Error controlled meso-macro-scale material modeling and computation

Paper in proceeding, 2004

In constitutive modeling, a key issue is to choose the complexity of a model such that model and discretization errors are properly balanced. In other words, there is no point in choosing a complex, and computationally demanding, constitutive model if the solution of the structural problem has low quality. In this paper, we consider combined material model and FE-mesh adaptivity in the context of Computational Meso-Macro-scale Modeling (CMM). 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. The suggested adaptive procedure is applied to a particle/matrix composite with hyperelastic constituents.