Is smaller always stiffer? On size effects in supposedly generalised continua

Abstract

Heterogeneous materials having constitutive behaviour described by more generalised continuum theories incorporating additional degrees of freedom such as couple stress, micropolar or micromorphic elasticity are expected to exhibit size effects in which there is an apparent increase in stiffness as the size scale reduces. Here we briefly demonstrate that for a simple heterogeneous material the size effect predicted when loaded in bending depends on the nature of the sample surface. Diverse size effects may thus be exhibited by the same material. We then show by detailed finite element analysis of a more representative material with regular heterogeneity that this diversity of size effects might actually be observed in practice thereby providing an explanation for the contradictory size effects that have sometimes been reported for real materials.