Issue 35

J. Kramberger et alii, Frattura ed Integrità Strutturale, 35 (2016) 142-151; DOI: 10.3221/IGF-ESIS.35.17 144 Figure 2 : Inelastic hysteresis energy for the stabilized cycle. The damage initiation criterion is a phenomenological model for predicting the onset of damage due to stress reversals and the accumulation of inelastic strain in a low-cycle fatigue analysis. It is characterized by the accumulated inelastic hysteresis energy per cycle,  w, in a material point when the structures response is stabilized in the cycle. The cycle number (N 0 ), in which damage is initiated, is given by: 2 0 1 c N c w   (1) where c 1 and c 2 are material constants. The damage evolution law describes the rate of degradation of the material stiffness per cycle once the corresponding initiation criterion has been reached. For damage in ductile materials Abaqus/Standard assumes that the degradation of the stiffness can be modeled using a scalar damage variable D [11, 15, 16, 17]. At any given cycle during the analysis the stress tensor in the material is given by the scalar damage equation:   1 D     (2) where  is the effective (or undamaged) stress tensor that would exist in the material in the absence of damage computed in the current increment. Once the damage criterion is satisfied at the material integration point, the damage state is calculated and updated based on the inelastic hysteresis energy for the stabilized cycle. The rate of damage per cycle is given by: 4 3 c c w dD dN L   (3) where c 3 and c 4 are material constants, and L is the characteristic length associated with the material point and based on the finite element geometry. Material lost its load capacity when D=1 . When such conditions are satisfied in certain finite element, such element can be removed from the mesh. In such a way damage (crack) propagation can be monitored in computational model. C OMPUTATIONAL MODELS he discussion from the previous sections shows that the lotus-type porous material behavior is controlled by the porosity. Thus, in this study we have used two-dimensional pore structure as a basis for the finite element simulations. The reasonably homogeneous pore structure of lotus-type porous material was simplified and T σ ε 3 2 1 1 2 Δ w Δ ε = const.