Hybrid multiscale integration for directionally scale separable problems

This manuscript presents the formulation and implementation of a hybrid multiscale integration scheme for multiscale problems that exhibit different scale separation characteristics in different directions. The proposed approach employs the key ideas of the variational multiscale enrichment at directions that exhibit poor scale separation and computational homogenization at directions with good scale separability. The proposed approach is particularly attractive for surface degradation problems in structures operating in the presence of aggressive environmental agents. Formulated in the context of variational multiscale principles, we develop a novel integration scheme that takes advantage of homogenization-like integration along directions that exhibit scale separation. The proposed integration scheme is applied to the reduced order variational multiscale enrichment (ROVME) method in order to arrive at a computationally efficient multiscale solution strategy for surface degradation problems. Numerical verifications are performed to verify the implementation of the hybrid multiscale integrator. The results of the verifications reveal high accuracy and computational efficiency, compared with the direct ROVME simulations. A coupled transport-thermo-mechanical analysis is presented to demonstrate the capability of the proposed computational framework.

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