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Paper   IPM / M / 15551
School of Mathematics
  Title:   High order phase-field model with the local and second order max-entropy approximants
  Author(s):  Fatemeh Amiri
  Status:   Published
  Journal: Front. Struct. Civ. Eng.
  Year:  2018
  Pages:   DOI: 10.1007/s11709-018-0475-5
  Supported by:  IPM
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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