A finite strain quadrilateral based on least-squares assumed strains

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Areias, P. (Author) Other; Rabczuk, T. (Author) Other; César de Sá, J. (Author) FEUP

Journal

Title: Engineering Structures

Vol. 100

Pages: 1-16

ISSN: 0141-0296

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 4 Citations

Scientific classification

FOS: Engineering and technology > Mechanical engineering

CORDIS: Technological sciences > Engineering > Mechanical engineering

Other information

Authenticus ID: P-00G-BDR

DOI: 10.1016/j.engstruct.2015.05.035

Abstract (EN): 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) over bar and (F) over bar 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16