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CONTENTS
Volume 5, Number 4, August 2008
 

Abstract
In the present paper a 3D thermo-hygro-mechanical model for concrete is used to study explosive spalling of concrete cover at high temperature. For a given boundary conditions the distribution of moisture, pore pressure, temperature, stresses and strains are calculated by employing a threedimensional transient finite element analysis. The used thermo-hygro-mechanical model accounts for the interaction between hygral and thermal properties of concrete. Moreover, these properties are coupled with the mechanical properties of concrete, i.e., it is assumed that the mechanical properties (damage) have an effect on distribution of moisture (pore pressure) and temperature. Stresses in concrete are calculated by employing temperature dependent microplane model. To study explosive spalling of concrete cover, a 3D finite element analysis of a concrete slab, which was locally exposed to high temperature, is performed. It is shown that relatively high pore pressure in concrete can cause explosive spalling. The numerical results indicate that the governing parameter that controls spalling is permeability of concrete. It is also shown that possible buckling of a concrete layer in the spalling zone increases the risk for explosive spalling.

Key Words
concrete; high temperature; explosive spalling; thermo-hygro-mechanical model; microplane model; finite elements.

Address
Joško Ožbolt, Goran Periškic, Hans-Wolf Reinhardt and Rolf Eligehausen : Institute for Construction Materials Stuttgart, Germany

Abstract
A previously published multiscale model for early-age cement-based materials [Pichler, et al.2007. ?A multiscale micromechanics model for the autogenous-shrinkage deformation of early-age cement-based materials.? Engineering Fracture Mechanics, 74, 34-58] is extended towards upscaling of viscoelastic properties. The obtained model links macroscopic behavior, i.e., creep compliance of concrete samples, to the composition of concrete at finer scales and the (supposedly) intrinsic material properties of distinct phases at these scales. Whereas finer-scale composition (and its history) is accessible through recently developed hydration models for the main clinker phases in ordinary Portland cement (OPC), viscous properties of the creep active constituent at finer scales, i.e., calcium-silicate-hydrates (CSH) are identified from macroscopic creep tests using the proposed multiscale model. The proposed multiscale model is assessed by different concrete creep tests reported in the open literature. Moreover, the model prediction is compared to a commonly used macroscopic creep model, the so-called B3 model.

Key Words
concrete; calcium-silicate-hydrates; early-age concrete; multiscale modeling; logarithmic creep; continuum micromechanics; Laplace-Carson transformation.

Address
Ch. Pichler : Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, A-1040 Vienna, Austria
R. Lackner : FG Computational Mechanics, Technical University of Munich, Arcisstra?e 21, 80333 Munich, Germany

Abstract
A local behavior law, which includes elasticity, plasticity and damage, is developed in a three dimensional numerical model for concrete. The model is based on the Discrete Element Method (DEM)and the computational implementation has been carried out in the numerical Code YADE. This model was used to study the response of a concrete slab impacted by a rigid missile, and focuses on the extension of the compacted zone. To do so, the model was first used to simulate compression and hydrostatic tests. Once the local constitutive law parameters of the discrete element model were calibrated, the numerical model simulated the impact of a rigid missile used as a reference case to be compared to an experimental data set. From this reference case, simulations were carried out to show the importance of compaction during an impact and how it expands depending on the different impact conditions. Moreover, the numerical results were compared to empirical predictive formulae for penetration and perforation cases, demonstrating the importance of taking into account the local compaction process in the local interaction law between discrete elements.

Key Words
impact missile; compaction; concrete model; discrete element method.

Address
Wenjie Shiu, Frederic-Victor Donze and Laurent Daudeville : Laboratoire ?Sols Solides Structures et Risques?, UMR5521, Universite Joseph Fourier,Grenoble Universite, BP53, 38041 Grenoble cedex 9, France

Abstract
This article focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young?s modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. The proposed approach is then applied to a rock impact on a concrete slab in order to validate the coupled method and compare computation times.

Key Words
Jessica Rousseau*, Emmanuel Frangin, Philippe Marin and Laurent Daudeville Universit Joseph Fourier/INPG/CNRS Laboratoire Sols, Solides, Structures, Risques (3S-R) DU BP53, 38041 Grenoble Cedex 9, France

Address
Jessica Rousseau, Emmanuel Frangin, Philippe Marin and Laurent Daudevill : Universit Joseph Fourier/INPG/CNRS Laboratoire Sols, Solides, Structures,Risques (3S-R) DU BP53, 38041 Grenoble Cedex 9, France

Abstract
The present parametric study deals with the meso-scale modelling of concrete subjected to cyclic compression, which exhibits hysteresis loops during unloading and reloading. Concrete is idealised as a two-dimensional three-phase composite made of aggregates, mortar and interfacial transition zones (ITZs). The meso-scale modelling approach relies on the hypothesis that the hysteresis loops are caused by localised permanent displacements, which result in nonlinear fracture processes during unloading and reloading. A parametric study is carried out to investigate how aggregate density and size, amount of permanent displacements in the ITZ and the mortar, and the ITZ strength influence the hysteresis loops obtained with the meso-scale modelling approach.

Key Words
concrete; fracture; cyclic loading; compression; damage mechanics; plasticity; Meso-scale.

Address
Rasmus Rempling : Chalmers University of Technology, Goteborg, Sweden
Peter Grassl : Department of Civil Engineering, University of Glasgow, Glasgow, UK

Abstract
Crack opening governs many transfer properties that play a pivotal role in durability analyses. Instead of trying to combine continuum and discrete models in computational analyses, it would be attractive to derive from the continuum approach an estimate of crack opening, without considering the explicit description of a discontinuous displacement field in the computational model. This is the prime objective of this contribution. The derivation is based on the comparison between two continuous variables: the distribution if the effective non local strain that controls damage and an analytical distribution of the effective non local variable that derives from a strong discontinuity analysis. Close to complete failure, these distributions should be very close to each other. Their comparison provides two quantities: the displacement jump across the crack [U] and the distance between the two profiles. This distance is an error indicator defining how close the damage distribution is from that corresponding to a crack surrounded by a fracture process zone. It may subsequently serve in continuous/discrete models in order to define the threshold below which the continuum approach is close enough to the discrete one in order to switch descriptions. The estimation of the crack opening is illustrated on a one-dimensional example and the error between the profiles issued from discontinuous and FE analyses is found to be of a few percents close to complete failure.

Key Words
crack opening; damage model; strong discontinuity; fracture.

Address
Frederic Dufour : R&DO - Institut GeM, Ecole Centrale Nantes, CNRS, France
Gilles Pijaudier-Cabot : Laboratoire des fluides complexes, Universite de Pau et des Pays de l?Adour, CNRS, France
Marta Choinska : Institut GeM, Universite de Nantes, CNRS, France
Antonio Huerta : Laboratoire de Calcul Numeric, Univ. Politecnica de Catalunya, Barcelona, Spain

Abstract
In this work we simulate explicitly the dynamic fracture propagation in reinforced concrete beams. In particular, adopting cohesive theories of fracture with the direct simulation of fracture and fragmentation, we represent the concrete matrix, the steel re-bars and the interface between the two materials explicitly. Therefore the crack nucleation within the concrete matrix, through and along the re-bars, the deterioration of the concrete-steel interface are modeled explicitly. The numerical simulations are validated against experiments of three-point-bend beams loaded dynamically under various strain rates. By extracting the crack-tip positions and the crack mouth opening displacement history, a two-stage crack propagation, marked by the attainment of the peak load, is observed. The first stage corresponds to the stable crack advance, the second one, the unstable collapse of the beam.

Key Words
dynamic fracture; cohesive elements; crack propagation time.

Address
Rena C. Yu, Xiaoxin Zhang and Gonzalo Ruiz : ETSI de Caminos, C.y P., Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain

Abstract
The paper presents a methodology to model three-dimensional reinforced concrete members by means of embedded discontinuity elements based on the Continuum Strong Discontinuous Approach (CSDA). Mixture theory concepts are used to model reinforced concrete as a 3D composite material constituted of concrete with long fibers (rebars) bundles oriented in different directions embedded in it. The effects of the rebars are modeled by phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel action. The paper presents the constitutive models assumed for the components and the compatibility conditions chosen to constitute the composite. Numerical analyses of existing experimental reinforced concrete members are presented, illustrating the applicability of the proposed methodology.

Key Words
finite elements; fracture mechanics; strong discontinuities; mixture theory; finite elements with embedded discontinuities. J. Oliver : E.T.S. d?Enginyers de Camins, Canals i Ports, Technical University of Catalonia (UPC) Campus Nord UPC, Modul C-1, c/Jordi Girona 1-3, 08034 Barcelona, Spain A. E. Huespe : CIMEC/Intec, Conicet, Guemes 3450, Santa Fe 3000, Argentina G. Diaz : E.T.S. d?Enginyers de Camins, Canals i Ports, Technical University of Catalonia (UPC) Campus Nord UPC, Modul C-1, c/Jordi Girona 1-3, 08034 Barcelona, Spain

Address
O. L. Manzoli : Department of Civil Engineering, Sao Paulo State University (UNESP), Av. Luiz Edmundo C. Coube, S/N, 17030-360, Bauru, SP, Brazil
J. Oliver : E.T.S. d?Enginyers de Camins, Canals i Ports, Technical University of Catalonia (UPC) Campus Nord UPC, Modul C-1, c/Jordi Girona 1-3, 08034 Barcelona, Spain
A. E. Huespe : CIMEC/Intec, Conicet, Guemes 3450, Santa Fe 3000, Argentina
G. Diaz : E.T.S. d?Enginyers de Camins, Canals i Ports, Technical University of Catalonia (UPC) Campus Nord UPC, Modul C-1, c/Jordi Girona 1-3, 08034 Barcelona, Spain

Abstract
This paper deals with damage induced anisotropy modeling for concrete-like materials. A thermodynamics based constitutive relationship is presented coupling anisotropic damage and elasticity, the main idea of the model being that damage anisotropy is responsible for the dissymmetry tension/compression. A strain written damage criterion is considered (Mazars criterion extended to anisotropy in the initial model). The biaxial behavior of a family of anisotropic damage model is analyzed through the effects of yield surface modifications by the introduction of new equivalent strains.

Key Words
constitutive relations; anisotropic damage; yield function; multiaxial behaviour.

Address
F. Ragueneau, R. Desmorat and F. Gatuingt : LMT-Cachan (ENS Cachan/CNRS/Universite Paris 6/UniverSud Paris) 61, Avenue du president Wilson, 94235 Cachan, France


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