Abstract
We verify the objectivity (invariance to rigid body rotations) ordinary state-based peridynamic models published in the literature that differ in their formulas. We find and explain the sources for the differences between these published formulas. We demonstrate that a primary cause leading to these differences is the way in which the peridynamic volume dilatation is defined in the different formulations. We show that the equations of motion derived from one approach apply to deformations with small or large rotations and is objective. The other approach is valid only for deformations with zero/infinitesimal rotations, thus it is not objective. We also show that both state-based models recover the correct bond-based formulations with the appropriate Poisson ratio values when the term containing the volume dilatation vanishes.
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