Improved accuracy of Dirichlet-like microscopic solutions on Representative Volume Elements

This work focuses on the improvement of Dirichlet Boundary Value Finite Element solutions on Representative Volume Elements (RVE). For random microstructure Finite Element calculations, it is well-known that Periodic Boundary Conditions (PBC) applied on fixed size periodic RVE are much more precise than classical Dirichlet boundary conditions, so-called Uniform Strain Boundary Conditions (USBC), at the expense of additional efforts. The numerical experiments reported here clearly reveal that the inaccuracy of USBC is mainly due to boundary effects located around and in artificially cut inclusions because of the classical RVE cubic shape.