Lattice Discrete Particle Model for Fiber-Reinforced Concrete. I: Theory

The lattice discrete particle model (LDPM) is a mesoscale model for heterogeneous materials. Developed for concrete, it simulates material mesostructure by modeling coarse aggregate particles and their surrounding mortar as polyhedral cells. A tetrahedralization of the particle centers generates a lattice framework where each lattice member is associated with a triangular-shaped plane of contact (facet) between two cells. Compatibility equations are formulated by describing the deformation of an assemblage of particles through rigid-body kinematics. Equilibrium equations are obtained through the force and moment equilibrium of each cell. The material behavior is assumed to be governed by a vectorial constitutive law imposed at the facets. A natural extension for this discrete model is to include the effect of dispersed fibers as discrete entities within the mesostructure. The LDPM incorporates this effect by modeling individual fibers randomly placed within the framework according to a given fiber volume fraction. The number and orientation of the fibers crossing each facet is computed and the contribution of each fiber to the facet response is formulated on the basis of a previously established micromechanical model for fiber-matrix interaction. The theory for the developed model, entitled the LDPM-F, is discussed herein. A subsequent companion paper will address model calibration and validation through the numerical simulation of experimental test results.