Cost-effectiveness of super-element and mean-field homogenization approaches for linear elastic multiscale problems requiring localization
Published in Computers & Structures, 2026
Riveted assemblies play a crucial role in the strength and failure of aeronautical structures subjected to shock and impact. Such computations necessitate accurate modeling of both the full-scale structure and the local assembly zone to evaluate the structure’s survivability. To address this type of multiscale problem, two types of numerical approaches may seem appropriate: super-element and (mean-field) homogenization approaches. The accuracy and the efficiency of a perforated membrane Hybrid-Trefftz Displacement super-element, the Transformation Field Analysis approach and a Mori–Tanaka homogenization with Transformation Field Analysis localization approach were compared by considering geometrically and materially linear single and multi hole cases. The results showed that all approaches successfully localized the perforated plate fields. The Mori–Tanaka homoge nization with Transformation Field Analysis localization approach was as efficient as the super-element approach, while the integrated Transformation Field Analysis approach was costlier. These results suggest that Mori–Tanaka homogenization with Transformation Field Analysis localization is a promising candidate for future materially nonlinear extensions, which remain to be investigated. Another perspective will concern the replacement of the analytical interior modes of the super-element with a non-analytical approach.
Recommended citation: P.V.K. Nguyen, B. Langrand, F. Massa, C. Hubert, N. Leconte, Cost-effectiveness of super-element and mean-field homogenization approaches for linear elastic multiscale problems requiring localization, Computers & Structures 332 (2026) 108459.
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