A mixed constant-stress smoothed-strain element with a cubic bubble function for elastoplastic analysis using second-order cone programming

Xi Wen Zhou, Feng Tao Liu, Zhen Yu Yin, Yin Fu Jin, Cheng Bo Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review


This paper proposes a novel optimization-based finite element method with a mixed constant-stress smoothed-strain element to solve elastoplastic problems. The proposed computational framework has three advantages: (1) in the proposed mixed constant-stress smoothed-strain element, the strain is smoothed on the edge-based smoothing domain, and the stress is assumed to be constant in each smoothing domain; (2) the cubic bubble shape function is introduced at the centroid of the element to enrich the displacement field. This makes the proposed approach accurate and free of volumetric locking for low-order elements; (3) the discrete elastoplastic boundary-value problem is formulated as a standard second-order cone problem based on the generalized Hellinger–Reissner variational principle, which is quickly and efficiently solved by the primal-dual interior-point algorithm. The proposed approach is validated on several classical problems of geotechnical engineering: the bearing capacity of footing and pipe under small deformation and slope stability. All the obtained results demonstrate that the proposed method adopting the novel mixed constant-stress smoothed-strain element offers competitively high computational accuracy and efficiency.

Original languageEnglish
Article number104701
JournalComputers and Geotechnics
Publication statusPublished - May 2022


  • Elastoplasticity
  • Mixed element
  • Second-order cone programming
  • Smoothed finite element method

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Computer Science Applications

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