Lattice-based peridynamic modeling of linear elastic solids

Concrete is a complex material often used in civil engineering structures. This quasi-brittle material, when reinforced with steel, develops cohesive cracks under loading even though it has adequate strength to carry service loads. Concrete often cracks even before the application of load, due to temperature changes and shrinkage. The displacement field in the structure drastically changes as the cracks initiate and propagate. Thus, concrete fails to satisfy the most fundamental assumptions of continuum mechanics. To overcome the limitations of continuum mechanics, Silling introduced the peridynamic method in 1998. Gerstle and his colleagues generalized the peridynamic model in 2007, introducing the micropolar peridynamic model by considering not only the forces between the particles but also the moments. Both the peridynamic and the micropolar peridynamic model require huge amounts of computational effort to analyze even simple civil engineering problems as they require many particles and associated force computations. The present work specializes the micropolar peridynamic model by assuming that the particles are arranged in a lattice configuration. The peridynamic lattice requires fewer force calculations than previous computational implementations of the peridynamic model. Using this newer technique, with a micropolar peridynamic force model, we have a model that is both mathematically and physically defensible and simple to model on a computer. Concrete is a material which has limited resolvability, which means that, a very sharp corner or a very thin section is not possible to manufacture because of limitations associated with the aggregate size. In this context, the lattice-based peridynamic model is essentially appropriate for modeling concrete structures. This thesis presents the fundamental assumptions for developing the lattice-based linear elastic peridynamic model. The microelastic constants for the lattice micropolar peridynamic model are derived and successfully implemented. A convergence study demonstrates the accuracy of this model. The results are compared to a previous version of the peridynamic model. Only linear elastic behavior is considered in this study. A damage model must still be developed for the application of this method to reinforced concrete structures