Thermodynamically consistent nonlocal kernel with boundary effect compensation and its application to the coupled phase field-nonlocal integral elasticity equations for modeling of martensitic transformations

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.

Keywords:

• Nonlocal integral elasticity
• CTP kernel
• boundary effects
• martensitic transformation
• phase field approach

Additional information

Funding

The support of Isfahan University of Technology and Iran National Science Foundation is gratefully acknowledged.