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Modélisation élastoplastique avec endommagement du béton de structures. Application aux calculs statiques et dynamiques de structures en béton armé et béton précontraint

Abstract : This thesis seeks to study the effects of cracking at a structural level of reinforced and prestressed concrete structures when subject to static, cyclic and dynamic loading. This is done by exploring the constitutive equations of materials at a structural level and by developing appropriate numerical tools. A macroscopic model coupling plasticity with damage is used for modelling the non-linear behaviour of concrete. For the plastic part, the elastoplastic law is adapted to the specific behaviour of concrete. The (micro)cracking of the material is presented at the macroscopic level in terms of plastic strains, and the occurrence and development of damage by the evolution of plastic variables. In particular, the plastic porosity models the irreversible variation of connected porous space created by micro-cracking. This physical significance is at the basis of a phenomenological coupling of the plasticity model with the damage model. Damage effects are then accounted for by a degradation of elastic moduli as a function of the chosen damage variable: the plastic porosity. This material law is used within a multi-fiber finite beam element which is the extension of the well established planar multi-layer beam element to the three dimensional case. This numerical tool allows to account for material and geometrical non linear effects in the structural analysis of beam type structures subject to various loadings at low computation costs. For prestressing, the formulation takes into account the relative displacement between prestressing tendon and surrounding concrete. It is thus treated as a boundary problem at steel-concrete interface. These developments are implemented in a finite element program. Through a set of numerical applications, we show the field of application of these developments, as well as their limits, as design tools for structural engineers.
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Franz-Josef Ulm. Modélisation élastoplastique avec endommagement du béton de structures. Application aux calculs statiques et dynamiques de structures en béton armé et béton précontraint. Mécanique [physics.med-ph]. Ecole Nationale des Ponts et Chaussées, 1994. Français. ⟨tel-00529366⟩

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