Parallel Inelastic Heterogeneous Multi-Scale Simulations

  • Ramin Shirazi Nejad
  • Christian WienersEmail author
Part of the Mathematical Engineering book series (MATHENGIN)


We recall the heterogeneous multi-scale method for elasticity and its extension to inelasticity within a two-scale energetic approach, where the fine-scale material properties are evaluated in Representative Volume Elements. These RVEs are located at Gauß points of a coarse finite element mesh. Within this \(\text {FE}^2\) method the displacement is approximated on a coarse-scale, and depending on the strain at the Gauß points in every RVE a periodic micro-fluctuation and the internal variables describing the material history in this RVE are computed. Together, this defines the global energy and the dissipation functional, both depending on coarse-scale displacements as well as on fluctuations and internal variables on the micro-scale. Here we introduce a parallel realisation of this method which allows the computation of 3D micro-structures with fine resolution. It is based on the parallel representation of the RVE with distributed internal variables associated to each Gauß points, and a parallel multigrid solution method in the nonlinear computation of the micro-fluctuations and for the up-scaling of the algorithmic tangent within the incremental loading steps of the macro-problem. The efficiency of the method is demonstrated for a simple damage model combined with elasto-plasticity describing a PBT matrix material with glass fibre inclusions. For this investigation we use the material models in J. Spahn (Ph.D. thesis Kaiserslautern 2015) and the software developed by R. Shirazi Nejad (Ph.D. thesis Karlsruhe 2017).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Karlsruhe Institute of TechnologyKarlsruheGermany

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