Paradoxical size effects in composite laminates and other heterogeneous materials

Size effects in which there is an apparent increase in stiffness with reducing size scale are forecast in those heterogeneous materials that have constitutive behaviour described by more generalized continuum theories such as couple stress, micropolar or micromorphic elasticity. This short paper considers possibly the simplest heterogeneous material exhibiting such size effects, a two phase composite laminate consisting of alternating layers of stiff and compliant material, and shows that when loaded in bending the nature of the size effect actually depends on the composition of the sample surfaces. The laminate material is apparently capable of exhibiting a diversity of size effects some of which are compatible with the predictions of generalized continuum theories while others are contradictory. Another heterogeneous material consisting of a periodic or regular array of voids within a classically elastic matrix is then considered. Detailed finite element analysis shows that the diversity of size effects encountered in the laminate material may also be observed in this more representative material thereby providing some insight into the contradictory size effects that have sometimes been reported elsewhere in the literature.