SUMMARYFor a material exhibiting hysteresis such as quasi-brittle materials, it is natural to consider that hysteresis and fatigue are related to each other. One shows in the present work that damage, from the continuum damage mechanics point of view, may be seen as the link between both phenomena. One attempts, hence, to set up a unified modelling of hysteresis and damage. Numerical examples are given for concrete and validate the proposed model of internal sliding and friction coupled with damage. The problem of a proper phenomenological modelling of the micro-defects closure effect leading to a dissymmetric tension/ compression response and to stiffness recovery in compression is also addressed. Cyclic and fatigue applications are in mind, and also random fatigue and seismic responses.

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