On uniform fields in heterogeneous media

Abstract

Uniform elastic strain fields are found in two-phase fibrous media of arbitrary transverse geometry, and in two-phase media of any phase geometry. In initially stress-free fibrous solids, a single uniform field can be created by certain proportionally changing tractions derived from a uniform overall stress. In the presence of phase eigenstrains, many overall stress states can be superimposed to create uniform strain fields in fibrous media. The existence of such fields is exploited to establish a number of exact results for two-phase fibre systems. These include universal connections between phase and overall moduli, and between components of phase stress and strain fields; expressions for new transformation influence functions and concentration factors in terms of their mechanical counterparts; and also expressions for the overall stresses and strains caused by phase eigenstrains. Examples are presented for macroscopically monoclinic fibrous composites with transversely isotropic phases. In two-phase media of arbitrary phase geometry there is only a single uniform stress and strain field for each non-vanishing eigenstrain state. The existence of this field is utilized in derivation of exact connections between transformation and mechanical influence functions and concentration factors.