A data-driven elastoplastic super element method for multiscale modeling of history-dependent responses in metamaterials

Mechanical metamaterials have attracted considerable attention due to their exceptional mechanical properties, making them promising candidates for advanced structural applications. However, accurate and efficient prediction of the history-dependent, nonlinear mechanical behavior of elastoplastic metamaterial structures remains challenging. In this work, we propose a data-driven elastoplastic super element (DD-EPSE) framework to model the elastoplastic response of metamaterials. Unlike traditional representative volume element (RVE)-based homogenization that relies on scale separation and equivalent stress-strain relationships, DD-EPSE treats each unit cell as a structural element governed by force-displacement relationships at control points, with nodal forces serving as internal variables. After eliminating rigid-body motions, the incremental force-displacement response is captured by a specially designed artificial neural network framework, which enforces objectivity and equilibrium. A support vector machine (SVM) classifier is incorporated to identify plastic zones within metastructures. The method is validated through extensive numerical simulations and experiments on triply periodic minimal surface (TPMS)-based metamaterials under diverse loading conditions. Results demonstrate that DD-EPSE accurately predicts the force-displacement response and plasticity distribution of large-scale metastructures, while reducing computational cost by several orders of magnitude compared to direct numerical simulations. In addition, its applicability to other metamaterial topologies is validated through transfer learning, exemplified by beam-lattice structures. The DD-EPSE framework provides an efficient tool for modeling and designing of mechanical metamaterials with history-dependent nonlinear behavior.