Integration efficiency for model reduction in micro-mechanical analyses

• Published in: Computational mechanics 2018-08, Vol.62 (2), p.151-169
• Main Authors: van Tuijl, Rody A., Remmers, Joris J. C., Geers, Marc G. D.
• Format: Article
• Language: English
• Subjects: Approximation; Classical and Continuum Physics; Computational Science and Engineering; Cost analysis; Cyclic loads; Empirical analysis; Engineering; Interpolation; Model reduction; Original Paper; Reduced order models; Theoretical and Applied Mechanics; Variations
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-017-1490-4

Micro-structural analyses are an important tool to understand material behavior on a macroscopic scale. The analysis of a microstructure is usually computationally very demanding and there are several reduced order modeling techniques available in literature to limit the computational costs of repetitive analyses of a single representative volume element. These techniques to speed up the integration at the micro-scale can be roughly divided into two classes; methods interpolating the integrand and cubature methods. The empirical interpolation method (high-performance reduced order modeling) and the empirical cubature method are assessed in terms of their accuracy in approximating the full-order result. A micro-structural volume element is therefore considered, subjected to four load-cases, including cyclic and path-dependent loading. The differences in approximating the micro- and macroscopic quantities of interest are highlighted, e.g. micro-fluctuations and stresses. Algorithmic speed-ups for both methods with respect to the full-order micro-structural model are quantified. The pros and cons of both classes are thereby clearly identified.