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.