Peridynamic solutions to micropolar beam

Peridynamics (PD) is a non local continuum mechanics theory developed by Silling in 2000. The inception of peridynamics can be dated back to the works of Piola according to dell’Isola et al. [1]. Classical continuum theory (CCM) was there to study the materials response to deformation and loading conditions deformation response of materials and structures subjected to external loading conditions without taking into effect the atomistic structure. Classical continuum theory can be applied to various challenging problems but its governing equation have a limitation that it cannot be applied on any discontinuity such as a crack, as the partial derivatives with respect to space are not defined at a crack. To overcome this limitation , a new non local continuum approach i.e Peridynamics (PD) was developed.It was introduced as it governing equations donot contain any partial derivative with respect to space so it can be applied at cracks also. We can also think of Peridynamics as the continuum version of molecular dynamics. This behaviour of peridynamics makes it handy for multi-scale analysis of materials. Peridynamics finds it usefulness in other fields also such as moisture, thermal, fracture, aerospace etc., so that multiscale analysis can be done . The analysis of structure due to progressive failure is challenge. These challenges can be overcome by techniques such as using both nonlocal and classical (local) theories. But Peridynamic theory is computationally costly compared to the finite element method. While analyzing structures with compelxity , utilize structural idealizations is to be done to make computations feasible. Peridynamics has been catching the eyes of the researchers as its formulation include integral equations , unlike the partial differential equations in classical continuum theory. This method is still in early stages, a lot of research work is to be done to make it feasible for a large no. of problems.