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| Paper IPM / M / 15551 |
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| Abstract: | |
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We approximate the fracture surface energy functional based on phase-field method with smooth local
(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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