Stress resultant plasticity for shells revisited

Abstract

In this work, we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the Ilyushin-Shapiro two-surface yield function with isotropic and kinematic hardening. The main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity. Four different algorithms are derived and compared. Three of them yield practically identical final results, yet they differ considerably in computational efficiency and implementation complexity, since they solve different sets of equations and they use different procedures that choose active yield surfaces. One algorithm does not provide acceptable accuracy. It turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently. Several numerical examples are presented to illustrate the Ilyushin-Shapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms.

Weak coupling of shell and beam computational models for failure analysis of steel frames

“…The twocurve yield criterion (16) calls for an application of a multi-surface computational algorithm for plasticity (see e.g. [33,15]). …”

“…4), and can be calculated by using (2). The almost linear plastic work versus end-rotation curves are presented for L ref ¼ L2 in Table 4 in Appendix, together with the hardening and the softening parameters of the beam material model, K h N ð Þ and K s N ð Þ, respectively, calculated with (13) and (15). Fig.…”

“…The softening modulus that corresponds to (15) is two times larger than K # s in (21). curve from Fig.…”

“…elastoplastic) shell finite element formulation (see e.g. [8,31,29,7,16,40,36,11,15]) in order to study response of the representative part of a frame member (RPFM) up to its complete collapse. Such a response naturally includes local Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/finel buckling and/or steel localized failure, since the RPFM fails due to a subtle combination of localized material failure and local buckling.…”

Multisurface plasticity for Cosserat materials: Plate element implementation and validation

“…Herein, we make use of the Procedure 1 . It is in fact more robust than the Procedure 2 , even though it is slightly more demanding from a computational point of view .…”