A multiscale finite element method for the localization analysis of homogeneous and heterogeneous saturated porous media with embedded strong discontinuity model. (26th May 2017)

• Record Type: Journal Article
• Authors: Lu, Mengkai; Zhang, Hongwu; Zheng, Yonggang; Zhang, Liang
• Is Part Of: International journal for numerical methods in engineering. Volume 112:Number 10(2017)
• Page Start: 1439
• Page End: 1472
• Publication Date: 2017-05-26
• Subjects: multiscale finite element method -- porous media -- localization -- embedded strong discontinuity -- enhanced coarse element -- numerical base function; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5564
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: This paper presents a multiscale finite element method with the embedded strong discontinuity model for the strain localization analysis of homogeneous and heterogeneous saturated porous media. In the proposed method, the strong discontinuities in both displacement and fluid flux fields are considered. For the localized fine element, the mathematical description and discrete formulation are built based on the so‐called strong discontinuity approach. For the localized unit cell, numerical base functions are constructed based on a newly developed enhanced coarse element technique, that is, additional coarse nodes are dynamically added as the shear band propagating. Through the enhanced coarse element technique, the multiscale finite element method can well reflect the softening behavior at the post‐localization stage. Furthermore, the microscopic displacement and pore pressure are obtained with the solution decomposition technique. In addition, a non‐standard return mapping algorithm is given to update the displacement jumps. Finally, through three representative numerical tests comparing with the results of the embedded finite element method with fine meshes, the high efficiency and accuracy of the proposed method are demonstrated in both material homogeneous and heterogeneous cases. Copyright © 2017 John Wiley & Sons, Ltd.