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Cyclic softening is a plastic mechanism that affects the strength of various structural materials while in operation, including that of many advanced alloys and modern composites whose mechanical behavior exhibits significant nonlocality. This paper introduces a mechanistically informed data-driven approach that harnesses a novel description of gradient plasticity, based on the discrete Laplace operator for surfaces of arbitrary curvature, to capture cyclic softening in nonlocal shell structures. Specifically, the proposed approach combines the methods and tools of data science with those of mechanics so that large volumes of training data are not required. Moreover, the yield surface defined in conventional cyclic plasticity is herein extended to incorporate the second-order gradient of the plastic strain (rate). Leveraging this extended plasticity model, the features which represent the yield surface and its evolution …