Issue 35

N. Oudni et alii, Frattura ed Integrità Strutturale, 35 (2016) 278-284; DOI: 10.3221/IGF-ESIS.35.32 279 M ODEL he influence of microcracking due to external loads is introduced via a single scalar damage variable d ranging from 0 for the undamaged material to 1 for completely damaged material. The stress-strain relation reads [6]:     0 0 ij ij kk ij 0 0 1 υ υ ε σ σ δ     E 1 d E 1 d          (1) 0 E and 0  are the Young's modulus and the Poisson's ratio of the undamaged material; ij ε and ij σ are the strain and stress components, and ij δ is the Kronecker symbol. The elastic (i.e., free) energy per unit mass of material is   0 1 1 2 ij ijkl kl d C      (2) Where 0 ijkl C is the stiffness of the undamaged material. This energy is assumed to be the state potential. The damage energy release rate is 0 1 2 ij ijkl kl Y C d         (3) With the energy of dissipated energy: d d         (4) Since the dissipation of energy ought to be positive or zero, the damage rate is constrained to the same inequality because the damage energy release rate is always positive. D AMAGE EVOLUTION he evolution of damage is based on the amount of extension that the material is experiencing during the mechanical loading. An equivalent strain is defined as   3 2 1 i i        (5) Where .  is the Macauley bracket and i  are the principal strains. The loading function of damage is   ,  f         (6) Where  is the threshold of damage growth. Initially, its value is 0  , which can be related to the peak stress t f of the material in uniaxial tension: 0 0 t f E   (7) In the course of loading  assumes the maximum value of the equivalent strain ever reached during the loading history. T T