This book reviews recent theoretical, computational and experimental developments in mechanics of random and multiscale solid materials. The aim is to provide tools for better understanding and prediction of the effects of stochastic (non-periodic) microstructures on materials’ mesoscopic and macroscopic properties. Particular topics involve a review of experimental techniques for the microstructure description, a survey of key methods of probability theory applied to the description and representation of microstructures by random modes, static and dynamic elasticity and non-linear problems in random media via variational principles, stochastic wave propagation, Monte Carlo simulation of random continuous and discrete media, fracture statistics models, and computational micromechanics.

An area at the intersection of solid mechanics, materials science, and stochastic mathematics, mechanics of materials often necessitates a stochastic approach to grasp the effects of spatial randomness. Using this approach, Microstructural Randomness and Scaling in Mechanics of Materials explores numerous stochastic models and methods used in the m

Considering the uncertainties in mechanical engineering in order to improve the performance of future products or systems is becoming a competitive advantage, sometimes even a necessity, when seeking to guarantee an increasingly high safety requirement. Mechanical Engineering in Uncertainties deals with modeling, quantification and propagation of uncertainties. It also examines how to take into account uncertainties through reliability analyses and optimization under uncertainty. The spectrum of the methods presented ranges from classical approaches to more recent developments and advanced methods. The methodologies are illustrated by concrete examples in various fields of mechanics (civil engineering, mechanical engineering and fluid mechanics). This book is intended for both (young) researchers and engineers interested in the treatment of uncertainties in mechanical engineering.

The finite element method (FEM) can be successfully applied to various field problems in solid mechanics, fluid mechanics and electrical engineering. This text discusses finite element methods for structures with large stochastic variations.

Mechanical behaviors of materials are highly influenced by their architectures and/or microstructures. Hence, progress in material science involves understanding and modeling the link between the microstructure and the material behavior at different scales. This book gathers contributions from eminent researchers in the field of computational and experimental material modeling. It presents advanced experimental techniques to acquire the microstructure features together with dedicated numerical and analytical tools to take into account the randomness of the micro-structure.

The papers in this volume deal with materials science, theoretical mechanics and experimental and computational techniques at multiple scales, providing a sound base and a framework for many applications which are hitherto treated in a phenomenological sense. The basic principles are formulated of multiscale modeling strategies towards modern complex multiphase materials subjected to various types of mechanical, thermal loadings and environmental effects. The focus is on problems where mechanics is highly coupled with other concurrent physical phenomena. Attention is also focused on the historical origins of multiscale modeling and foundations of continuum mechanics currently adopted to model non-classical continua with substructure, for which internal length scales play a crucial role.

Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic. When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems. The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.