A finite strain quadrilateral based on least-squares assumed strains

P. Areias, T. Rabczuk, J. César de Sá

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


When compared with advanced triangle formulations (e.g. Allman triangle and Arnold MINI), specially formulated low order quadrilateral elements still present performance advantages for bending-dominated and quasi-incompressible problems. However, simultaneous mesh distortion insensitivity and satisfaction of the Patch test is difficult. In addition, many enhanced-assumed (EAS) formulations show hourglass patterns in finite strains for large values of compression or tension; EAS elements often present convergence difficulties in Newton iteration, particularly in the presence of high bulk modulus or nearly-incompressible plasticity. Alternatively, we discuss the adequacy of a new assumed-strain 4-node quadrilateral for problems where high strain gradients are present. Specifically, we use relative strain projections to obtain three versions of a selectively-reduced integrated formulation complying a priori with the patch test. Assumed bending behavior is directly introduced in the higher-order strain term. Elements make use of least-square fitting and are generalization of classical B and F techniques. We avoid ANS (assumed natural strains) by defining the higher-order strain in contravariant/contravariant coordinates with a fixed frame. The kinematical part of the constitutive updating is based on quadratic incremental Green-Lagrange strains. Linear tests and both hyperelastic and elasto-plastic constitutive laws are used to test the element in realistic cases.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalEngineering Structures
Publication statusPublished - 2015 Oct 1

Bibliographical note

Funding Information:
The authors gratefully acknowledge financing from the “Fundação para a Ciência e a Tecnologia” under the Project PTDC/EME-PME/108751 and the Program COMPETE FCOMP-01-0124-FEDER-010267.


  • Bending behavior
  • Element technology
  • Finite strains
  • Plasticity

ASJC Scopus subject areas

  • Civil and Structural Engineering


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