matscipy.fracture_mechanics.energy_release

Functions

J_integral(a, deformation_gradient, virial, ...)

Compute the energy release rate from the J-integral.
matscipy.fracture_mechanics.energy_release.J_integral(a, deformation_gradient, virial, epot, e0, tip_x, tip_y, r1, r2, mask=None)

Compute the energy release rate from the J-integral. Converts contour integral into a domain integral. See: Li, Shih, Needleman, Eng. Fract. Mech. 21, 405 (1985); Jin, Yuan, J. Nanosci. Nanotech. 5, 2099 (2005) Domain function is currently fixed: q(r) = (r-r1)/(r2-r1)

Parameters:

  • a (ase.Atoms) – Relaxed atomic configuration of the crack.

  • deformation_gradient (array_like) – len(a) x 3x3 array of atomic deformation gradients.

  • virial (array_like) – len(a) x 3x3 array of atomic virials.

  • epot (float) – Potential energy per atom of the cracked configuration.

  • e0 (float) – Reference energy (cohesive energy per atom of the bulk crystal at equilibrium).

  • tip_x (float) – Position of the crack tip.

  • tip_y (float) – Position of the crack tip.

  • r1 (float) – Volume integration is carried out in region at a distance between r1 and r2 from the crack tip.

  • r2 (float) – Volume integration is carried out in region at a distance between r1 and r2 from the crack tip.

  • mask (array_like) – Include only a subset of all atoms into J-integral computation.

Returns:

J – Value of the J-integral.

Return type:

float