The peridynamics theory is a reformulation of nonlocal continuum mechanics that incorporates material particle interactions at finite distances into the equation of motion. State-based peridynamics is an extension of the original bond-based peridynamics theory wherein the response of an individual particle depends collectively on its interaction with neighboring particles through the concept of state variables. In this paper, the more recent non-ordinary state-based Peridynamics formulations of both the total (referential) Lagrangian approach as well as the updated (spatial) Lagrangian approach are formulated. In doing so, relations of the state variables are defined through various nonlocal differential operators in both material and spatial configurations in the context of finite deformation. Moreover, these nonlocal differential operators are mathematically and numerically shown to converge to the local differential operators, and they are applied to derive new force states and deformation gradients.
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