Introduction — Field of application
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The law of behavior ENDO_HETEROGENE aims to model the damage of heterogeneous materials and was developed specifically for geomaterials (for example argillite). This law is based on a probabilistic model of rock fracturing developed as part of a collaboration between BRGM and LMT -Cachan around the thesis of Nicolas Guy [:ref:`bib1 <bib1>`]. This model takes into account the effect of rock heterogeneity on its probability of failure. The initial distribution of micro-defects is in fact given as a function of this heterogeneity using a classical Poisson-Weibull model. The model is then based on the consideration of two thresholds: a priming threshold and a propagation threshold based on the intensity factor of regularized stresses.

Regularizing constraints allows us to:


* to obtain results independent of spatial discretization


* to evaluate the two thresholds from the same quantity, i.e., the regularized constraint


* to calculate the intensity factor of "regularized" stresses without refining the mesh and with good precision.

Finally, this model explicitly provides a crack path and takes into account the interaction of cracks in relation to each other.


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