An objective time-integration procedure for isotropic rate-independent and rate-dependent elastic-plastic constitutive equations.

*(English)*Zbl 0714.73023Summary: In a large class of rate-independent and rate-dependent elastic-plastic constitutive equations the elasticity is modeled in hypoelastic form, with the stress rate being taken as the Jaumann derivative, so as to make the constitutive model properly frame-indifferent or objective. Here, we present a fully-implicit, stable time-integration procedure for implementing such constitutive models in displacement-based finite element procedures. The numerical procedure preserves the very desirable feature of incremental objectivity. The overall procedure is a generalization of the well known “radial-return” algorithm of classical rate-independent plasticity, and it is therefore well suited for implementation in large-scale finite element codes. As an example, we have implemented the time-integration procedure in the finite element code ABAQUS. To check the incremental objectivity, accuracy, and stability of the algorithm some representative problems are solved.

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74C99 | Plastic materials, materials of stress-rate and internal-variable type |

74S05 | Finite element methods applied to problems in solid mechanics |

74B20 | Nonlinear elasticity |

74A20 | Theory of constitutive functions in solid mechanics |

74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |

74C20 | Large-strain, rate-dependent theories of plasticity |