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International Journal for Multiscale Computational Engineering
Factor de Impacto: 1.016 Factor de Impacto de 5 años: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i4.20
pages 365-377


Kai Schrader
Bauhaus-Universität Weimar, Institute of Structural Mechanics, D-99423 Weimar, Germany
Carsten Konke
Bauhaus-Universität Weimar, Institute of Structural Mechanics, Germany


In recent years design and assessment of engineering structures are done in numerical simulation environments, applying state-of-the-art models from CAD, computational mechanics and visual analytics. Over the last two decades there has been a strong trend toward integration of theoretical and numerical models from material science on different scales up to the atomic lattice into simulation models for engineering applications, by applying multiscale models in combination with homogenization techniques or concurrent multiscale models. Especially for investigating new and heterogeneous materials, multiscale models can be applied to study material physics, such as damage initiation and propagation, on appropriate scales and integrate this information into large-scale engineering models. A major drawback of multiscale models in materials science is their enormous demand for computing power with respect to computing time and main memory. This paper suggests a method to split a heterogeneous material model, consisting of a matrix material and embedded inclusions with interfacial transition zones, into zones of elastic and inelastic behavior and to customize the discretization methods for these two zones in an appropriate way. We propose the application of structured and unstructured meshes in a hybrid fashion and to solve the resulting equation systems with several million degrees of freedom by iterative solver techniques. In order to consider the damage evolution behavior, a regularized anisotropic damage model is used and the incremental-iterative solution for this problem is based on sequential linear analysis, following the sawtooth concept of Rots et al. (2006).


  1. Basermann, A., Reichel, B., and Schelthoff, C., Preconditioned cg methods for sparse matrices on massively parallel machines. DOI: 10.1016/S0167-8191(97)00005-7

  2. Bathe, K. J., Finite Element Procedures.

  3. Bell, N. and Garland, M., Efficient sparse matrix-vector multiplication on cuda.

  4. Caballero, A., Lopez, C. M., and Carol, I., 3D meso-structural analysis of concrete specimens under uniaxial tension. DOI: 10.1016/j.cma.2005.05.052

  5. Chapman, B., Jost, G., and van der Pas, R., Using OpenMP: Portable Shared Memory Parallel Programming.

  6. Garboczi, E. J., Three-dimensional mathematical analysis of particle shape using x-ray tomography and spherical harmonics: Application to aggregates used in concrete. DOI: 10.1016/S0008-8846(02)00836-0

  7. Gropp, W., Lusk, E., and Skjellum, A., Using MPI: Portable Parallel Programming with the Message-Passing Interface.

  8. Haefner, S., Eckardt, S., Luther, T., and Koenke, C., Mesoscale modeling of concrete: Geometry and numerics. DOI: 10.1016/j.compstruc.2005.10.003

  9. Karypis, G. and Kumar, V., A software package for partitioning unstructured graphs, partitioning meshes, and computing fillreducing orderings of sparse matrices.

  10. Kelley, C. T., Iterative methods for linear and nonlinear equations. DOI: 10.1137/1.9781611970944

  11. Kim, H. J. and Swan, C. C., Voxel-based meshing and unit-cell analysis of textile composites. DOI: 10.1002/nme.594

  12. Klawonn, A. and Rheinbach, O., Robust feti-dp methods for heterogeneous three dimensional elasticity problems. DOI: 10.1016/j.cma.2006.03.023

  13. Loghin, D. and Wathen, A. J., Schur complement preconditioning for elliptic systems of partial differential equations. DOI: 10.1002/nla.322

  14. Raabe, D., Continuum scale simulation of engineering materials: Fundamentals–microstructures–process applications.

  15. Rots, J. G., Belletti, B., and Invernizzi, S., Event-by-event strategies for modelling concrete structures.

  16. Rots, J. G. and Invernizzi, S., Regularized sequentially linear saw-tooth softening model. DOI: 10.1002/nag.371

  17. Shan, Z. and Gokhale, A. M., Digital image analysis and microstructure modeling tools for microstructure sensitive design of materials. DOI: 10.1016/j.ijplas.2003.11.003

  18. Toselli, A. and Widlund, O., Domain decomposition methods—algorithms and theory.

  19. Wang, Z. M., Kwan, A. K. H., and Chan, H. C., Mesoscopic study of concrete 1: Generation of random aggregate structure and finite element mesh. DOI: 10.1016/S0045-7949(98)00177-1

  20. Wriggers, P. and Moftah, S. O., Mesoscale models for concrete: Homogenisation and damage behaviour. DOI: 10.1016/j.finel.2005.11.008