Challenges and Limitations in Multiscale Predictive Scientific Simulations
Wing Kam Liu
Department of Mechanical Engineering, Northwestern University, Evanston, IL

One of the new initiatives in predictive science that is relevant to National Interest is the thermo-mechanical-electrical-electronic predictive science subjected to extreme environments. Our major aim is to achieve a paradigm shift from empirical approaches of microsystem/materials design to one which is based on multi-scale predictive science. While the former relies on tests on prototypes, the proposed approach can treat situations where full duration system level tests are not feasible. This change in paradigm will offer many benefits in the design and maintenance of Microsystems, because it is neither possible nor practical to pretest new designs for the long lifetimes and the environmental conditions that are required. It is anticipated that these approaches will be applicable throughout science and engineering. For example, the recent news of the failure of the missile defense system test may be due to aging and corrosion that cause mechanical parts to jam . Such problems may be prevented utilizing our proposed predictive science system to perform better design with novel materials.

The proposed approach is based on four pillars:

1. Multidisciplinary Predictive Science. The development and advancement of predictive theory and methodologies for materials damage and failure, material stability, aging, and radiation effects, culminating in constitutive models that can be used for prediction of the performance of microsystems in satellites.
2. The development of an integrated computational system that spans the scales from quantum mechanics to continuum mechanics for prediction of mechanical and electrical performance under harsh environments.
3. A program that addresses the following challenges in validation, verification, and uncertainty quantification (V&V, UQ):
   a. V&V of methods for which only incomplete experimental information can be provided.
   b. V&V by a limited numbers of experiments of synergistic factors such as aging and radiation.
   c. V&V of methods that link large ranges of space and time scales.
4. A focus problem: the prediction of the failure modes and system reliability in the RF communication microsystem. We are discussing with several aerospace companies and selected DOE scientists to come up with the details of the focus problem.

Molecular dynamics is probably the most widely used method to study interfacial phenomena. However, it relies on accurate empirical interatomic potential to make reliable predictions. These potentials are usually obtained by fitting parameters of an assumed form of the potential to first-principle calculations. Although embedded atomic method (EAM) potentials are very good for metals, and Tersoff and Brenner potentials are excellent for covalent-bonded materials, it is suspected that these potentials are generally applicable for materials interfaces. The reason is that materials at the interfaces may be very different in terms of their crystallography and electronic structure, which dictate their mutual bonding. Typical empirical interatomic potentials may not be valid or may not be available to treat novel combination of materials. To make things worse, environmental effects such as oxidation and corrosion are generally hard to model because potentials that incorporate chemical reactions are rare and first-principle calculations are generally too expensive for many researchers. In addition, generating the interfacial geometry at the atomistic scale is a challenge because it largely depends on the specific manufacturing process and environment. A general framework needs to be developed to generate and test empirical interatomic potentials in a timely and reliable manner.

Another challenge is to estimate the thermal conductivity in continuum modeling of material interfaces. Besides the aforementioned problems of employing MD to estimate thermal conductivity, classical MD and even quantum MD based on the Born-Oppenheimer approximation treat each atom as classical particle, and hence give inaccurate results for materials with relative high Debye temperatures. Silicon, diamond, aluminum, and chromium all have Debye temperatures above 400 K, and thus quantum effects on thermal properties are very important at room temperature. For single material, thermal conductivity can be estimated from Boltzmann transport theorem that can incorporate quantum effects, but it cannot be used to treat material interfaces and defects.

There is also an immediate need to develop uncertainty quantification and propagation, validation and verification methods for multiscale simulation models and methods. Usually, multiscale continuum methods employ some sort of homogenization or statistical averaging to reduce the number of degrees of freedom. The error introduced through average may grow exponentially in size as it is propagated toward larger scales or it may remain bounded. A faithful method that quantifies and propagates such error will be important for both the design of multiscale methods and the reliability of the target system of interest. On the other hand, multiscale models obviously require experimental validation at different length and time scales, which may not be feasible. Then the way that we design limited validation experiments that are both feasible and sufficient to validate a multiscale model is crucial. It is likely that this must come from experience and physical understanding of both the experimentalist and theorists to investigate mechanisms that directly couple with one another instead of performing experiments for all the time and length scales. Similarly, verification of codes of coupled multiscale codes may be performed by direct numerical simulations (DNS). DNS is very computationally intensive and must be performed for only limited extent, and hence require judgment from experienced researchers. A methodology would be helpful to guide the validation and verification of multiscale models and methods.

It is noted that these predictive scientific computing methodologies are applicable to many other applications such as structural materials, and re-entry vehicles, among others.