continuous across an interface in a medium while the traction vector field across the same interface is discontinuous and must satisfy the Laplace–Young equation. The present work aims to elaborate an efficient numerical approach to dealing with the interface effects described by the coherent interface model and to determining the size-dependent effective elastic moduli of nanocomposites. To achieve this twofold objective, a computational technique combining the level set method and the extended finite element method is developed and implemented. The numerical results obtained by the developed computational technique in the two-dimensional (2D) context are compared and discussed with respect to the relevant exact analytical solutions used as benchmarks. The computational technique elaborated in the present work is expected to be an efficient tool for evaluating the overall size-dependent elastic behaviour of nanomaterials and nano-sized structures.