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Damage model with time delay. Numerical and analytical study of the evolution of the characteristic length. (Modèle d’endommagement à effet retard. Etude numérique et analytique de l’évolution de la longueur caractéristique.) (French. English summary) Zbl 1120.74736
Summary: This paper studies the one dimensionnal time delay damage model. It is well known that this type of model prevents the mesh dependency localisation. The model problem on a clamped uniaxial bar submitted to a step load at its extremity is studied here. When the material behaviour is elastic with damage, an analytical solution is produced which gives the size of the localisation as a function of the step load. This solution is proved to be the limit of a discrete finite element solution when the mesh size is smaller and smaller. The model is then extended to elasto platic and visocplastic cases and here again the localisation zone is proven numerically to be independent of the mesh size.

MSC:
74R05 Brittle damage
74R20 Anelastic fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
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