Efficient monolithic solution of FE2 problems

The concurrent FE2-method is a very powerful and flexible computational tool for multi-scale problems. However the effort high. conventional, staggered (“nested Newton”) solution scheme solves microscopic problem iteratively within each macroscopic Newton-Raphson (NR) iteration, although deformation gradients as boundary conditions at micro scale are only estimates. In this contribution monolithic FE2scheme proposed, solving displacements of both scales in common NR loop, which proved being faster by saving expansive micro-scale iterations.