Anisotropic 3D delay-damage model to simulate concrete structures

Abstract

High dynamic loadings lead to material degradation and structural failure. This is even more the case for concrete structures where the parts initially in compression break in tension due to waves propagation and reflection. The dissymmetry of the material behavior plays a major role in such cases, dissymmetry mainly due to damage induced anisotropy. Loading induced damage is most often anisotropic and one proposes here to take advantage of such a feature to build a damage model for concrete, dissymmetric in tension and in compression, 3D, suitable for dynamic computations. A single 2nd order tensorial damage variable D D D is considered with a damage law ensuring a damage rate proportional to the square of the positive part of the strain tensor. One focus in the present work on viscous regularizations for the anisotropic damage model proposed, regularizations of Norton-Perzyna type. Numerical examples of dynamic failures illustrate the ability and the efficiency of the model to deal with 3D structures. RÉSUMÉ. Lors d'un chargement de dynamique transitoire sur une structure en béton, il n'est pas rare d'avoir des réflexions d'ondes de compression qui en devenant des ondes de traction peuvent provoquer la rupture. La dissymétrie du comportement joue alors un rôle majeur, dissymétrie principalement due à l'endommagement anisotrope induit. Nous considérerons donc un modèle d'endommagement pour le béton, 3D, capable de représenter cette dissymétrie et adapté aux chargements dynamiques. Nous considérerons une variable d'endommagement tensorielle d'ordre 2, D D D, avec une loi d'évolution proportionnelle à la partie positive du tenseur des déformations. Le travail présenté ici traite plus particulièrement de la régularisation visqueuse du modèle d'endommagement anisotrope proposé ainsi que son traitement numérique. Un exemple de calcul de structure montre la pertinence et l'efficacité du modèle.

Numerical determination of the tensile response and the dissipated fracture energy of concrete: role of the mesostructure and influence of the loading rate

“…To achieve the design and analyses of these structures, it is important to investigate the dynamic mechanical response of concrete. Several macroscopic models for concrete have been developed to perform nonlinear numerical analysis of such problems. In these models, a rate effect in tension has often been introduced to represent the experimental data for loading strain rates exceeding 1 /s .…”

A meso-mechanical model for concrete under dynamic tensile and compressive loading

“…At the macro scale, the ingredients that characterize concrete's heterogeneity are not represented and one considers it as a homogeneous material. Therefore, in this case, the constitutive models need to have recourse to (visco)plasticity coupled with a continuum damage formulation [32,16,43,2,21,34,20,15,36,14]. This leads to models with a relatively high number of parameters, which are difficult to relate to physical mechanisms that occur during failure.…”

Intrinsic dissipation of a modular anisotropic damage model: Application to concrete under impact

“…A visco-damage law has to be defined. Following [7] a delay-damage law which bounds the damage rate can be used, expressed next either in terms of trace rate or in terms of active damage rate…”

“…The corresponding constitutive models, even with induced anisotropy, are now most often implemented with localization limiters, i.e. either in a nonlocal form [1,2] or as visco-damage models [3,4,5] or both [6,7]. This allows to gain some numerical robustness as mesh independency of the converged finite element solution.…”