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New Phase-Field Models with Applications to Materials Genome Initiative

  • Peicheng ZhuEmail author
  • Yangxin Tang
  • Yeping Li
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)

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.

Keywords

Phase-field models Material Genome Initiative Materials science Martensitic phase transitions Interface motion by interface diffusion Configurational force Partial differential equations Elasticity system Weak solutions Simulations Shape memory alloys Sintering 

Notes

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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Materials Genome Institute and Department of MathematicsShanghai UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsShanghai UniversityShanghaiPeople’s Republic of China
  3. 3.Institute of Statistics and Applied MathematicsAnhui University of Finance and EconomicsBengbuPeople’s Republic of China
  4. 4.Department of MathematicsEast China University of Science and TechnologyShanghaiPeople’s Republic of China

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