Molecular dynamics
Numerical methods have been developed for modelling the mechanical response of FGMs, with the finite element method being the most popular one. Initially, the variation of material properties was introduced by means of rows (or columns) of homogeneous elements, leading to a discontinuous step-type variation in the mechanical properties. Later, Santare and Lambros developed functionally graded finite elements, where the mechanical property variation takes place at the element level. Martínez-Pañeda and Gallego extended this approach to commercial finite element software. Contact properties of FGM can be simulated using the Boundary Element Method (which can be applied both to non-adhesive and adhesive contacts). Molecular dynamics simulation has also been implemented to study functionally graded materials. M. Islam studied the mechanical and vibrational properties of functionally graded Cu-Ni nanowires using molecular dynamics simulation.