Peridynamic beams, plates, and shells: A nonordinary, state-based model

Peridynamics is a nonlocal formulation of continuum mechanics in which forces are calculated as integral functions of displacement fields rather than spatial derivatives. The peridynamic model has major advantages over classical continuum mechanics when displacements are discontinuous, such as in the case of material failure. While multiple peridynamic material models capture the behavior of solid materials, not all structures are conveniently analyzed as solids. Finite Element Analysis often uses 1D and 2D elements to model thin features that would otherwise require a great number of 3D elements, but peridynamic thin features remain underdeveloped despite great interest in the engineering community. This work develops nonordinary state-based peridynamic models for the simulation of thin features. Beginning from an example nonordinary state-based model, lower dimensional peridynamic models of plates, beams, and shells are developed and validated against classical models. These peridynamic models are extended to incorporate brittle and plastic material failure, compounding the peridynamic advantages of discontinuity handling with the computational simplicity of reduced-dimension features. These models will allow peridynamic modeling of complex structures such as aircraft skin that may experience damage from internal forces or external impacts.