\(H\)-adaptive finite element methods for dynamic problems, with emphasis on localization. (English) Zbl 0794.73071

Belytschko, T.; Tabbara, M.

Int. J. Numer. Methods Eng. 36, No. 24, 4245-4265 (1993).

Summary: \(H\)-adaptive procedures for the finite element solution of transient solid mechanics problems are studied, with particular emphasis on problems involving localization due to material instability. Various types of error criteria are examined and it is shown that for problems involving plastic response or localization, an error criterion based on an \(L_ 2\)-projection of strains is the most effective for the constant strain elements considered here. Examples of one-dimensional and two- dimensional localization (shear band formation) problems are given.

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74H55	Stability of dynamical problems in solid mechanics

Keywords:

shear band formation; material instability; error criteria; plastic response

Software:

DYNA3D

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