Frontiers of Structural and Civil Engineering
>> 2019,
Volume 13,
Issue 2
doi:
10.1007/s11709-018-0475-5
RESEARCH ARTICLE
High-order phase-field model with the local and second-order max-entropy approximants
1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746, Iran |
Accepted: 2018-05-31
Available online: 2019-03-12
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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.
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