Abstract
Advanced materials are crucial to economic security and human well-being. American then-President Obama launched in 2011 the Materials Genome Initiative (MGI) that is a novel and multi-stakeholder effort so that discovery and deployment of advanced materials can be significantly accelerated while the cost can be considerably reduced. Integrated computation is a key tool of MGI. Phase-field approach is a young, however, has now emerged as a powerful tool in theoretical and numerical analysis of phenomena at the meso-scale, therefore it has important applications to MGI. We shall mainly review two types of phase-field models, formulated recently by Alber and the first author of this article, for solid-solid phase transitions driven by configurational forces, with applications to martensitic phase transitions in, e.g. smart materials like shape memory alloys, and to sintering which is a process in, for instance, powder metallurgy. Mathematical and numerical investigations of these models will be presented and open problems related to the models are listed. Finally we shall also introduce phase-field crystal method which can be regarded as an extension of phase-field approach.
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Acknowledgements
The authors would like to express their sincere thanks for the anonymous reviewer(s) for his/her useful comments. Zhu and Tang are supported in part by the Start-up grant of 1000-plan Scholar Program from Shanghai University, and by Key grant (Grant No. 2017YFB0701502) from the Ministry of Science and Technology of P. R. China, and Li is supported in part by the National Science Foundation of China (Grant No. 11671134) and the Ph.D. Program Foundation of Ministry of Education of China (Grant No. 20133127110007).
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Zhu, P., Tang, Y., Li, Y. (2019). New Phase-Field Models with Applications to Materials Genome Initiative. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_18
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