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Computational plasticity: The variational basis and numerical analysis. (English) Zbl 0847.73078
Summary: The quasistatic problem of elastoplasticity with combined kinematic and isotropic hardening is considered, with particular emphasis on variational aspects and numerical approximations of this problem. It is shown that the problem may be formulated variationally in two alternative, dual forms; both formulations are variational inequalities, but they differ from each other in the forms they take, and in the sets of variables they use. These problems are referred to as primal and dual formulations, and for each formulation the issue of existence and uniqueness of solutions is discussed in detail. Error analysis of temporally semi-discrete, spatially semi-discrete and fully-discrete approximations of the quasistatic problem is given in the context of both variational formulations. Finally, some popular solution algorithms are reviewed, and their properties are investigated. Of particular interest are conditions under which such algorithms converge, and the role played by the choice of algorithmic moduli in the behavior of these algorithms.

74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74S99 Numerical and other methods in solid mechanics