Weak solutions and simulations to a new phase-field model with periodic boundary

ABSTRACT

We prove the existence and investigate the large-time behavior of weak solutions for a new phase-field model with periodic boundary conditions, which is suitable for structural transformation driven by configurational forces, such as martensitic transformation in shape memory alloys. Furthermore, the evolution of martensitic phase transition in MnNi alloys is simulated by employing this model.

Keywords:

• Galerkin method
• existence
• large-time behavior
• weak solutions
• phase-field simulations

AMS Classifications:

• 35K65
• 74N20

Acknowledgments

We are greatly thankful to Prof. Zhu for his helpful discussion. This work is supported by the Physical Basis and Mechanism of High-throughput Parallel Computing (No. 2017YFB0701502).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the Physical Basis and Mechanism of High-throughput Parallel Computing (No. 2017YFB0701502).