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

Yongzhen Wang; Shengyu Duan; Chunwang He; Ying Li; Qinglei Zeng; Daining Fang

doi:10.1016/j.ijplas.2026.104623

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

Yongzhen Wang
, Shengyu Duan
, Chunwang He
, Ying Li
, Qinglei Zeng^*
, Daining Fang

^*此作品的通讯作者

Tsinghua University
Northeastern University China
Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

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.

源语言	英语
文章编号	104623
期刊	International Journal of Plasticity
卷	198
DOI	https://doi.org/10.1016/j.ijplas.2026.104623
出版状态	已出版 - 3月 2026
已对外发布	是

访问文件

10.1016/j.ijplas.2026.104623

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{d3f90d36dd884b878a7a8e7476eba21e,

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

abstract = "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.",

keywords = "Artificial neural network, Elastoplastic response, Mechanical metamaterials, Super element, Support vector machine",

author = "Yongzhen Wang and Shengyu Duan and Chunwang He and Ying Li and Qinglei Zeng and Daining Fang",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier Ltd.",

year = "2026",

month = mar,

doi = "10.1016/j.ijplas.2026.104623",

language = "English",

volume = "198",

journal = "International Journal of Plasticity",

issn = "0749-6419",

publisher = "Elsevier Ltd.",

}

TY - JOUR

T1 - A data-driven elastoplastic super element method for multiscale modeling of history-dependent responses in metamaterials

AU - Wang, Yongzhen

AU - Duan, Shengyu

AU - He, Chunwang

AU - Li, Ying

AU - Zeng, Qinglei

AU - Fang, Daining

PY - 2026/3

Y1 - 2026/3

N2 - 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.

AB - 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.

KW - Artificial neural network

KW - Elastoplastic response

KW - Mechanical metamaterials

KW - Super element

KW - Support vector machine

UR - https://www.scopus.com/pages/publications/105028987626

U2 - 10.1016/j.ijplas.2026.104623

DO - 10.1016/j.ijplas.2026.104623

M3 - Article

AN - SCOPUS:105028987626

SN - 0749-6419

VL - 198

JO - International Journal of Plasticity

JF - International Journal of Plasticity

M1 - 104623

ER -

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

摘要

访问文件

其它文件与链接

学术指纹

引用此