Extrapolation locking and its sanitization in Koiter's asymptotic analysis

The implicit corotational method and its use in the derivation of nonlinear structural models for beams and plates

“…We also know (see [Garcea et al 1998;1999;2005]) that, with an appropriate choice of configuration variables u := {σ, d} and the corresponding choice p := {ε, q}, these terms could be written in mixed form as…”

“…The proposed approach does not require any ad hoc assumptions about the structural model at hand, nor does it depend on any particular parametrization of the rotation tensor, but rather it actually behaves as a black-box tool able to translate known linear models into the corresponding nonlinear ones. Moreover, the direct use of a mixed (stress/strain) description provides an automatic and implicitly coherent methodology for generating models free of nonlinear locking effects [Garcea et al 1998;1999;2005] in a format directly suitable for use in FEM implementations.…”

Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method

“…Asymptotic analysis essentially corresponds to the implementation of Koiter's approach to nonlinear elastic stability [Koiter 1945;Budiansky 1974] into a FEM numerical context. While being less diffuse than path-following approaches within computational mechanics (maybe because of its high demands in terms of modeling accuracy) it has been described in detail in many papers (for example, [Casciaro et al 1992;Flores and Godoy 1992;Lanzo et al 1995;Pacoste and Eriksson 1995;Lanzo and Garcea 1996;Wu and Wang 1997;Poulsen and Damkilde 1998;Garcea et al 1999;Garcea 2001;Boutyour et al 2004;Casciaro 2005;Silvestre and Camoti 2005;Chen and Virgin 2006;Schafer and Graham-Brady 2006;Rahman and Jansen 2010] and references therein), so it only needs to be briefly summarized here.…”

“…Frame-independence plays an important role in element setup and the lack of it can result in spurious locking, which we called nonlinear interpolation locking in [Casciaro 2005] (also see [Salerno and Lanzo 1997]), which can significantly affect the numerical solution. The equation format (that is, mixed or compatible) also plays an important role in the convergence of the iterative solution processes and in the accuracy of the extrapolation results (see [Garcea et al 1998;1999]). These topics will be discussed and the use of mixed FEM interpolations and a mixed format is suggested.…”

“…Even small inaccuracies in this evaluation, deriving from geometrical incoherencies in the higher-order terms of the expansion of the ε[d] law or in its finite element representation, significantly affect the accuracy of the solution and can make it unreliable. It is also very sensitive to the format used in the extrapolation, to avoid extrapolation locking (see [Garcea et al 1999]), and the use of a mixed equation format is generally needed to obtain a robust implementation.…”