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

: Diehl, Patrick; Franzelin, Fabian; Pflüger, Dirk; Ganzenmüller, Georg C.


International Journal of Fracture 201 (2016), Nr.2, S.157-170
ISSN: 0376-9429
ISSN: 1573-2673
ISSN: 0020-7268
Fraunhofer SCAI ()
Fraunhofer EMI ()
bond-based peridynamics; EMU-ND; critical traction; sparse grids

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 δ/ΔX=3 for a wide range of materials, if an error of 5 % is acceptable.