Molecular Dynamics Simulation and Homogenization Analysis

In the framework of continuum mechanics, the material properties have mainly been determined through experiments using specimens of sufficiently large dimensions in comparison to the dimensions of any inherent fabric. This is particularly true for micro-inhomogeneous materials where the specimen is large compared to the size of this local structure. This procedure, which provides the system of governing equations and the experiment-based material properties, is referred to as the macro-phenomenological scheme. 

If we use the macro-phenomenological approach, we do not include the intrinsic properties, which represent the movement at a molecular-level. In this sense it is a difficult procedure to establish a correct system of governing and constitutive equations. For example, if we consider the experimental results for a micro-inhomogeneous material, we frequently observe differences if the specimen size is changed. The experimental results are only intrinsically true for the size range of that experiment. In this sense, the macro-phenomenological scheme is interpolation-based. 

The high-level radioactive wastes (HLW s) produced at nuclear power plants must be isolated from the population for an extremely long time, i.e., more than 10,000 years. There are plans to construct HLW disposal facilities in deep underground repositories. Thus, the safety of the barrier system must be evaluated for time scales in excess of 10,000 years this is beyond the scope of any conventional scientific experiment-based approach. We need to use an alternative method that is based on a macro-phenomenological approach. 

All materials consist of particles, i.e., atoms and/or molecules. It is possible to determine the forces that act on these particles by using the modern scientific techniques of quantum mechanics and chemical-bond models. Molecular simulation methods provide material properties as a set of particle behaviors under the above chemical-bond forces (Allen and Tildesley 1987 Ueda 1990 Kawamura 1990) The Molecular Dynamics method (MD Fig. 1.1) solves the equation of motion directly in a finite difference scheme, using a very short time step, i.e., less than 1 fs (femtosecond 1 fs = 10 s). The Monte Carlo Method (MC) calculates a probability of occurrence of the particle configuration. Note that since the Molecular Mechanics Method (MM) does not treat the behavior of a molecular group, we exclude MM from the molecular simulation methods. 

Molecular simulations allow scientists to predict future occurrences with some accuracy. However in the foreseeable future it is virtually impossible to consider the sample size of the bentonite buffer that will be used in the HLW repositories using molecular simulation methods. One cc of water has about 0.3 x 10 molecules and bentonite can absorb more water than the volume of the solid crystals. Even the most-advanced parallel processor computer can only simulate about a hundred million particles. The elapsed time is also limited since we can obtain the results for at most 1 ns (=10 s). Thus, the use of molecular simulations to forecast events that might occur in, for example, nuclear waste repositories is limited by computer resources. 

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