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A simple assumed-strain quadrilateral shell element for finite strains and fracture

Areias, P.; Cesar de Sa, J.M.A.; Cardoso, Rui P.R.


P. Areias

J.M.A. Cesar de Sa

Rui P.R. Cardoso


© 2014, Springer-Verlag London. This work recovers an established technique for improving quadrilateral shell element performance in both out-of-plane and in-plane bending cases using a mixed formulation. A four-field variational principle is established and we relate, at the discrete level, the Lagrange multipliers and secondary right Cauchy–Green field with the displacement and rotation fields. This is the main contribution of this work. High coarse-mesh accuracy is observed for distorted meshes and the robustness is shown to be adequate for crack propagation simulations. A consistent director normalization is performed, as an alternative to our recent spherical interpolation. Covariant metric components are deduced and exact linearization of the shell element is performed. Full assessment of the element is accomplished, showing similar performance to more costly approaches such as enhanced assumed strain. Patch test is satisfied ab-initio and benchmarks present very accurate results. Numerical experimentation for geometrically and material nonlinear problems is presented, as well as one fracture example using our recently proposed cracked edge technique.


Areias, P., Cesar de Sa, J., & Cardoso, R. P. (2015). A simple assumed-strain quadrilateral shell element for finite strains and fracture. Engineering with Computers, 31(4), 691-709.

Journal Article Type Article
Publication Date Oct 13, 2015
Journal Engineering with Computers
Print ISSN 0177-0667
Electronic ISSN 1435-5663
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 31
Issue 4
Pages 691-709
Keywords shells, finite strain, plasticity, fracture
Public URL
Publisher URL
Additional Information Additional Information : Published online: 23 August 2014