Methods for Solving Finite Element Mesh-Dependency Problems in Geotechnical Engineering—A Review

Jiangxin Liu, Lijian Wu, Kexin Yin, Changjun Song, Xiaolin Bian and Shengting Li
Additional contact information
Jiangxin Liu: Research Institute of Highway Ministry of Transport, Beijing 100088, China
Lijian Wu: Research Institute of Highway Ministry of Transport, Beijing 100088, China
Kexin Yin: Department of Civil and Airport Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
Changjun Song: Research Institute of Highway Ministry of Transport, Beijing 100088, China
Xiaolin Bian: Research Institute of Highway Ministry of Transport, Beijing 100088, China
Shengting Li: Research Institute of Highway Ministry of Transport, Beijing 100088, China

Sustainability, 2022, vol. 14, issue 5, 1-20

Abstract: The instabilities of soil specimens in laboratory or soil made geotechnical structures in field are always numerically simulated by the classical continuum mechanics-based constitutive models with finite element method. However, finite element mesh dependency problems are inevitably encountered when the strain localized failure occurs especially in the post-bifurcation regime. In this paper, an attempt is made to summarize several main numerical regularization techniques used in alleviating the mesh dependency problems, i.e., viscosity theory, nonlocal theory, high-order gradient and micropolar theory. Their fundamentals as well as the advantages and limitations are presented, based on which the combinations of two or more regularization techniques are also suggested. For all the regularization techniques, at least one implicit or explicit parameter with length scale is necessary to preserve the ellipticity of the partial differential governing equations. It is worth noting that, however, the physical meanings and their relations between the length parameters in different regularization techniques are still an open question, and need to be further studied. Therefore, the micropolar theory or its combinations with other numerical methods are promising in the future.

Keywords: mesh dependency; finite element method; viscosity theory; nonlocal theory; high-order gradient; micropolar theory (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2071-1050/14/5/2982/pdf (application/pdf)
https://www.mdpi.com/2071-1050/14/5/2982/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jsusta:v:14:y:2022:i:5:p:2982-:d:763714

Access Statistics for this article

Sustainability is currently edited by Ms. Alexandra Wu

More articles in Sustainability from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().