Jean-Baptiste Colliat

Multiscale in time and stability analysis of operator split solution procedures applied to thermomechanical problems

Purpose - The purpose of this paper is to study the partitioned solution procedure for thermomechanical coupling, where each sub-problem is solved by a separate time integration scheme. Design/methodology/approach - In particular, the solution which guarantees that the coupling condition will preserve the stability of computations for the coupled problem is studied. The consideration is further generalized for the case where each sub-problem will possess its particular time scale which requires different time step to be selected for each sub-problem. Findings - Several numerical simulations are presented to illustrate very satisfying performance of the proposed solution procedure and confirm the theoretical speed-up of computations which follow from the adequate choice of the time step for each sub-problem. Originality/value - The paper confirms that one can make the most appropriate selection of the time step and carry out the separate computations for each sub-problem, and then enforce the coupling which will preserve the stability of computations with such an operator split procedure.

Failure model for heterogeneous structures using structured meshes and accounting for probability aspects

Purpose – The purpose of this paper is to discuss the inelastic behavior of heterogeneous structures within the framework of finite element modelling, by taking into the related probabilistic aspects of heterogeneities.Design/methodology/approach – The paper shows how to construct the structured FE mesh representation for the failure modelling for such structures, by using a building‐block of a constant stress element which can contain two different phases and phase interface. All the modifications which are needed to enforce for such an element in order to account for inelastic behavior in each phase and the corresponding inelastic failure modes at the phase interface are presented.Findings – It is demonstrated by numerical examples that the proposed structured FE mesh approach is much more efficient from the non‐structured mesh representation. This feature is of special interest for probabilistic analysis, where a large amount of computation is needed in order to provide the corresponding statistics. On...

Modélisation jusqu'à rupture de murs en maçonnerie chargés dans leur plan

ABSTRACT This paper deals with modeling of mechanical behaviour of masonry walls submitted to in-plane loading. The adopted strategy consists of modelling separately the appropriate local failure mechanisms of thoug elements and mortar joints. A particular attention is dedicated to brick crushing mechanisms which were captured with strong displacement discontinuities within the framework of incompatible mode method. A perfect plasticity model including di-latancy has been employed for the joints modeling. This model has been compared with two experimental results. We show that we are able to well reproduce the global behaviour of such structure (stiffness and peak load) and thus construct reliable predictive model of the masonry walls by using only the experimental characteristics of their components.

Probability Based Size Effect Representation for Failure in Civil Engineering Structures Built of Heterogeneous Materials

In this work we discuss the failure analysis of civil engineering structures built of heterogeneous materials. The material heterogeneities call for a detailed representation of typical micro or meso-structure, which can be provided with the structured FE mesh representation as illustrated herein for 2D case and two-phase material. The building-block of such a representation is the constant stress triangular element that can contain two different phases and phase interface, along with all modifications needed to account for inelastic behavior in each phase and the corresponding inelastic failure modes at the phase interface. We further show by numerical simulations that the proposed structured FE mesh approach is much more efficient than the non-structured mesh representation. This feature is of special interest for probabilistic analysis, where a large amount of computation is needed in order to provide the corresponding statistics. One such case of probabilistic failure analysis is also considered in this work, where the geometry of the phase interface remains uncertain since it is obtained as the result of the Gibbs random process. This computation is further used to provide the appropriate probabilistic description of material parameters of phenomenological model of localized failure in terms of correlated random fields. Subsequent Monte Carlo computations of failure phenomena in simple tension test performed with such probabilistic phenomenological model clearly show the capability of presented approach to recover the size effects anywhere within a range between the two classical bounds which are Continuum Damage Mechanics and Linear Fracture Mechanics.

Modelling the influence of temperature on accelerated leaching in ammonium nitrate

This study proposes two models for accelerated leaching in ammonium nitrate under variable temperature. The first approach assumes a thermoactivated linear relationship between degradation and the square root of time. The second approach introduces, within a phenomenological model, the thermoactivation of diffusion and hydrates solubility. These two approaches enable one to analyse accelerated leaching tests to identify the concrete variability in order to get rid of the influence of temperature. Cette étude consiste à proposer deux modélisations de la lixiviation accélérée au nitrate d’ammonium sous température variable. La première approche suppose une relation linéaire thermoactivée entre la dégradation et la racine carrée du temps. La seconde approche introduit dans un modèle phénoménologique la thermoactivation de la diffusion et de la solubilité rétrograde des hydrates. Ces deux approches permettent de dépouiller des essais de type DANA afin d’identifier la variabilité du béton en s’affranchissant de l’influence de la température.

Critical probability of percolation over bounded region in N-dimensional Euclidean space

Following H. Tomita and C. Murakami we propose an analytical model to predict critical probability of percolation. It is based on the excursion set theory which allows us to consider N-dimensional bounded regions. Details are given for the 3D case and statistically Representative Volume Elements are calculated. Finally generalisation to the N-dimensional case is made.

Influence of the spatial variability of leaching kinetics parameters on the lifespan of a concrete structure

This works aims at studying, through the Monte Carlo method, the influence of the leaching kinetics parameters spatial variability on the lifespan of a concrete structure. The considered structure is a tunnel for nuclear waste storage. It is observed that the expected value for the lifespan estimated when considering the material spatial variability is significantly lower than the lifespan estimated with a single simulation considering uniform parameter fields, equal to the expected value for each parameter. Le but de cette étude est d’évaluer, par la mise en œ uvre de la méthode de Monte Carlo, l’influence de la variabilité spatiale des paramètres les plus influents par rapport à la cinétique de dégradation en lixiviation sur la vitesse de propagation dans une structure en béton du front de dissolution de la portlandite. La structure considérée est un tunnel de stockage de déchets radioactifs. Nous observons que l’espérance de la durée de vie estimée en tenant compte de la variabilité spatiale des propriétés du béton est sensiblement inférieure à la durée de vie estimée en considérant des champs uniformes, égaux à l’espérance des paramètres considérés.

Modeling thermomechanical behaviour of cellular structure made of brittle material

Publisher Summary This chapter discusses the modeling of thermo-mechanical behavior of brittle material using shell elements. The structures of this kind are encountered in many practical engineering problems and their uses are widespread in civil engineering. From a physical point of view, the material exhibits brittle behavior in traction and in compression. Moreover, considering that cracking appears perpendicularly to load direction in tension and in parallel to this direction in compression, it has been noted that the failure of such material is mainly driven by positive strains. According to such experimental aspect, Rankine like plasticity model was written, which contrary to standard approach employs the yield criterion based on strain tensor principal values and not on the stress tensor.

The embedded finite element method (E-FEM) for multicracking of quasi-brittle materials

Dealing with brittle or quasi-brittle failure within a finite element (FE) context is a well-known problem and basically requires to implement new methods since the finite element method (FEM) has originally been thought for continuum media, i.e., without discontinuities. The models using traditional FEM and based on the linear fracture mechanics require mesh refinements in order to model the singularity of the stress field around the crack tip. Several numerical schemes have been used in this view: the double noding technique, local or general remeshing, boundary elements, cohesive zone models, smeared cracks models, and models with embedded discontinuities. The latter family is the most physically based because cracks are nothing else but real discontinuities within the material itself. Moreover the released energy corresponding to the crack opening process is dissipated onto the discontinuity. Thus no mesh dependency is observed and no numerical treatments of the strain localization are required. Their numerical implementations can be made according to two main ways: the extended finite element method (X-FEM), which corresponds to a global kinematic enrichment, and the embedded finite element method (E-FEM), which is a local enhancement.

Numerical Simulation of Sorption-Desorption Isotherme for Cement-Based Materials

One of the most important issues in civil engineering about structures is their durability. A structure during his lifetime faces different environmental situations, like different relative humidities, and different cycles of drying and saturation will be imposed on it, so it is very critical to characterize materials behavior against these changes. Some informations are needed to predict it, one of these informations is desorption and sorption isotherm. In cement based materials just as cement paste, there remain generally extremely fine pores, consequently obtaining isotherms experimentally is considered as a substantially time-consuming experience. Therefore, it is of interest to model the isotherm from a numerical point of view. This physical phenomenon has been a field of study of intense researches, however, there are not many models relying on true physical effects which take place during drying and saturation. In the present work, in order to model a porous media, a numerical morphology of the geometry of the porous media has been presented by means of a random field excursion through the selection of a random field and a threshold. Random field parameters are defined based on experimental values. Once the porous media has been reproduced, the morphological analysis must be done in order to model water transfers.