| This dissertation focuses on the nonlocal continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel capabilities. A more generalized role is defined for influence functions in the state-based peridynamic model which allows for the strength of nonlocal interactions to be modulated. This enables the connection between different peridynamic constitutive models, establishing a hierarchy that reveals that some models are special cases of others. Furthermore, this allows for the modulation of the strength of nonlocal interactions, even for a fixed radius of interactions between material points in the peridynamics model. The multiscale aspect of peridynamics is demonstrated through its connections to molecular dynamics. Using higher-order gradient models, it is shown that peridynamics can be viewed as an upscaling of molecular dynamics, preserving the relevant dynamics under appropriate choices of length scales. The state-based peridynamic model is shown to be appropriate for the description of multiscale and multimodel systems. A formulation for nonlocal interface problems involving scalar fields is presented, and derivations of nonlocal transmission conditions are derived. Specializations that describe local, nonlocal, and local/nonlocal transmission conditions are considered. Moreover, the convergence of the nonlocal transmission conditions to their classical local counterparts is shown. In all cases, results are illustrated by numerical experiments. |
