An efficient monolithic solution scheme for FE2 problems

The FE2 method is a very flexible but computationally expensive tool for multiscale simulations. In conventional implementations, the microscopic displacements are iteratively solved within each macroscopic iteration loop, although strains imposed as boundary conditions at micro-scale only represent estimates. order to reduce number of iterations, present contribution presents monolithic scheme, which and macro-scale in common Newton–Raphson loop. this case, linear system equations by static condensation, so that limited modifications conventional, staggered scheme necessary. proposed algorithm implemented into commercial FE code Abaqus. Benchmark examples demonstrate saves up ? 60% computational costs.