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Examples

Mechanics

Examples which only include mechanics and fracture are within examples/mechanics.

  • The first example is an elastic wave propagating through a cube from an initial Gaussian radial displacement profile1. The example can be run with: 

    ./CabanaPD/build/install/bin/ElasticWave CabanaPD/examples/mechanics/inputs/elastic_wave.json

  • The next example is the Kalthoff-Winkler experiment2, where an impactor causes crack propagation at an angle from two pre-notches on a steel plate. 

    ./CabanaPD/build/install/bin/KalthoffWinkler CabanaPD/examples/mechanics/inputs/kalthoff_winkler.json

  • Another example is crack branching in a pre-notched soda-lime glass plate due to traction loading3. 

    ./CabanaPD/build/install/bin/CrackBranching CabanaPD/examples/mechanics/inputs/crack_branching.json

  • An example with multiple random pre-notches is also available. 

    ./CabanaPD/build/install/bin/RandomCracks CabanaPD/examples/mechanics/inputs/random_cracks.json

  • The next example is a fragmenting cylinder due to internal pressure4. This problem can either run with PD only or with hybrid PD-DEM contact. 

    ./CabanaPD/build/install/bin/FragmentingCylinder CabanaPD/examples/mechanics/inputs/fragmenting_cylinder.json

  • An example highlighting plasticity simulates a tensile test based on an ASTM standard dogbone specimen. 

    ./CabanaPD/build/install/bin/DogboneTensileTest CabanaPD/examples/mechanics/inputs/dogbone_tensile_test.json

  • An example demonstrating the peridynamic stress tensor computation simulates a square plate under tension with a circular hole at its center5. 

    ./CabanaPD/build/install/bin/PlateWithHole CabanaPD/examples/mechanics/inputs/plate_with_hole.json

  • An example of multi-material simulation demonstrates crack propagation in a pre-notched plate with a stiff inclusion under traction loading. 

    ./CabanaPD/build/install/bin/CrackInclusion CabanaPD/examples/mechanics/inputs/crack_inclusion.json

Powder dynamics

Examples which only include mechanics and fracture are within examples/dem.

  • An example using DEM-only demonstrates powder filling in a container. 
    ./CabanaPD/build/install/bin/PowderFill CabanaPD/examples/mechanics/inputs/powder_fill.json

Thermomechanics

Examples which demonstrate temperature-dependent mechanics and fracture are within examples/thermomechanics.

  • The first example is thermoelastic deformation in a homogeneous plate due to linear thermal loading6. 

    ./CabanaPD/build/install/bin/ThermalDeformation CabanaPD/examples/thermomechanics/thermal_deformation.json

  • The second example is crack initiation and propagation in an alumina ceramic plate due to a thermal shock caused by water quenching7. 

    ./CabanaPD/build/install/bin/ThermalCrack CabanaPD/examples/thermomechanics/thermal_crack.json

Thermomechanics with heat transfer

Examples with heat transfer are within examples/thermomechanics.

  • The first example is pseudo-1d heat transfer (no mechanics) in a cube. 

    ./CabanaPD/build/install/bin/ThermalDeformationHeatTransfer CabanaPD/examples/thermomechanics/heat_transfer.json
    The same example with fully coupled thermomechanics can be run (with a much smaller timestep) using thermal_deformation_heat_transfer.json.

  • The second example is pseudo-1d heat transfer (no mechanics) in a pre-notched cube. 

    ./CabanaPD/build/install/bin/ThermalDeformationHeatTransferPrenotched CabanaPD/examples/thermomechanics/heat_transfer.json

References

  1. P. Seleson and D.J. Littlewood, Numerical tools for improved convergence of meshfree peridynamic discretizations, in Handbook of Nonlocal Continuum Mechanics for Materials and Structures, G. Voyiadjis, ed., Springer, Cham, 2018. doi:10.1007/978-3-319-22977-5_39-1 ↩

  2. J.F. Kalthoff and S. Winkler, Failure mode transition at high rates of shear loading, in Impact Loading and Dynamic Behavior of Materials, C.Y. Chiem, H.-D. Kunze, and L.W. Meyer, eds., Vol 1, DGM Informationsgesellschaft Verlag (1988) 185-195. ↩

  3. F. Bobaru and G. Zhang, Why do cracks branch? A peridynamic investigation of dynamic brittle fracture, International Journal of Fracture 196 (2015): 59–98. doi:10.1007/s10704-015-0056-8 ↩

  4. D.J. Littlewood, M.L. Parks, J.T. Foster, J.A. Mitchell, and P. Diehl, The peridigm meshfree peridynamics code, Journal of Peridynamics and Nonlocal Modeling 6 (2024): 118–148. doi:10.1007/s42102-023-00100-0 ↩

  5. A.S. Fallah, I.N. Giannakeas, R. Mella, M.R. Wenman, Y. Safa, and H. Bahai, On the computational derivation of bond-based peridynamic stress tensor, Journal of Peridynamics and Nonlocal Modeling 2 (2020): 352–378. doi:10.1007/s42102-020-00036-9 ↩

  6. D. He, D. Huang, and D. Jiang, Modeling and studies of fracture in functionally graded materials under thermal shock loading using peridynamics, Theoretical and Applied Fracture Mechanics 111 (2021): 102852. doi:10.1016/j.tafmec.2020.102852 ↩

  7. C.P. Jiang, X.F. Wu, J. Li, F. Song, Y.F. Shao, X.H. Xu, and P. Yan, A study of the mechanism of formation and numerical simulations of crack patterns in ceramics subjected to thermal shock, Acta Materialia 60(11) (2012): 4540–4550. doi:10.1016/j.actamat.2012.05.020 ↩