Adaptive computational meso–macro-scale modeling of elastic composites

We consider combined material model and FE-mesh adaptivity in the context of computational meso–macro-scale modeling (CMM), whereby the coupling between different geometrical scales is taken into account. The macro-scale model is then replaced by the homogenized response of a representative volume element (RVE). In practice, the RVE is analyzed as a “small-scale” finite element problem, which is solved for each (Gauss) point in the domain. The high cost of this strategy clearly motivates the use of adaptive techniques based on a posteriori error estimates for the combined model and discretization error, whereby the solution of an appropriate dual problem is utilized. The suggested adaptive procedure is applied to a particle/matrix composite with hyperelastic constituents.