Strain-Gradient Effects in Microlayers

An analytic solution is obtained for two composite-body problems using the strain-gradient theory of elasticity as developed by Mindlin. The investigation is concerned with the effects produced by strain-gradients, especially bonding stresses in the vicinity of an interface separating two dissimilar materials when higher-order contact conditions prevail at the common boundary. The composite body under consideration consists of an infinite elastic strip (microlayer) embedded in two semi-infinite elastic regions. The first problem concerns the case of uniform tension at infinity applied in a direction perpendicular to the microlayer. The second considers simple shear applied at infinity parallel to the microlayer. It is shown that the stresses that develop in the vicinity of an interface may be at large variance with the classical results. The magnitude of these stresses may be many times greater than the classical values, thus emphasizing the uncertainty of the classical approach in this instance. This variance is significant when one material is much more rigid than the other, as encountered in the practical case of composite materials.