Damage and fracture mechanics free download

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The objective of this exercise is to offer the possibility to pass from one theory to the other during a same calculation or to obtain, from one theory, information on how to use the other. It deals with energetic considerations, from which it is easy to relate local damage variables and global fracture variables.

These considerations start with the assumption of a specific form of the free reversible energy stored in the material during straining. Let us emphasise that this section deals with the simplest possible forms of such energy. A load denoted as Q is applied to the structure, q is the corresponding displacement, and K is the global stiffness. At uniform and constant temperature the state laws provide the stress-strain relations and the definition of the energy release rates.

For the two considered cases, we obtain 7 Since Y is a quadratic function and K decreases when A increases - see Eq. One possible method is to transform a given damage zone into an equivalent crack. This equivalence is thermodynamically acceptable if the consumption of energy is the same during the two processes.

For this, one needs to know the distribution of damage around the macrocrack, which is approximated as follows. The evolution law of damage is nonlocal. In fact, the wavelength 2njw is proportional to the internal iength of the nonlocal continuum for more details, see Reference [2]. The wavelength is also a function of the evolution law of damage.

The calculation of the approximated fracture energy performed with the smallest value of the wavelength calculated for a uniaxial tensile test and corresponds to mode I crack opening. Opening q 0 0. Evolution of the stiffness with the crack, t theoretical, e experimental. Zairi and M. Elhoud, N. Renton and W. Amirat, A. Benmoussat and K. Plekhov, O. Naimark, R. Valiev and I. Benachour, A. Hadjoui and F. Marsavina and T. Aliha, M. Ayatollahi and B. Belamri, T. Tamine and A. Tiberkak, M.

Bachene, B. Hachi, S.