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Irregular lattices are used to model threedimensional (3D) structural components consisting of a bulk material, curvilinear reinforcement, and their interface. Domain discretization is highly automated and involves the semi-random placement of nodal points within the domain, followed by Voronoi tessellation of the nodal point set. A technique is given for the Voronoi partitioning of nonconvex domains. For discretizing nonconvex domains, and for effective gradation of nodal point density, a minimum allowable distance between nodes is maintained and the domain is saturated with nodes. To accelerate this computationally expensive operation, a partitioned domain search is used during the filling process. Reinforcement, and its interface with the bulk material, are discretely modeled and freely positioned in the domain, irrespective of the geometry of the irregular lattice representing the bulk material. This method of discretization facilitates model construction, results interpretation, and possible revisions to the model. While the focus is on automated domain discretization and the modeling of reinforcement, elastic properties of the model are demonstrated through examples involving nodal stress calculations and deflection analyses of prestressed concrete beams.

An irregular lattice model is proposed for simulating quasistatic fracture in softening materials. Lattice elements are defined on the edges of a Delaunay tessellation of the medium. The dual ͑Voronoi͒ tessellation is used to scale the elemental stiffness terms in a manner that renders the lattice elastically homogeneous. This property enables the accurate modeling of heterogeneity, as demonstrated through the elastic stress analyses of fiber composites. A cohesive description of fracture is used to model crack initiation and propagation. Numerical simulations, which demonstrate energy-conserving and grid-insensitive descriptions of cracking, are presented. The model provides a framework for the failure analysis of quasibrittle materials and fiber-reinforced brittle-matrix composites.

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