13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- Figure 1: (a) Biaxial failure data for Gislocarbon. The data was extracted from Brocklehurst [2], Sato et al. [29], Jortner [30], Bradshaw [24] and Greenstreet [31]. (b) Drucker-Prager hyperbolic plastic potential function in the meridional plane. Experimental data was extracted from Brocklehurst [2]. Figure 2: (a) Numerical solution of cyclic uniaxial loading in tension. (b) Numerical Solution for Full Cyclic Loading (Path: O-A-B-C-D-E). 3.3. Model Behaviour To present the behaviour of the DP model a single monotonic uni-axial loading and full cyclic monotonic uni-axial loading element is simulated. This uses a linear elastic quadratic full integration element. The material properties used for each model are presented in Table 1. The element mesh size of 7.4 x 7.4 mm was utilised, as it represents the by Bazant et al. [32] defined characteristic length of Gislocarbon [33]. The model was implemented in the FE environment of ABAQUS/Standard (Version 6.9). The non-local DP model monotonic uni-axial loading response, in Figure 2a, shows the softening response and the stiffness degradation (damage formation). The full cyclic (tension and compression) monotonic uni-axial loading response, in Figure 2b, resembles the hysteresis curve of (a) (b)
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