Proposal of a new governing equation of crack propagation caused by change of temperature and its analysis

2014 Fiscal Year Final Research Report

• Project/Area Number: 25610031
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyoto University
• Principal Investigator: ISO Yuusuke 京都大学, 情報学研究科, 教授 (70203065)
• Co-Investigator(Kenkyū-buntansha): WAKANO Isao 京都大学, 情報学研究科, 講師 (00263509) ; FUJIWARA Hiroshi 京都大学, 情報学研究科, 助教 (00362583) ; MYGDALSKYY Volodymyr 京都大学, 工学研究科, 特任講師 (70598896) ; KIMURA Masato 金沢大学, 数物科学系, 教授 (70263358)
• Project Period (FY): 2013-04-01 – 2015-03-31
• Keywords: 応用数学 / 数理モデリング / 破壊力学 / 数値解析 / 微分方程式 / シミュレーション工学

Outline of Final Research Achievements

It is known that slow propagation of cracks caused by change of temperature at tips of cracks sometimes happen, and the aim of this research is to give a new mathematical model for the phenomena. In our research of two years, we have both positive results and a negative result. We have succeeded in giving a new mathematical model of crack propagation based on the phase-field approach and in giving a proof to a new numerical scheme to solve hyperbolic equations accurately. These results are significant and are positive ones in this resear program. On the other hand, we should conclude that the original aim is related highly nonlinear analysis and is, at present, too difficult to establish a new governing equation within only two years.

Free Research Field

数物系科学