On coupled gradient-dependent plasticity and damage theories with a view to localization analysis.

*(English)*Zbl 0968.74007Summary: Combinations of gradient plasticity with scalar damage and of gradient damage with isotropic plasticity are proposed and implemented within a consistently linearized formulation. Both constitutive models incorporate a Laplacian of a strain measure and an internal length parameter, which makes them suitable for localization analysis. We use the theories for finite element simulations of localization in a one-dimensional model problem. The physical relevance of coupling hardening/softening plasticity with damage governed by different damage evolution functions is discussed, and the sensitivity of results with respect to the discretization and to model parameters is analyzed. The model which combines gradient-damage with hardening plasticity is used to predict fracture mechanisms in a compact tension test.

##### MSC:

74A45 | Theories of fracture and damage |

74R20 | Anelastic fracture and damage |

74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |

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