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For the past three decades the mechanics of structured media, frequently called micromechanics, has been recognized as an important new approach in the analysis of material behaviour. This book discusses the modern use of mathematical analysis to the stochastic mechanics of discrete media. The theoretical study is therefore based on set and measure theory and the application of point processes.
List of contents
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.
