Abstract

In this article, the thermodynamically consistent compensated two-phase (CTP) kernel is employed for nonlocal integral elasticity based phase field modeling of stress-induced martensitic transformations. Utilizing a proper thermodynamic framework, the stress-strain relation with the CTP kernel is shown to be thermodynamically consistent. The coupled Ginzburg–Landau and local/nonlocal elasticity equations are solved using the finite element method. The advantages of the CTP kernel over previous kernels are shown through stress-induced martensitic growths in a simply connected region, in presence of a hole, in presence of a crack, and in a sample with a preexisting nucleus. In contrast to other widely used nonlocal kernels, for the CTP kernel, no ill-posedness is observed, the normalization and locality recovery conditions are satisfied and the boundary effects are entirely compensated. The numerical convergence of a phase field-nonlocal integral elasticity problem is studied, which indicates that the CTP kernel does not suffer from the numerical convergence issues of previous kernels. The present study provides a better insight into the CTP kernel and its application to the modeling of various phenomena at the nanoscale.

摘要

在这篇文章中，热力学一致的补偿两相 (CTP) 核用于非局部积分弹性的基于应力诱导马氏体相变的相场建模。利用适当的热力学框架，与 CTP 核的应力-应变关系被证明是热力学一致的。使用有限元方法求解耦合的 Ginzburg–Landau 和局部/非局部弹性方程。CTP 内核相对于之前内核的优势体现在简单连接区域、存在孔、存在裂纹以及具有预先存在的核的样品中的应力诱导马氏体生长。与其他广泛使用的非本地内核相比，对于 CTP 内核，没有观察到不适定性，归一化和局部恢复条件得到满足，边界效应得到完全补偿。研究了相场-非局部积分弹性问题的数值收敛性，这表明 CTP 内核不会遇到以前内核的数值收敛问题。本研究提供了对 CTP 内核及其在纳米级各种现象建模中的应用的更好洞察。