Numeerisen analyysin ja laskennallisen tieteen seminaari

23.1.2006  klo 14.15  U356

Fredrik Larsson, Chalmers University of Technology
Aspects on adaptive meso-macro-scale modeling in solid mechanics

In constitutive modeling, a key issue is to choose the complexity of  a model such that accuracy and efficiency are well balanced.  Furthermore, there is no point in choosing a complex, and  computationally demanding, constitutive model if the solution of the  structural problem has low quality. With this in mind at the solution  of large scale (structural) problems, we consider a set of  hierarchical models of increasing accuracy (and computational cost)  as part of a Concurrent Multiscale Modeling (CMM) strategy based on  the assumption of complete scale separation. The coarsest model is  that of a homogenized macroscopic model, while the finer levels are  defined through the homogenized response of a sub-scale problem  solved on a Representative Volume Element (RVE) with suitable  boundary conditions. In practice, this sub-scale problem is solved  using finite elements at each spatial quadrature (Gauss) point in the  macro-domain. The high cost of this strategy clearly motivates the  use of adaptive techniques, since the sub-scale effects that cannot  be homogenized a priori usually occur only in certain parts of the  domain. Such parts of the domain are, for instance, areas of high  stresses or areas of high influence on the chosen output quantity. In  other parts of the domain the use of a less accurate macroscopic  model can reduce the computational cost considerably without any  major influence on the accuracy.