Issue 41

A. Mardaliazad et alii, Frattura ed Integrità Strutturale, 41 (2017) 504-523; DOI: 10.3221/IGF-ESIS.41.62 514 3, which indicates that after this point the current failure surface . . c f   is the same as the residual strength level r   . This tabulated damage function of the KCC model can be determined by up to 13 pairs of η - λ parameters. The variation of η and λ is summarized in Tab. 2. η λ Current failure surface position 0 ≤ η < 1 0 ≤ ߣ < ߣ m . . y c f m         η = 1 ߣ = ߣ m . . c f m      1 ≥ η > 0 ߣ m ≤ ߣ ≤ ߣ end . . m c f r         Table 2 : The KCC damage evaluation parameters. This material model implements shear damage accumulation by including the rate effect enhancement and different scenarios in tension and compression as Eq. (19).     1 2 3 , 0 [1 100 ( 1)](1 ) , 0 ( ) [1 100 ( 1)](1 ) ( ), 0 ( ) p b f f t p b f f t yield d d v v d d p s r p r f d d d p uniaxial s r p r f b f k p triaxial                                    (19) where, 1 2 3 ( ) 3 p       and t f are pressure (positive in compression) and maximum tensile strength, respectively. The p d  is, the effective plastic strain increment equal to (2 3) p p ij ij de de (and (1 3) p p p ij ij ij kk e      is the deviatoric part of strain). The parameter s  expresses the strain rate effect user-defined factor; if it is equal to 0, the strain-rate effects is toggled off, while if it is equal to 100, the strain-rate effects is included. The parameter f r is the dynamic increase factor that accounts for the strain rate effects. Parameters 1 b and 2 b govern the softening in compression and uniaxial tensile strain, respectively, whereas, 3 b , affects the triaxial tensile strain softening. These b-parameters can be determined by iteration until the value of the fracture energy, f G , converges for a specified characteristic length, which is associated with the localization width (i.e. the width of the localization path transverse to the crack advance). To describe the rock compaction behaviour in LS-DYNA, this *MAT_072R3 is used in conjunction with an Equation-of- State (EOS), namely *EOS_TABULATED_COMPACTION. This EOS provides a function of the current and previous volumetric strain v  for the current element pressure p . The stress tensor can be computed as being a point on a movable surface by means of known pressure. This surface can be a yield or a failure surface. This function should be specified by users as a series of , , v p K  sets, where K is the bulk modulus correspondent to the different v p   pairs [20]. These series can be generated internally by the automatic input generation mode of this material model. In case of an essential change of stiffness of a material, the linear bulk modulus which is defined as the 20, can be adjusted. 2 1 2 1 v v p p K       (20) The most significant improvement provided by the third release of this material model is the automatic input parameter generation capability, based solely on the unconfined compression strength [29]. This makes the use of the KCC model easier and accessible to most users, since there is no need to carry out extensive material characterization tests. The KCC model was originally developed to analyze the mechanical behaviour of concrete, and although the response of sandstone is expected to be similar to concrete, the results of the automatic input generation mode are only a rough estimation for