Stochastic Mechanics of Discrete Media [Paperback]

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.
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.
1 Introduction to the Probabilistic Analysis.- 1.1 Historical Remarks on Probability and its Application in Mechanics.- (i) The notion of probability.- (ii) Continuity and discontinuity.- (iii) Determinism and Probabilism.- 1.2 Topological Spaces, Sets and Operators.- (i) Topological Spaces and Sets.- (ii) Vector spaces and convexity.- (iii) Linear operators and bilinear forms.- 1.3 Probability and Random Variables.- (i) Probability.- (ii) Random variables.- 1.4 Probability Measures.- (i) General remarks on measures.- (ii) Probability measures.- 1.5 Dependence of Random variables.- (i) Independent random variables.- (ii) Dependent random variable.- 1.6 Stochastic Processes.- (i) Characteristics of stochastic processes.- (ii) Regularity and Continuity.- (iii) Some basic stochastic processes.- (iv) Random fields.- 2 Phenomenology of Discrete Media.- 2.1 Classification of Materials.- (i) Introduction.- (ii) Classification of microstructures.- (iii) Idealized microstructures and fundamental concepts.- 2.2 Statistical Models of Discrete Media.- (i) Disorder effects.- (ii) The local approach.- (iii) Molecular dynamics and correlation functions.- (iv) Lattice models.- (v) Pelƒ'