Smeared crack approach coupled with cohesive zone model has been an attractive way for the realistic simulations of dynamic fracturing of rocks and frequently utilized in the framework of the Finite Element Method (FEM). In many cases, cohesive elements (CEs) with initially-zero-thickness are inserted at the onset of numerical simulations and these are used to express the dynamic fracturing, which is called "intrinsic cohesive zone model (ICZM)". However, since the ICZM must introduce penalty terms to express the intact behavior of the CEs, this tends to render higher compliance of bulk rock, resulting in smaller wave propagation speed. In this paper, by introducing a so-called "extrinsic cohesive zone model (ECZM)", which adaptively inserts the CEs, we compared the results of 3-D dynamic fracturing simulations by the ICZM and ECZM using the experimental data obtained from the dynamic spalling test for rocks. Using the same Young's modulus, Poisson's ratio, density and strengths estimated from the experiments, our results suggest that the outcome of the ICZM and experiment showed large discrepancy especially for the intact stress wave propagation while the ECZM showed good agreement with the experiment. Therefore, our results could have some implications on the current situation in which more and more simulations using the ICZM such as in hybrid FEM-DEM have been applied to rock fracture mechanics problems.
Hybrid finite element method (FEM)-discrete element method (DEM) has been increasingly applied to the simulation of dynamic fracturing of rocks including blasting problems. In the majority of these simulations in previous research, cohesive zone models have been applied where cohesive elements (CEs) with initially-zero-thickness were inserted at the onset of simulation (e.g. Mahabadi et al., 2010; Rougier et al., 2014; An et al., 2017) and used to express fracturing behavior. This approach is a so-called "intrinsic cohesive zone model (ICZM)". Since the ICZM must introduce penalty terms to express the intact behavior of the CEs, this may render higher compliance of bulk rock, resulting in smaller wave propagation speed. On the other hand, a so-called "extrinsic cohesive zone model (ECZM)" has also been proposed for ceramics and concrete which adaptively inserts the CEs where and when they are needed (e.g. Ortiz and Pandolfi, 1999; Ruiz et al, 2001; Pandolfi and Ortiz, 2002). This approach has been rarely applied to the dynamic fracturing problems of rocks except our in-house 2-D Dynamic Fracture Process Analysis (DFPA) code (e.g. Cho et al., 2003).