Abstract
Hierarchical two-scale methods are computationally very powerful as there is no direct coupling between the macro- and microscale. Such schemes develop first a microscale model under macroscopic constraints, then the macroscopic constitutive laws are found by averaging over the microscale. The heterogeneous multiscale method (HMM) is a general top-down approach for the design of multiscale algorithms. While this method is mainly used for concurrent coupling schemes in the literature, the proposed methodology also applies to a hierarchical coupling. This contribution discusses a hierarchical two-scale setting based on the heterogeneous multi-scale method for quasi-static problems: the macroscale is treated by continuum mechanics and the finite element method and the microscale is treated by statistical mechanics and molecular dynamics. Our investigation focuses on an optimised coupling of solvers on the macro- and microscale which yields a significant decrease in computational time with no associated loss in accuracy. In particular, the number of time steps used for the molecular dynamics simulation is adjusted at each iteration of the macroscopic solver. A numerical example demonstrates the performance of the model
Original language | English |
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Pages (from-to) | 571-572 |
Journal | Proceedings in Applied Mathematics and Mechanics |
Volume | 14 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2014 |
Event | 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics: GAMM 2014 - Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany Duration: 10 Mar 2014 → 14 Mar 2014 |
Fields of Expertise
- Advanced Materials Science
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
- Theoretical