Numerical Modelling Of Nano Inclusions In Small And Large Deformations Using A Level-Set/Extended Finite Element Method

In this work, a numerical procedure is proposed to model nano inclusions in both small and large elastic deformations in a continuum framework. An extended finite element method is combined with the level-set method. The interface between the matrix and the inclusions is modelled as an imperfect interface using the Laplace-Young model and is described implicitly through arbitrary mesh using a level-set function. Associated weak forms are derived in small and large deformations. As no mesh of the interface is needed, arbitrary inclusions shapes or distributions can be studied. The advantage of the a continuum approach, in contrast with the molecular dynamics approach, is that a large number of nano inclusions can be modelled at low computational costs, to determine the effective properties of a material containing arbitrarily distributed nano inclusions. The proposed procedure allows modelling size dependent effective properties in nanomaterials. Numerical examples in small and large elastic deformations are proposed to demonstrate the capabilities of the method.