SalehaniIrani 3D Coupled Traction separation law

3D Coupled (3DC) cohesive law of Salehani and Irani with no damage

Description

This class implements the non-stateful traction separation law proposed by Salehani and Irani (2018). This material model is an extension to 3 dimensions of the 2-dimensional traction-separation law proposed by Xu and Needleman Xu and Needleman (1993). This traction separation law should only be used for monotonic loading conditions as it will not produce realistic results for unloading and reloading. This model can be used for 1D, 2D and 3D problems.

The traction separation relationship is defined by: Ti=ϕiδiΔiδiexp[j=1d(Δjδj)α]T_i = \frac{\phi_i}{\delta_i}\frac{\Delta_i}{\delta_i} \exp [ -\sum_{j=1}^{d}(\frac{\Delta_j}{\delta_j})^{\alpha}] where ii and jj are indices representing the displacement jump component with the index 1 being associated with the opening direction, α\alpha is a model parameter with values α=1\alpha = 1 if j==1j==1 or α=2\alpha = 2 if j==2,3j == 2,3, dd is a parameter representing the number of dimensions of the problem, Δi\Delta_i is the current gap value and δi\delta_i is the characteristic length of separation related to the maximum sustainable traction. The symbol ϕi\phi_i represents the work of separation and is defined as ϕi=Ti,maxλδi\phi_i = T_{i,max} \lambda \delta_i where λ=e\lambda = e if i==1i==1 or λ=2e\lambda = \sqrt{2 e} if i==2,3i == 2,3. The parameter Ti,maxT_{i,max} represents the maximum allowed traction that the interface can withstand in the ithi-th direction. Note that the values of maximum allowed traction can be different in the normal and tangential directions, however T2,maxT_{2,max} is assumed to be equal to T3,maxT_{3,max}. The same restrictions on Ti,maxT_{i,max} apply to δi\delta_i

Examples

[./czm_3dc]
  type = SalehaniIrani3DCTraction
  boundary = 'Block0_Block1 Block1_Block2'
  normal_gap_at_maximum_normal_traction = 1
  tangential_gap_at_maximum_shear_traction = 0.5
  maximum_normal_traction = 500
  maximum_shear_traction = 300
  base_name = 'czm_b012'
[../]
(contrib/moose/modules/solid_mechanics/test/tests/cohesive_zone_model/czm_multiple_action_and_materials.i)

References

  1. Mohsen Khajeh Salehani and Nilgoon Irani. A coupled mixed-mode cohesive zone model: an extension to three-dimensional contact problems. arXiv preprint arXiv:1801.03430, 2018.[BibTeX]
  2. X-P Xu and A Needleman. Void nucleation by inclusion debonding in a crystal matrix. Modelling and Simulation in Materials Science and Engineering, 1(2):111, 1993.[BibTeX]