Investigation of surface stress effect in 3D complex nano parts using FEM and modified boundary Cauchy–Born method

• Modified boundary Cauchy–Born method is utilized to model industrial models.
• For the first time, modified boundary Cauchy–Born method is used to model 3D transition metals.
• A modified arc-length method is also utilized to guarantee the convergency of the solutions.

In this paper the surface effects in 3D complex parts are investigated via classical FEM and the modified boundary Cauchy–Born method, which are continuum based theories, and the results are compared with molecular dynamics simulations. The boundary Cauchy–Born covers the weakness of the surface Cauchy–Born in modeling edge and corner elements, so the results are in better agreement with molecular dynamics simulations. Using super convergent patch recovery method, MBCB shows more precise results in comparison with BCB as it can model acute and obtuse angles which cannot be modeled via BCB. The flexibility of MBCB in modeling 3D complex and non-right angle geometries are utilized to model industrial examples under free relaxation condition. Unlike samples in previous works, the complexity of geometry proposed here results in highly nonlinear problems where the MBCB method can no longer guarantee convergency of the solutions. Therefore, a new and modified arc-length method is developed and utilized to overcome this nonlinearity.