A Micromechanical Analysis of the Radial Elastic Response Associated with Slender Reinforcing Elements within a Matrix

Abstract

This paper addresses the elastic modulus associated with the radial interaction between a slender axisymmetric reinforcing element and a matrix. In particular, reinforcing elements with a significant surface structure are considered, and the elastic modulus of an interface model is defined to characterize the local elastic behavior resulting from the mechanical interaction that is not explicitly captured at a larger scale of modeling (i.e., a scale at which the surface structure is not explicitly modeled). An analytical justification for the elastic modulus is presented by determining the difference in the strain energy stored in a matrix that has a homogenized (or smoothed) interface traction distribution versus a more concentrated traction distribution that may occur with a complicated surface structure. Due to the importance of strain energy in driving cracks, it is postulated that the elastic modulus should be such that the composite with an idealized interface will store the same amount of strain energy as the actual composite having an interface with a surface structure. Analytical results show that the elastic modulus increases with the ratio of the contact area to the interface area and with a decrease in the period associated with a periodic traction distribution. A numerical example shows the effect of the elastic modulus on the prediction of longitudinal cracking in a quasibrittle matrix.