There are about three input files that PMAP reads, the model including the atomic and particle coordinate and ID data, if coupling to a FEA mesh the FE mesh data and material properties are read from an FEA input file, and most importantly the global PMAP input file which contains all of the simulation control parameters. The first two input files have been discussed in Section II.B. and Appendix C.6.; the development of the GP model is performed with a separate crystal tessellation code, the usage of which is described in detail in Appendix C.1. The main input file's directives are listed and described in full detail in Appendix D. along with instructions to compile and run PMAP.
Also included in Appendix D are the corresponding input files for the examples described in Chapter II. The purpose of this is for the reader to become familiar with the simulation
process and the data files that are required to carry out these kinds of concurrent multiscale simulations. By explaining this we hope that more people will become involved in developing not only new multiscale methods but also to be able to write code to realize their creations.
1. Post-processing
Most of the utility programs used with PMAP are for post processing purposes.
These include conversion programs to convert the output files of PMAP to other formats usable by other mainstream programs such as VMD130, AtomEye131, and gnuplot132 for visualization. Other programs are for data analysis, model manipulation and detailed debugging of simulations. A full list of these programs is provided in Table VIII of Appendix E. General post processing program explanations are described in Appendix E and deeper analysis programs are described in Appendix F, such detailed molecular structure analysis which can identify atomic defects using several different techniques including, Coordination Number, Common Neighbor Analysis133, Near Neighbor Grouping134, Coordination Vector, and void identification.
With these utility programs the PMAP output data files can easily be manipulated, analyzed, and phenomena debugged and understood. Many of these programs are not restricted for use with PMAP but are programed to have general functionality for use in many other applications.
D. Summary
The PMAP procedures have been described in detail and the capabilities illustrated. The general structure of PMAP is very similar to most MD simulation programs for the GP computational contribution. For FEA coupling a simple FEM solver is used periodically during the iterations. Both of these components are easy to be recognized individually, but the strength of PMAP comes from their combination.
Common topics for code improvement are better memory consumption, more efficient computational techniques, parallel algorithms, and more intuitive model development programs. However the most important improvements to be made are theoretical in nature and will be discussed in the recommendations in Chapter VIII.
CONCLUSIONS AND RECOMMENDATIONS
Although there has been great progress in the use of MD to investigate crack propagation and the origins of failure there are two main shortcomings:
First, most work concentrates on crack propagation rather than crack nucleation.
These defects are both theoretically and practically important since they are the key properties for understanding the underlying mechanisms of failure.
Secondly, much work has imposed special treatments to ensure that the crack propagates along a desired path. These treatments are convenient when using the cohesive zone model (CZM) to investigate and model the crack propagation behavior;
however their effectiveness must be further validated because the crack propagation essentially depends on how it was nucleated.
From the modeling perspective, the methods used today have a difficult time linking the behaviors of materials on the nanoscale to the large scale bulk properties.19 This is mainly due to the complicated question: what is the minimum size of material that can be considered a continuum? The answer to this question is highly material dependent. Another reason for ambiguous answers to this question is due to the strong surface effects at the nanoscale. These effects become more significant when the area/volume ratio increases. This indicates that the surface energy is very important to consider on the nanoscale and must be included if an accurate material model is to be used at these small scales. In the elastic range continuum models are incredibly reliable and can be applied to discrete materials having a size of a few nanometers.47 However these continuum models break down when plasticity is involved at these small scales, such that the minimum required model size for plasticity remains unsolved.
This gap in capability prevents atomistic-based models from predicting large scale material behavior thereby failing to link the two classes of multiscale analysis together. If micron sized models can be developed it would open a door to solving important problems in engineering based on a fundamental atomistic foundation.
The GP method and the related GP-FEA method have been introduced as candidates for this gap in capability. It has been seen to have a natural interface between scale domains where physical variables such as displacement and force may smoothly pass from one scale to another. Atomic phenomena such as dislocations may be passed into higher scale domains via the scale-duality concept50 by decomposing particles into their constituent atoms. In addition, it has been mathematically proven48,50 that all calculations in the particle domain can be conducted at the atomistic domain scale using the same potential, parameters and numerical algorithm as is used for the model's atomistic scale. Thus the GP method is essentially an extension of MD and can be easily delivered to applications by modifying existing MD codes.