One of the most common methods to implement peridynamics numerically is based on the discretization of the whole body by means of a structured and regular grid of nodes and a constant horizon size. That leads to an inefficient use of computational resources as well as to the impossibility to explore the multi-scale capabilities of peridynamics within a unique framework. Adaptive grid refinement and scaling seem to be a promising strategy to reduce those limitations, allowing to increase the resolution of the analysis and to reach the interested length-scale only in the desired regions. The application of such an approach in the peridynamic solutions requires certainly to be investigated, in particular, this is done by the comparison of numerical peridynamic solutions with the analytical solutions of classic linear elasticity theory.

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