# 4.37.3. Wilkins

The Wilkins failure model, proposed by Wilkins [[1]] is implemented with the form:

(4.260)\[ d = \frac{1}{d_{\text{crit}}} \int_0^{\bar{\varepsilon}^p} w_1 w_2 d\bar{\varepsilon}^{p},\]

where \(w_1\) represents a pressure-dependent term defined as,

\[w_1 = \left( \frac{1}{1 - \frac{p}{B}} \right) ^{\alpha},\]

with \(\alpha\) and \(B\) as fitting parameters and \(p\) is mean hydrostatic stress, and \(w_2\) represents a Lode-angle-related term defined as,

\[w_2 = (2 - A)^{\beta},\]

with \(\beta\) as fitting parameter, and \(A\) defined as a function of deviatoric principal stresses (\(s_1 \geq s_2 \geq s_3\)),

\[A = \max \left( \frac{s_2}{s_3}, \frac{s_2}{s_1} \right) .\]

The failure process initiates once the integral term reaches the critical failure parameter, such that \(d = 1\).

## 4.37.3.1. User Guide

    #
    # WILKINS Failure model definitions
    #
    WILKINS ALPHA    = <real>
    WILKINS BETA     = <real>
    WILKINS PRESSURE = <real>

[1]

M.L. Wilkins, Streit, R.D., and J.E. Reaugh. Cumulative-strain-damage model of ductile fracture: simulation and prediction of engineering fracture tests. Technical Report UCRL-53058, Lawrence Livermore National Laboratory, Livermore, CA, 1980.