A New Shell Element for Elasto-Plastic Finite Strain Analyses

Rita G. Toscano, Eduardo N. Dvorkin


The MITC4 shell element (Dvorkin E.N. and Bathe K.J., Engng. Computations, Vol. 1, pp. 77-88, 1984) is very successful and it provides excellent solutions for infinitesimal strain analyzes using either elastic or elasto-plastic material models in linear or nonlinear geometrical formulations.
In (Dvorkin et al., Comput. Meth. Appl. Mechs. Engng., vol. 125, pp.17-40, 1995) the element formulation was extended for finite strain elasto-plastic analyzes and even tough the new element provides very good solutions it presents some room for improvements. In previous publications we presented a new shell element formulation, the MITC4-3D that we developed for finite strain analysis using the MITC4 strains interpolation and 3D constitutive relations (hyperelastic and elasto-plastic materials).
Some of the basic features of our new element are:
• The shell geometry is interpolated using mid-surface nodes and director vectors.
• The node displacements and transverse shear strains are interpolated using the original MITC4 formulation.
• For interpolating the director vectors special care is taken to avoid spurious director vector stretches.
• Additional degrees of freedom are considered to include a linear thickness stretching. These thickness-stretching degrees of freedom are condensed at the element level.
• The elasto – plastic formulation is developed following the work of Simo and co-workers: multiplicative decomposition of the deformation gradient tensor and maximum plastic dissipation (associate plasticity).
• Special consideration is given to the formulation efficiency.
In this paper we are going to discuss the basic features of the MITC4-3D element and present further verification / validation examples.

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