International Journal of Fracture

, Volume 201, Issue 2, pp 157–170 | Cite as

Bond-based peridynamics: a quantitative study of Mode I crack opening

  • Patrick Diehl
  • Fabian Franzelin
  • Dirk Pflüger
  • Georg C. Ganzenmüller
Original Paper

Abstract

This paper shows a new approach to estimate the critical traction for Mode I crack opening before crack growth by numerical simulation. For quasi-static loading, Linear Elastic Fracture Mechanics predicts the critical traction before crack growth. To simulate the crack growth, we used bond-based peridynamics, a non-local generalization of continuum mechanics. We discretize the peridynamics equation of motion with a collocation by space approach, the so-called EMU nodal discretization. As the constitutive law, we employ the improved prototype micro brittle material model. This bond-based material model is verified by the Young’s modulus from classical theory for a homogeneous deformation for different quadrature rules. For the EMU-ND we studied the behavior for different ratios of the horizon and nodal spacing to gain a robust value for a large variety of materials. To access this wide range of materials, we applied sparse grids, a technique to build high-dimensional surrogate models. Sparse grids significantly reduce the number of simulation runs compared to a full grid approach and keep up a similar approximation accuracy. For the validation of the quasi-static loading process, we show that the critical traction is independent of the material density for most material parameters. The bond-based IPMB model with EMU nodal discretization seems very robust for the ratio \({\delta }/{\varDelta X}=3\) for a wide range of materials, if an error of 5 % is acceptable.

Keywords

Bond-based peridynamics EMU-ND Critical traction Sparse grids 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Patrick Diehl
    • 1
  • Fabian Franzelin
    • 2
  • Dirk Pflüger
    • 2
  • Georg C. Ganzenmüller
    • 3
  1. 1.Institut für Numerische SimulationBonnGermany
  2. 2.IPVS/SGSStuttgartGermany
  3. 3.Fraunhofer EMIFreiburgGermany

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