MULTISCALE MODELING, HETEROGENEOUS PERCEPTION

The purpose of multiscale models is to determine the locally averaged global constitutive behavior of heterogeneous materials taking into account the effect of the micro and macro-structure, which may exhibit all kinds of heterogeneity,. And these micro-structural details, such as particle/fiber volume fraction, fiber orientation, crack density and orientation, and constitutive properties of the individual constituents, certainly have a substantial impact on the overall properties of the materials.

In multiscale models the global- (macro) scale analysis, i.e., the problem of interest, is performed concurrently with the local- (meso, micro) scale analyses, with the number of local scales determined by the physical problem and limited by the available computational power. In principle, this approach can be used on as many continuum length scales as necessary as long as the assumption of separation of scales and the limits of continuum mechanics are valid.The effective constitutive behavior of one scale is then governed by the behavior of the consecutive nested smaller scales, such that the only model input parameters are the material properties of individual constituents at the smallest length scale and respective fracture properties (and chemical properties) at each appropriate length scale.

The simultaneous solution of both global and local problems (with two-way coupling) is considerably advantageous in cases where the microstructure changes and/or its behavior is history dependent. These changes can be physical, such as crack localization and/or viscoelasticity, or chemical, such as oxidation.