Stochastic Mechanics of Discrete Media

1 Introduction to the Probabilistic Analysis.- 1.1 Historical Remarks on Probability and its Application in Mechanics.- 1.2 Topological Spaces, Sets and Operators.- 1.3 Probability and Random Variables.- 1.4 Probability Measures.- 1.5 Dependence of Random variables.- 1.6 Stochastic Processes.- 2 Phenomenology of Discrete Media.- 2.1 Classification of Materials.- 2.2 Statistical Models of Discrete Media.- 2.3 Probabilistic Models of Discrete Media.- 2.4 Markov Processes and Stochastic Differential Equations.- 3 Random Evolution and Geometric Probabilities.- 3.1 Wide-sense Markov Processes.- 3.2 Interaction effects in Discrete Media.- 3.3 Introduction to Geometric Probabilities.- 3.4 Some Fundamental Concepts of Stereology.- 4 Applications of the Stochastic Analysis.- 4.1 The Response Behaviour of Discrete Solids.- 4.2 The response of Polycrystalline Solids.- 4.3 The Stochastic Analysis of Fibrous and Polymeric Networks.- 4.4 Simple Fluids and the Flow in Fully Saturated Porous Media.- References.