Analysis of crack propagation phenomena of phase-field model

本文从理论和数值两方面对作者和木村博士提出的相场模型的有效性进行了估计。从理论上研究了相场平衡态的空间分布与正则化参数的关系。数值计算还表明，损伤基值（或微裂纹密度）控制裂纹线的数量。3-对三维裂纹扩展进行了数值研究，并对裂纹面的扭转进行了分析。开发了FreeFem++三维数值数据的立体观察器，目前正在进行大规模裂纹扩展的数值代码开发。

Validity of the phase-field model that is introduced by the author and Dr. Kimura is estimated both theoretically and numerically. Relation between the spatial profile of the equilibrium state of phase-field and the regularization parameter is studied theoretically. It is also shown numerically that the basement value of the damage (or the micro-crack density) controls the number of crack lines. 3-dimensional crack propagation is studied numerically, and the twist of crack surface is investigated. The stereo-viewer for 3-dimensional numerical data of FreeFem++ is developed, and the numerical code development for the large scale crack propagation is now in progress.