Meso-macro-scale constitutive modeling with error control

Paper in proceeding, 2004

We consider combined material model and FE-mesh adaptivity in the context of computational meso-macro-scale modeling, 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. In this presentation we discuss, in particular, one major source of macro-scale model error for given mesostructural morphology and constitutive models of the meso-constituents: The size, or degree of "representativeness", of the RVE. Results will be shown for a composite meso-structure with stiff particles embedded in a soft matrix while assuming that both constituents respond as hyperelastic continua with perfect bond. It seems as a reasonable strategy to aim at equibalancing this model error and the macro-scale discretization error for given loading.