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

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.


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


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