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**Calcul à la rupture: régularisation de Norton-Hoff et Lagrangien augmenté.**
*(French)*
Zbl 0545.73020

The paper deals with a kinematical method based on limit analysis and leading to a numerical treatment of three-dimensional bodies obeying a non-differentiable yielding criterion.

The failure evaluation discussed in section 2, is based on the results given by M. Frémond and A. Friaâ [C. R. Acad. Sci., Paris, Sér. A 286, 107-110 (1978; Zbl 0372.73022)], according to which the total energy derived from the dynamic loading of the structure under certain elementary conditions is smaller than the dissipated plastic energy. In section 3, it is shown that, according to Friaâ’s investigation [A. Friaâ, La loi de Norton-Hoff généralisée en plasticité et viscoplasticité. Thèse d’état, Univ. P. et M. Curie (1979)], it is possible to replace the plastic energy required at the limit, when the viscous component tends to zero, by the energy dissipated by a Norton-Hoff viscoplastic fluid material. In section 4, the problem for the calculation of the Norton-Hoff flow is developed, based on the finite-element theory. Finally, in section 5, an algorithm for the evaluation of fracture is established and several numerical results are presented.

The following problems are considered: i) the study of a perforated plate, subjected to a co-planar load for a von-Mises material; ii) the calculation of a two-dimensional structure composed of a Coulomb material and subjected to a maximum compression; iii) the evaluation of the limit height for a clay embankment of Camclay type; and finally, iv) an approximate three-dimensional calculation for a von-Mises material.

The paper is original, clearly written and useful for calculations in elastoplasticity.

The failure evaluation discussed in section 2, is based on the results given by M. Frémond and A. Friaâ [C. R. Acad. Sci., Paris, Sér. A 286, 107-110 (1978; Zbl 0372.73022)], according to which the total energy derived from the dynamic loading of the structure under certain elementary conditions is smaller than the dissipated plastic energy. In section 3, it is shown that, according to Friaâ’s investigation [A. Friaâ, La loi de Norton-Hoff généralisée en plasticité et viscoplasticité. Thèse d’état, Univ. P. et M. Curie (1979)], it is possible to replace the plastic energy required at the limit, when the viscous component tends to zero, by the energy dissipated by a Norton-Hoff viscoplastic fluid material. In section 4, the problem for the calculation of the Norton-Hoff flow is developed, based on the finite-element theory. Finally, in section 5, an algorithm for the evaluation of fracture is established and several numerical results are presented.

The following problems are considered: i) the study of a perforated plate, subjected to a co-planar load for a von-Mises material; ii) the calculation of a two-dimensional structure composed of a Coulomb material and subjected to a maximum compression; iii) the evaluation of the limit height for a clay embankment of Camclay type; and finally, iv) an approximate three-dimensional calculation for a von-Mises material.

The paper is original, clearly written and useful for calculations in elastoplasticity.

Reviewer: P.S.Theocaris

### MSC:

74R20 | Anelastic fracture and damage |

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

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