Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind and upwind approximations

                                
==Abstract==

Materials such as composites are heterogeneous at the micro-scale, where
several constituents with different material properties can be distinguished like elastic
inclusions and the elasto-plastic matrix with isotropic hardening. One has to deal with
these heterogeneities on the micro-scale and then perform a scale transition to obtain the
overall behavior on the macro-scale, which is often referred to as homogenization. The
present contribution deals with the combination of numerically inexpensive mean-field
and numerically expensive full-field homogenization methods in elasto-plasticity coupled
to adaptive finite element method (FEM) which takes into account error generation and
error transport at each time step on the macro-scale. The proposed adaptive procedure
is driven by a goal-oriented a posteriori error estimator based on duality techniques. The
main difficulty of duality techniques in the literature is that the backwards-in-time al gorithm has a high demand on memory capacity since additional memory is required to
store the primary solutions computed over all time steps. To this end, several down wind and upwind approximations are introduced for an elasto-plastic primal problem by
means of jump terms [1]. Therefore, from a computational point of view, the forwards-in time duality problem is very attractive. A numerical example illustrates the effectiveness
of the proposed adaptive approach based on forwards-in-time method in comparison to
backwards-in-time method.

== Full Paper ==
<pdf>Media:Draft_Sanchez Pinedo_51292704961_file.pdf</pdf>