Heterogeneous Elastic Materials

The following sections are included:

• Effective Equations on the Macroscale

• The Effective Elastic Coefficients

• Application to Fiber-Reinforced Composite

• Elastic Panels with Periodic Microstructure

  • Order Estimates

  • Two-Scale Analysis and Effective Equations

  • Homogeneous Plate — A Limiting Case

• Variational Principles and Bounds for the Elastic Moduli

  • First Variational Principle and the Upper Bound

  • Second Variational Principle and the Lower Bound

• Hashin–Shtrikman Bounds

• Partially Cohesive Composites

  • Effective Equations on the Macroscale

  • Variational Principles

  • Bounds for Particulate Composites

  • Size Effects for Particulate Composites

  • Critical Radii for Particulate Composites

• Appendix 5A. Properties of a Tensor of Fourth Rank

• References