CavityVolumeOpening

Source: models/solid_mechanics/traction_separation_law/CavityVolumeOpening.py

The viscous (cavitation) part of the normal jump, which is the smeared cavity volume measured from the initial state,

\[ [\![u]\!]_n^v = N V(f, N) - N_0 V_0, \qquad N V(f, N) = \frac{4h}{3\sqrt{\pi}} \frac{f^{3/2}}{N^{1/2}}. \]

\(N_0\) and \(f_0\) are the initial cavity density and area fraction, so a pristine boundary opens by zero. Both must be strictly positive: \(f_0 = 0\) is the singular point of the damage law.

Differentiating this expression in time reproduces the Sham-Needleman viscous opening rate term by term, so the algebraic form is carried here rather than a rate; the time integration of \(f\) and \(N\) then supplies the rate implicitly and the identity holds exactly at every converged step instead of only to integration order.

Inputs

cavity_fraction — input · Scalar · required

Physical cavitated area fraction

cavity_density — input · Scalar · required

Cavity number density per unit boundary area

Outputs

viscous_normal_opening — output · Scalar · required

Viscous part of the normal jump, i.e. the smeared cavity volume

Parameters

cavity_shape_factor — parameter · Scalar · required

Cavity shape factor h(psi); h is about 0.61 at a tip angle of 75 degrees

initial_cavity_fraction — parameter · Scalar · required

Initial cavitated area fraction f_0, strictly positive

initial_cavity_density — parameter · Scalar · required

Initial cavity number density N_0, strictly positive