High-order phase-field model with the local and second-order max-entropy approximants

Abstract

We approximate the fracture surface energy functional based on phase-field method with smooth local maximum entropy (LME) and second-order maximum entropy (SME) approximants. The higher-order continuity of the meshfree methods such as LME and SME approximants allows to directly solve the fourth-order phase-field equations without splitting the fourth-order differential equation into two second-order differential equations. We will first show that the crack surface functional can be captured more accurately in the fourth-order model with smooth approximants such as LME, SME and B-spline. Furthermore, smaller length scale parameter is needed for the fourth-order model to approximate the energy functional. We also study SME approximants and drive the formulations. The proposed meshfree fourth-order phase-field formulation show more stable results for SME compared to LME meshfree methods.

Keywords

second-order maximum entropy / local maximum entropy / second- and fourth-order phase-field models / B-spline

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Acknowledgements

Fatemeh Amiri would like to thank “Presidency of Islamic Republic of Iran National Elites Foundation” and “School of Mathematics, Institute for Research in Fundamental Sciences (IPM)” for financial support during the project.

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