Automation of Finite Element Methods by Jože Korelc & Peter Wriggers

Author:Jože Korelc & Peter Wriggers
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.58)

The local tangent matrix and the Gauss point contribution to the global tangent matrix then follow directly from the general Eqs. (3.​68) and (3.​69) as

(5.59)

(5.60)

Evaluation of the Gauss-point contribution to the element tangent matrix (5.60) requires proper consideration of the implicit dependency introduced by the local iterative procedure (5.49). The “missing” implicit derivative is in (5.60) introduced as an AD exception. It can be observed, contrary to elasticity, that the element tangent matrix depends upon the chosen integration algorithm. Due to this reason the tangent is often called consistent tangent in the literature since it is consistent with the elasto-plastic algorithm, see e.g. Simo and Taylor (1985), Simo and Hughes (1998), de Souza Neto et al. (2008) and Korelc (2009). The tangent matrix (5.60) is equivalent to the one produced by the standard consistent linearization procedure introduced by Simo and Taylor (1985 ) .

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