Measurement of beam-correlated background neutrons from the Fermilab Booster Neutrino Beam in ANNIE Phase-I

Back, A.R.; Beacom, J.F.; Boschi, T.; Carber, D.; Catano-Mur, E.; Chen, M.; Drakopoulou, E.; Lodovico, F. Di; Elagin, A.; Eisch, J.; Fischer, V.; Gardiner, S.; Griskevich, J.; Grzan, D.; Hatcher, R.; Krennrich, F.; Kimmelman, B.; Kreymer, A.; Lee, W.; Locke, S.; Long, M.; Malek, M.; McGivern, C.; Moore, E.; Needham, M.; O'Flaherty, M.; Podczerwinski, J.; Richards, B.; Ritz, J.; Sanchez, M. C.; Smy, M.; Svoboda, R.; Tiras, E.; Vagins, M.; Wang, J.; Weatherly, P.; Weinstein, A.; Wetstein, M.; Wu, J.

doi:10.1088/1748-0221/15/03/P03011

It has been well established that the internal length scale related to the cell size plays a critical role in the response of architected structures. It this paper, a Volterra derivative-based approach for deriving nonlocal continuum laws directly from an energy expression without involving spatial derivatives of the displacement is proposed. A major aspect of the work is the introduction of a nonlocal derivative-free directionality term, which recovers the classical deformation gradient in the infinitesimal limit. The proposed directionality term avoids issues with correspondences under nonsymmetric conditions (such a unequal distribution of points that cause trouble with conventional correspondence-based approaches in peridynamics). Using this approach, we derive a nonlocal version of a shear deformable beam model in the form of integro-differential equations. As an application, buckling analysis of architected beams with different core shapes is performed. In this context, we also provide a physical basis for the consideration of energy for nonaffine (local bending) deformation. This removes the need for additional energy in an ad hoc manner towards suppressing zero-energy modes. The numerical results demonstrate that the proposed framework can accurately estimate the critical buckling load for a beam in comparison to 3-D simulations at a small fraction of the cost and computational time. Efficacy of the framework is demonstrated by analysing the responses of a deformable beam under different loads and boundary conditions.

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