Micropolar multiphase model for materials reinforced by linear inclusions

A macroscale multiphase model is proposed for assessing the mechanical behaviour of materials reinforced by linear inclusions, such as those commonly employed in geotechnical engineering. The model is developed with the help of the virtual work method and related principles, resulting in the derivation of equilibrium equations and boundary conditions for the matrix and reinforcement phases respectively. The basic concept is the idealization of the inclusions as 1-D-beams continuously distributed throughout the matrix, leading to a micropolar description which accounts for shear force and bending moment densities. The theory includes the possibility of different kinematics for the phases, with non-perfect bonding at the matrix–inclusion interface. Since all the parameters appearing in such a model have a clear mechanical significance, it becomes possible to deal with any boundary value problem involving inclusion-reinforced materials, in a very straightforward manner. Two examples of such problems are solved under the assumption of a linear elastic constitutive law for matrix and reinforcement phases, including their interaction.