On micro-to-macro connections in domain decomposition multiscale methods

• Published in: Computer methods in applied mechanics and engineering 2012-06, Vol.225-228, p.177-196
• Main Authors: Lloberas-Valls, O., Rixen, D.J., Simone, A., Sluys, L.J.
• Format: Article
• Language: English
• Subjects: Coarsening; Cracks; Domain decomposition; Domain decomposition methods; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Ingredients; Joints; Links; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Micro–macro connection; Multiscale analysis; Multiscale methods; Numerical analysis. Scientific computation; Physics; Quasi-brittle materials; Sciences and techniques of general use; Solid mechanics; Static elasticity (thermoelasticity...); Strain localization; Structural and continuum mechanics
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2012.03.022

► We study different connection methods for the concurrent multiscale analysis of failure phenomena. ► We use a non-overlapping domain decomposition technique (FETI). ► We consider higher resolution domains at areas affected by damage processes. ► Accuracy of micro-to-macro connection techniques is assessed by error indicators. Micro-to-macro connection techniques constitute a key ingredient in the formulation of multiscale strategies. In this contribution several connection methods are explored for the concurrent multiscale analysis of brittle heterogeneous materials. Particularly, these techniques are investigated in a domain decomposition strong coupling multiscale framework. The structural component under analysis is partitioned into a number of non-overlapping domains and a fine scale resolution is assigned therein in an adaptive manner exploiting a zoom-in technique. Mesh refinement is employed in the domains where crack coalescence and growth take place. The original contribution presented in this manuscript consists in the study of different strong and weak locality constraints that connect coarse and fine resolution domains. Standard collocation and average compatibility are considered and serve as a basis for the development of two new interscale links. The influence of different locality constraints is studied in terms of the mechanical response and the error distribution is compared to a full fine scale analysis.