Cyclic softening in nonlocal shells-A data-driven graph-gradient plasticity approach

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 (including the second-order gradient of the plastic strain) are extracted from the stress-strain data generated from representative volume elements (RVEs) that model shell's microstructure (e.g., void or particle content). Subsequently, a homogenized yield surface represented by an artificial neural network (ANN) and its evolution are learned via these extracted features. Importantly, the homogenized material model is trained to capture the Masing effect, which characterizes cyclic softening upon load reversal. Finally, this trained, homogenized, (second-) gradient plasticity model is integrated into a finite element framework to simulate nonlocal thin shells under cyclic loads. This proposed approach enables efficient computation and analyses on nonlocal thin shells, with a direct connection to the microstructural causes of non-locality, which serves to facilitate the material design process for modern shell applications. For instance, our approach successfully captures the size effect that arises in richly microstructured thin shells, without the need for higher-order stress. Also, the influence of the Masing effect on thin shell structures is herein captured effectively. The efficiency of our computational approach is furthermore compared to that of direct numerical simulation (DNS) and other computational homogenization techniques. Applying our approach to cyclic hardening would be a direct extension of this work. As a first implementation, however, the proposed approach does not yet consider the anisotropy induced by rich microstructures in nonlocal shells or control for noise in the training data. Our approach thus invites future development along multiple avenues.