Phase-field modeling and peridynamics for defect dynamics, and an augmented phase-field model with viscous stresses
Phase-field modeling and peridynamics for defect dynamics, and an augmented phase-field model with viscous stresses
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缺陷动力学的相场建模和近场动力学，以及具有粘性应力的增强相场模型
DOI：
10.1016/j.jmps.2021.104716
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发表时间：
2022
影响因子：
5.3
通讯作者：
Dayal, Kaushik
中科院分区：
文献类型：
--
作者：
Chua, Janel;Agrawal, Vaibhav;Breitzman, Timothy;Gazonas, George;Dayal, Kaushik
这项工作首先应用周期动力学和相场模型来预测具有非单调应力-应变响应的弹性固体中一维界面的惯性运动。在经典的非线性弹性力学中，众所周知，除了动量平衡外，亚音速界面还需要一个动力学定律才能获得唯一解；相比之下，对于超音速界面，仅动量平衡就足以提供唯一解。这项工作发现，近程动力学与这一经典结果是一致的，因为不同的正则化参数的选择为亚音速运动提供了不同的动力学，而为超音速运动提供了相同的动力学。相比之下，与弹性动力学相耦合的传统相场模型甚至不能定性地模拟界面的超音速运动。这项工作指出了标准相场模型的物理缺陷是：(1)没有高阶应力来平衡非物理应力奇点，以及(2)该模型能够访问能量景观的非物理区域。基于这些观察，本工作提出了一个增广相场模型来引入缺失的物理。该扩展模型增加了：(1)除了耗散相场演化之外，动量平衡的粘性应力，以规则化奇点；以及(2)对使系统远离能量景观的非物理区域的物理机制进行建模的增强驱动力。当耦合到弹性动力学时，增广模型正确地描述了亚音速和超音速界面运动。这种增广模型的计算量与传统相场模型基本相同，并且只需要对数值方法稍作修改，因此被提出作为传统相场模型的替代品。
This work begins by applying peridynamics and phase-field modeling to predict 1-d interface motion with inertia in an elastic solid with a non-monotone stress–strain response. In classical nonlinear elasticity, it is known that subsonic interfaces require a kinetic law, in addition to momentum balance, to obtain unique solutions; in contrast, for supersonic interfaces, momentum balance alone is sufficient to provide unique solutions. This work finds that peridynamics agrees with this classical result, in that different choices of regularization parameters provide different kinetics for subsonic motion but the same kinetics for supersonic motion. In contrast, conventional phase-field models coupled to elastodynamics are unable to model, even qualitatively, the supersonic motion of interfaces. This work identifies the shortcomings in the physics of standard phase-field models to be: (1) the absence of higher-order stress to balance unphysical stress singularities, and (2) the ability of the model to access unphysical regions of the energy landscape.Based on these observations, this work proposes an augmented phase-field model to introduce the missing physics. The augmented model adds: (1) a viscous stress to the momentum balance, in addition to the dissipative phase-field evolution, to regularize singularities; and (2) an augmented driving force that models the physical mechanism that keeps the system out of unphysical regions of the energy landscape. When coupled to elastodynamics, the augmented model correctly describes both subsonic and supersonic interface motion. The augmented model has essentially the same computational expense as conventional phase-field models and requires only minor modifications of numerical methods, and is therefore proposed as a replacement to the conventional phase-field models.
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影响因子：
5.4
作者：
J. Mehrmashhadi;M. Bahadori;F. Bobaru
通讯作者：
J. Mehrmashhadi;M. Bahadori;F. Bobaru
影响因子：
5.3
作者：
C. Albrecht;A. Hunter;A. Kumar;I. Beyerlein
通讯作者：
C. Albrecht;A. Hunter;A. Kumar;I. Beyerlein
伪动量：起源和后果
DOI：
--
发表时间：
2020
期刊：
Zeitschrift für Angewandte Mathematik und Physik
影响因子：
--
作者：
H. Singh;James Hanna
通讯作者：
James Hanna
DOI：
10.1137/050629951
发表时间：
2005
期刊：
SIAM J. Appl. Math.
影响因子：
--
作者：
H. Alber;P. Zhu
通讯作者：
H. Alber;P. Zhu
影响因子：
5.3
作者：
Agrawal, Vaibhav;Dayal, Kaushik
通讯作者：
Dayal, Kaushik