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Peridynamic (PD) theories have gained widespread diffusion among variousresearch areas, due to the ability of modeling discontinuities formation andevolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding somemodeling limitations, is widely employed in numerical simulations, due to itseasy implementation combined with physical intuitiveness and stability. In thepresent paper, several aspects of bond-based peridynamic models have beenreviewed and investigated. A detailed description of peridynamics theory,applications and numerical models has been presented. Employed BB-PD integralkernels have been displayed, together with their differences and commonalities;then, some consequences of their mathematical structure have been discussed.The kinematic role of nonlocality, the relation between kernel structure andmaterial impenetrability, and the role of PD kernel nonlinearity in cracksformation prediction have been critically analyzed and commented. Finally theidea of extending BB-PD to fluids is proposed and presented in the framework offading memory material, drawing some perspectives for a deeper and morecomprehensive understanding of the peridynamics in fluids.

Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics