A micromechanical analysis of the radial elastic response associated with slender reinforcing elements within a matrix

This paper addresses the elastic modulus associated with the radial interac tion between a slender axisymmetric reinforcing element and a matrix. In pa rticular, reinforcing elements with a significant surface structure are con sidered, and the elastic modulus of an interface model is defined to charac terize the local elastic behavior resulting from the mechanical interaction that is not explicitly captured at a larger scale of modeling (i.e., a sca le at which the surface structure is not explicitly modeled). An analytical justification for the elastic modulus is presented by determining the diff erence in the strain energy stored in a matrix that has a homogenized (or s moothed) interface traction distribution versus a more concentrated tractio n distribution that may occur with a complicated surface structure. Due to the importance of strain energy in driving cracks, it is postulated that th e elastic modulus should be such that the composite with an idealized inter face will store the same amount of strain energy as the actual composite ha ving an interface with a surface structure. Analytical results show that th e elastic modulus increases with the ratio of the contact area to the inter face area and with a decrease in the period associated with a periodic trac tion distribution. A numerical example shows the effect of the elastic modu lus on the prediction of longitudinal cracking in a quasibrittle matrix.