Stochastic Modeling of Microstructures

A major challenge in applied mathematics and mechanics of materials is

to describe various types of material microstructures. The details of

the microstructure of most natural and engineered materials are

usually obscure; uncertainty and randomness are the inherent features.

This complexity due to material heterogeneity has not been A major

challenge in applied mathematics and mechanics of materials is to

describe various types of material microstructures. The details of the

microstructure of most natural and engineered materials are usually

obscure; uncertainty and randomness are the inherent features. This

complexity due to material heterogeneity has not been adequately

described by current classical models and theories. Stochastic

Modeling of Microstructures presents a concise and unified

presentation of the basic principles and tools for the modeling of

real materials, natural and man-made, that possess complex, random

heterogeneity. The book uses the language and methods of random field

theory combined with the basic constructs of stochastic geometry and

geometrical/spatial statistics in order to give the reader the

knowledge necessary to model various types of material

microstructures. The application of the theoretical constructs

reviewed in the first three chapters to the analysis of empirical data

via the tools of statistical inference is also discussed. The final

chapters address practical aspects of specific modeling problems.

Features- ú First comprehensive introduction to the comparatively new

field of stochastic modeling of material microstructures ú

Presentation of basic tools required from the diverse subjects of

random field theory, stochastic geometry and spatial statistics ú

Provides background concepts from probability theory and stochastic

processes are provided ú Applications from various fields are

discussed, including stochastic wave propagation and the mechanics of