Finite element concepts for finite elastoplastic strains and isotropic stress response in shells: Theoretical and computational analysis. (English) Zbl 0957.74047
Summary: This paper presents finite element concepts accounting for finite elastoplastic strains and isotropic stress response in arbitrary shells. Three parameterization strategies for the calculation of thin and thick smooth shells as well as shell intersections are discussed in detail. In this context the importance of the deformation gradient for an efficient implementation is especially emphasized. According to the parameterizations, the computational plasticity algorithms are derived in general three-dimensional form for thick shell structures, and in a restricted two-dimensional form satisfying the plane stress state underlying thin shells. In order to describe arbitrary shell geometries, we apply the isoparametric concept to all proposed finite element formulations. These are based on quadrilateral 4-node mixed finite shell elements. The variational approaches are considered which use the enhanced assumed strain method, the assumed natural strain concept, and the reduced integration technique. By means of representative numerical examples, we demonstrate the performance of the three different finite element concepts.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K25 | Shells |
| 74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |
Keywords:
finite elastoplastic strains; isotropic stress response; shell intersections; computational plasticity algorithms; thick shell; thin shells; isoparametric concept; quadrilateral 4-node mixed finite shell elements; variational approaches; enhanced assumed strain method; assumed natural strain concept; reduced integration techniqueReferences:
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