Modified dynamic reliability model for damage accumulation

The earlier suggested model for the dynamics of element reliability distribution over a generalized strength (capacity) space [2] reflects the roles of both strength deterioration and failure processes. The present model is a modification of the previously suggested model and considers the interaction of the instantaneous stress (demand) with the instantaneous strength (capacity). Modified Smoluchowski´s probability of transition equation plays the role of the process generator allowing an iterative simulation for the processes of strength deterioration and failure from the initial strength distribution. A practical illustration of the suggested concept is demonstrated by a rather general simulation procedure, which avoids the need for any special assumptions regarding the transition rates within the processes in question. While keeping all the benefits and the attributes of the previously suggested model, the model addressed in this paper exhibits a more realistic matter-environment system behavior. The resultant damaged strength distribution shows tendency to the Weibull model, in which all the parameters change along the process. The calculated data show physically meaningful effect of the particular material parameters and environmental conditions.