An adaptive multiscale method for quasi-static crack growth

Pattabhi R. Budarapu, Robert Gracie, Stéphane P A Bordas, Timon Rabczuk

Research output: Contribution to journalArticle

125 Citations (Scopus)

Abstract

This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom-atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.

Original languageEnglish
Pages (from-to)1129-1148
Number of pages20
JournalComputational Mechanics
Volume53
Issue number6
DOIs
Publication statusPublished - 2014 Jan 1

Fingerprint

Multiscale Methods
Crack Growth
Adaptive Method
Crack propagation
Atoms
Crack tips
Crack Tip
Lennard-Jones potential
Cracks
Crack
Continuum
Lennard-Jones Potential
Self-consistency
Atomistic Simulation
Numerical methods
Lattice Structure
Triangular Lattice
Phantom
Boundary conditions
Model

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Mechanical Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Computational Mathematics

Cite this

Budarapu, P. R., Gracie, R., Bordas, S. P. A., & Rabczuk, T. (2014). An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 53(6), 1129-1148. https://doi.org/10.1007/s00466-013-0952-6

An adaptive multiscale method for quasi-static crack growth. / Budarapu, Pattabhi R.; Gracie, Robert; Bordas, Stéphane P A; Rabczuk, Timon.

In: Computational Mechanics, Vol. 53, No. 6, 01.01.2014, p. 1129-1148.

Research output: Contribution to journalArticle

Budarapu, PR, Gracie, R, Bordas, SPA & Rabczuk, T 2014, 'An adaptive multiscale method for quasi-static crack growth', Computational Mechanics, vol. 53, no. 6, pp. 1129-1148. https://doi.org/10.1007/s00466-013-0952-6
Budarapu, Pattabhi R. ; Gracie, Robert ; Bordas, Stéphane P A ; Rabczuk, Timon. / An adaptive multiscale method for quasi-static crack growth. In: Computational Mechanics. 2014 ; Vol. 53, No. 6. pp. 1129-1148.
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