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Complementary mixed finite element formulations for elastoplasticity. (English) Zbl 0687.73064

Summary: A global formulation of the principle of maximum plastic dissipation is systematically exploited to construct complementary mixed finite element formulations for elastoplasticity. Completely general return mapping integration algorithms are obtained as Euler-Lagrange equations of a temporally discretized Lagrangian functional. The flow rule is no longer enforced point-wise, but rather at the element level in a weak fashion that couples all Gauss points within an element. The resulting algorithms can be linearized exactly in closed-form for an arbitrary functional form of the yield condition and hardening law. The present approach enables one to extend successful superconvergent quadrilaterals to elastoplastic analysis. Numerical simulations involving plane-stress elastoplasticity are presented.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65K10 Numerical optimization and variational techniques
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
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