Issue 41

A. Mardaliazad et alii, Frattura ed Integrità Strutturale, 41 (2017) 504-523; DOI: 10.3221/IGF-ESIS.41.62 513 plan section. Moreover, it considers a value equal to 1⁄2 for the negative range of pressures. It is worth mentioning that this function was implemented in LS-DYNA and no input is required of the users. One of the most noteworthy features of the KCC model is decoupling the shear and compaction behaviour of the materials, which means that this model treats the deviatoric and volumetric responses separately. The deviatoric response is characterized by the migration of the current stress state between the fixed failure surfaces, while the response to pressure is defined by an equation of state as a function of volumetric strain increments. The damage accumulation of the KCC model, and accordingly the current failure surfaces are expressed schematically in Fig. 9. As can be seen in Fig. 9a, the state of stress is determined by a linear interpolation between the three failure surfaces. The stress-strain diagram corresponding to the unconfined compression test is indicated in Fig. 9c, which is determined by association of a damage accumulation function (shown in Fig. 9b. The response of the material to the initial loading, phase I in Fig. 9c, is considered as a linear elastic deformation before reaching point 1 in Fig. 9a. The current failure surface . . c f   is therefore the same as the yield strength level y   at this range. A hardening plasticity response occurs after yielding and before reaching the maximum strength. The KCC material model determines the current state of stress at this range (between point 1 and point 2) according to Eq. (17). . . ( ) c f m y y             (17) Based on the level of confining pressure, a softening response occurs after reaching the maximum strength and before obtaining a residual strength. The current state of stress corresponds to this area (between point 2 and point 3) is derived according to Eq. (18). . . ( ) c f m r r             (18) where η is the KCC damage parameter used to determine the relative location of the current failure surface, which is a function of another parameter, called the accumulated effective plastic strain λ . Figure 9 : a) the linear interpolation between failure surfaces, b) the damage function, c) unconfined compression stress-strain diagra m. As can be seen in Fig. 9b, the damage function is described so that initially and prior to the occurrence of any plasticity responses, the value of η is set to zero. It increases up to unity at a user-defined value m  , corresponding to point 2, where the maximum failure surface has been reached. The KCC model considers the hardening plasticity by means of this linear- piecewise function of η - λ . After point 2, where the softening takes place, η decreases to zero at end  corresponding to point (a) (b) (c)