Heterogeneous Media

1. Introduction
2. Homogeneous media with external and internal field sources
3. Volume and surface integral equations for physical fields in heterogeneous media
4. Numerical calculation of volume and surface potentials
5. Numerical solution of volume integral equations for static fields in heterogeneous media
6. Cracks in heterogeneous media
7. Time-harmonic fields in heterogeneous media
8. Quasistatic crack growth in heterogeneous media
9. The homogenization problem

Heterogeneous Media: Local Fields, Effective Properties, and Wave Propagation outlines new computational methods for solving volume integral equation problems in heterogeneous media. The book starts by surveying the various numerical methods of analysis of static and dynamic fields in heterogeneous media, listing their strengths and weaknesses, before moving onto an introduction of static and dynamic green functions for homogeneous media. Volume and surface integral equations for fields in heterogenous media are discussed next, followed by an overview of explicit formulas for numerical calculations of volume and surface potentials.

The book then segues into Gaussian functions for discretization of volume integral equations for fields in heterogenous media, static problems for a homogeneous host medium with heterogeneous inclusions, volume integral equations for scattering problems, and concludes with a chapter outlining solutions to homogenization problems and calculations of effective properties of heterogeneous media. The book concludes with multiple appendices that feature the texts of basic programs for solving volume integral equations as written in Mathematica.

• Outlines cutting-edge computational methods for solving volume integral equation problems in heterogeneous media
• Provides applied examples of approximation and other methods being employed
• Demonstrates calculation of composite material properties and the constitutive laws for averaged fields within them
• Covers static and dynamic 2D and 3D mechanical-mathematical models for heterogeneous media

Researchers in mechanical engineering and materials science; graduate students in each of these areas