Multiscale Modeling

What is multiscale modeling?

The purpose of multiscale models is to determine the locally averaged global constitutive behavior of heterogeneous materials taking into account the effect of the microstructure, which may exhibit all kinds of heterogeneity, including evolving cracks. 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 (generally, between 10−10 m and 103m). 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.

Consider a structural part which is statistically homogeneous at the global scale but microscopically heterogeneous, as shown in the Figure below, where the microstructure may contain inclusions as well as growing cracks. If the characteristic length scales in the problem can be separated, the use of continuum mechanics along with a few mathematical principles will produce appropriate and accurate ways to calculate the homogenized constitutive behavior of the micro-structure (so-called Representative Volume Element – RVE).


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. In most practical problems, there exists a sustainable amount of damage induced by the formation and growth of micro-cracks. In this case, multiscale modeling can be particularly effective, since the evolution of the microstructure is necessarily both spatially and time dependent.

Why use multiscale modeling?

The need for economically feasible and efficient applications has increased significantly the complexity of engineering structures. As the complexity of applications increase, more complex materials need to be designed, as most materials found in nature do not have the desired features. For example, in the aerospace industry, high-strength and low-weight fiber-reinforced composites are used to minimize fuel consumption and still satisfy the minimum structural design criteria. In military applications, highly dissipative viscoelastic polymers are combined with high-strength fibers in order to produce materials that can be used in protective devices, such as tank armor and soldier helmets.

The idea is to combine different materials with different properties and produce a third material that meets the design requirements, and which is inherently heterogeneous. From the engineering point of view, heterogeneous materials are desirable because they can be suitably designed to take advantage of particular properties of each constituent. For example, carbon fiber-reinforced composites have wide applicability due to their superior thermo-mechanical performance and low weight, obtained due to the fibers, and their versatility in shape (parts of any shape can be molded) due to the use of epoxy matrix.

Since the overall behavior of heterogeneous materials is strongly affected by the mechanical properties of the individual constituents as well as by geometrical characteristics, such as volume fraction, shape, size, spatial orientation and distribution of particles/fibers, MultiMech™, a unique two-way coupled multiscale computational software, is a natural choice of tool to perform effective and accurate analysis and design of such advanced materials. The term two-way coupled is used to denote that, in MultiMech™‘s approach, both global and local scale problems concurrently exchange information with each other, thus providing the most advanced solution available in market.

Besides, MultiMech™ is fully parallelized and the user can take advantage of multi-core (cluster) infrastructures in order to accelerate results, as shown in the Figure below for a particular multiscale benchmark problem.