Hill condition and overall properties of composites

Summary We discuss the Hill principle's role and applications in modern micromechanics of industrial composite materials. Uniform boundary conditions, fundamental in micromechanics, are introduced as a class of Hill solutions. Mixed uniform conditions, basic for experimental testing, are analysed. Domains of application of the Hill principle are reviewed, like homogeneization of heterogeneous media, definition of effective properties and size effect in heterogeneous materials. Generalization of the Hill condition is realized for arbitrary materials, in particular for nonlinear inelastic composites with imperfect interfaces. Received 9 September 1997; accepted for publication 23 December 1997