Issue 47

A. Chouiter et alii, Frattura ed Integrità Strutturale, 47 (2019) 30-38; DOI: 10.3221/IGF-ESIS.47.03 33 Critical area Critical point (M *) Figure 4 : Macroscopic-Microscopic scale. If the damage is isotropic, D is a scalar allowing the introduction of the effective stress notion: 1 D      (2)         * * 1 * 2 2 2 1 3 1 2 3 v eq H V eq M Sup with R R                       (3) Rv is the triaxiality function which depends on the triaxiality coefficient σ H /σ eq , in most cases this criterion is satisfied in high stress concentration zones with high triaxiality coefficient value σ H /σ eq . The third step consists in determining the damage evolution by solving the constitutive laws below which will be written in incremental form and will have to be solved by Newton's numerical method Benallal et al. [14]: 2 0 1 1 1 3 0 2 2 e p ij ij ij e ij kk ij ij D p ij ij eq eq v E D E D P if f f if ES D E E E E E p p R P                       (4) N UMERICAL P ROCEDURE he method used for solving the above constitutive equations is integration schemes such as the radial return method M. Ortiz and E. P. Popov [16]. The method used is a strain driven algorithm: It is assumed in a first step that the stress values and the other variables of the model are known at the initial time (t n ) and that the behavior is T