Stochastic modelling of materials subjected to monotonic and high-cycle loading

In this research two types of models are studied which account for the scatter in material response: (a) idealized one-dimensional stochastic micro-mechanical models for brittle and plastic materials subjected to monotonic loading; and (b) a stochastic continuum damage mechanical model for crack initiation in high-cycle fatigue.;The one-dimensional stochastic micro-mechanical model is represented by a set of either brittle or ideal-plastic, linear-elastic springs of equal stiffness that are joined in parallel. The failure displacements of the brittle springs and yield displacements of the elastic-plastic springs are modelled as a continuous or discrete correlated random field. The statistics of the random force-displacement and damage-displacement functions are derived for both cases. The brittle-model is further modified to include the formations of local stress concentrations at a damaged part of a structural component. These idealized models are shown to offer a viable alternative to empirical methods proposed in the literature for exploring the statistical behavior of brittle and plastic materials.;The stochastic continuum damage mechanics model is developed to study the statistical aspects of the failure life associated with crack initiation in high-cycle fatigue. A deterministic relation is established for the evolution of damage, defined as density of micro-cracks, such that it satisfies the dissipative inequalities obtained from the Clausius-Duhem inequality. The deterministic damage evolution is randomized using a correlated log-normal process to obtain a two-state Markov model for fatigue crack initiation. The mean, standard deviation and probability distribution of the random time to initiate a macroscopic crack are numerically computed for the Markov model.