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A sub-stepping scheme for multi-scale analysis of solids

The fully coupled finite element analysis of non-linear multi-scale solid mechanics problems requires extensive computing time. This paper proposes a sub-stepping procedure which obtains better initial guesses for the Newton–Raphson scheme adopted in the solution of the equilibrium problem of the representative volume elements. The resulting gain in robustness allows for larger load steps to be prescribed at the macroscopic scale, and is particularly noticeable in the finite strain regime where speed-up factors of four are observed. This is an important step towards the fully coupled multi-scale analysis of realistic problems.