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Large viscoelasto-plastic deformation of solids. (Russian. English summary) Zbl 1127.74044
The authors present a finite element analysis of strain-stress state of viscoelasto-plastic solids with large displacements, rotations and strains. The Lagrangian formulation of such problems creates significant difficulties due to constitutive equations in differential form. Thus the authors use an incremental method in mixed Lagrangian-Eulerian formulation which eliminates these difficulties. The equation of virtual powers in actual configuration is applied to nonlinear elastic materials and to ideally plastic isotropic materials. The method of successive loadings and the iterative rise of accuracy of stress-strain states are in the foundation of the proposed analysis. The space discretization is based on the finite element method. After loss of stability the growing of load is not monotone, therefore in this case the method of parametric continuation is used. The numerical investigations of strain-stress state of nine viscoelasto-plastic solids show the efficiency of the proposed finite element analysis.
MSC:
74S05 Finite element methods applied to problems in solid mechanics
74C20 Large-strain, rate-dependent theories of plasticity
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