دانلود رایگان مقاله محاسبه میدان eigen-stress و انرژی الاستیک در انتشار اتمیستی آلیاژها

Abstract

The structural evolution of alloys is affected by the elastic energy associated to eigen-stress fields. However, efficient calculations of the elastic energy in evolving geometries are actually a great challenge in promising atomistic simulation techniques such as Kinetic Monte Carlo (KMC) methods. In this paper, we report two complementary algorithms to calculate the eigen-stress field by linear superposition (a.k.a. LSA, Lineal Superposition Algorithm) and the elastic energy modification in atomistic interdiffusion of alloys (the Atom Exchange Elastic Energy Evaluation (AE4) Algorithm). LSA is shown to be appropriated for fast incremental stress calculation in highly nanostructured materials, whereas AE4 provides the required input for KMC and, additionally, it can be used to evaluate the accuracy of the eigen-stress field calculated by LSA. Consequently, they are suitable to be used on-the-fly with KMC. Both algorithms are massively parallel by their definition and thus well-suited for their parallelization on modern Graphics Processing Units (GPUs). Our computational studies confirm that we can obtain significant improvements compared to conventional Finite Element Methods, and the utilization of GPUs opens up new possibilities for the development of these methods in atomistic simulation of materials.

5. Conclusions and future works

Predictive simulation of alloys structural evolution, involved in critical scenarios such as structural steel members in nuclear plants, can benefit from the great advances in the field of high performance computing in order to overcome computational barriers. Nowadays, the use of KMC methods supported on FEM calculations represents a highly time-consuming process. Alternatively, this work proposes two different algorithms (LSA and AE4 ) to calculate the eigen-stress field and the elastic energy modification in atomistic interdiffusion of alloys. In particular, the main contributions of this paper include the following: 1. LSA allows fast calculation eigen-stress field of complex geometry sample. It also offers incremental on-the fly updating of the total stress-field after every atom exchange event in KMC simulations in a reasonably short computational time. 2. AE4 provides a critical input for KMC. Additionally, it can provide a scalar merit figure in order to evaluate the accuracy of the approximate stress field calculations. 3. Algorithms here proposed are massively parallel by their definition and, therefore, we develop a data-parallel approach to leverage Graphics Processing Units (GPUs). Predictive simulation of alloy structural evolution on GPUs is still at a relatively early stage and, in this sense, this work provides a relatively simple parallelization. But, with many other types of optimization still to be explored, this field seems to offer a promising and potentially fruitful area of research. On the physical framework, the present model may be developed through the implementation of another types of boundary conditions for the considered domain. On the hardware side, it is expected to get even higher accelerations on GPUs whenever the problem size keeps growing and larger device memory space is available. Moreover, we may anticipate that the benefits of our approach would also increase when parallelizing kmax most-internal loop since it would provide fine-grain parallelism, and also when using future GPU generations endowed with thousands of cores, and eventually grouped into GPU clusters to lift performance into unprecedented gains, where parallelism is called to play a decisive role.