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Transient large strain finite element analysis of solids. (English) Zbl 0666.73039
Computational methods for non-linear problems, Recent Adv. Non-Linear Comput. Mech. 2, 87-126 (1987).
[For the entire collection see Zbl 0651.00022.]
An explicit finite element procedure is described for fast dynamic analysis of elasto-plastic solids in plane and axisymmetric conditions. A Cauchy stress rate formulation is used (hydrocode methodology). This enables the treatment of large strains provided the definition of some objective stress rate is given. Two such definitions, the Zaremba- Jaumann-Noll (ZJN) stress rate and the Green-Naghdi (GN) stress rate are critically examined. A coherent constitutive model for elasto-plastic material behaviour with isotropic and kinematic hardening is recalled together with its implementation via the radial return method. Bilinear (4 node quadrilateral) and biquadratic (9 node Lagrange) isoparametric elements are considerd and analysed with particular reference to the controversial aspects related to the spatial integration (locking and spurious modes).

74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
74H45 Vibrations in dynamical problems in solid mechanics