Yukawa potentials in systems with partial periodic boundary conditions II : Lekner sums for quasi-two dimensional systems

Yukawa potentials may be long ranged when the Debye screening length is large. In computer simulations, such long ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we have provided Ewald sums for quasi-two dimensional systems with Yukawa interaction potentials [M. Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007) and M. Mazars, {\it Mol. Phys.}, Paper I]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two dimensional systems with Yukawa interaction potentials and we give some numerical tests for pratical implementations. The main result of this paper is to outline that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work : Lekner sums should not be used for quasi-two dimensional systems with Yukawa interaction potentials.Comment: 25 pages, 5 figures and 1 tabl

Stress state influence on nonlocal interactions in damage modelling

This paper presents a modification of an integral nonlocal damage model used to describe concrete behaviour. It aims at providing a better treatment of areas close to a boundary and a fracture process zone where the interactions between points should vanish. Modifications on the original integral nonlocal model are introduced by considering the stress state of points in the weight function used to compute the nonlocal variables. Computations show that local information such as strain or damage profiles are significantly different, leading to a narrower region where damage equal to 1 in the case of the modified nonlocal model. It allows to better approach a discontinuity of the displacement field upon failure and thus, improves the estimation of the crack opening that has been developed in post-processing for this type of calculation

Simplified modelling strategies to simulate the dynamic behaviour of R/C walls

International audienceA continuous damage model and different simplified numerical strategies are proposed to simulate the behaviour of reinforced concrete (R/C) walls subjected to earthquake ground motions. For 2D modelling of R/C walls controlled primarily by bending, an Euler multilayered beam element is adopted. For 3D problems, a multifibre Timoshenko beam element having higher order interpolation functions has been developed. Finally, for walls with a small slenderness ratio we use the Equivalent Reinforced Concrete model. For each case, comparison with experimental results of R/C walls tested on shaking table or reaction wall shows the advantages but also the limitations of the approach

Using damage mechanics to simulate the behavior of various reinforced concrete walls submitted to earthquake loading

International audienceA damage model and different simplified numerical strategies are proposed to simulate the behavior of reinforced concrete (RC) walls submitted to earthquake ground motions. For RC walls controlled primarily by bending the 20 Euler beam theory is adopted. When dealing with structures with a small slenderness ratio we use the Equivalent Reinforced Concrete model. Finally, for 30 problems a multifiber Timoshenko beam element with higher order interpolation functions has been developed. For each case, a comparison with experimental results shows the good basis of the approach

Simplified modelling strategies to simulate the dynamic behaviour of R/C walls

International audienceA continuous damage model and different simplified numerical strategies are proposed to simulate the behaviour of reinforced concrete (R/C) walls subjected to earthquake ground motions. For 2D modelling of R/C walls controlled primarily by bending, an Euler multilayered beam element is adopted. For 3D problems, a multifibre Timoshenko beam element having higher order interpolation functions has been developed. Finally, for walls with a small slenderness ratio we use the Equivalent Reinforced Concrete model. For each case, comparison with experimental results of R/C walls tested on shaking table or reaction wall shows the advantages but also the limitations of the approach

Ewald methods for inverse power-law interactions in tridimensional and quasi-two dimensional systems

In this paper, we derive the Ewald method for inverse power-law interactions in quasi-two dimensional systems. The derivation is done by using two different analytical methods. The first uses the Parry's limit, that considers the Ewald methods for quasi-two dimensional systems as a limit of the Ewald methods for tridimensional systems, the second uses Poisson-Jacobi identities for lattice sums. Taking into account the equivalence of both derivations, we obtain a new analytical Fourier transform intregral involving incomplete gamma function. Energies of the generalized restrictive primitive model of electrolytes ($\eta$-RPM) and of the generalized one component plasma model ($\eta$-OCP) are given for the tridimensional, quasi-two dimensional and monolayers systems. Few numerical results, using Monte-Carlo simulations, for $\eta$-RPM and $\eta$-OCP monolayers systems are reported.Comment: to be published in Journal of Physics A: Mathematical and Theoretical (19 pages, 2 figures and 3 tables

A macro-element for a shallow foundation to simulate Soil-Structure Interaction considering uplift

International audienceIn earthquake engineering, several approaches exist to take into account Soil–Structure Interaction (SSI): the following work is based on the “macro-element” concept. The particularity of the macro-element lies in the fact that the movement of a foundation is entirely described by a system of generalised variables (forces and displacements) defined at the foundation centre. The non-linear behaviour of the soil is reproduced using the classical theory of plasticity. This Note improves an already existing macro-element by adding the uplift behaviour of the foundation according to the plasticity theory. Comparisons with experimental results of a foundation submitted to cyclic loadings show the performance of the approach.Un macro-élément d'Interaction Sol-Structure pour une fondation superficielle prenant en compte un mécanisme de décollement. Dans le domaine du génie parasismique, plusieurs méthodes existent pour considérer l'Interaction Sol-Structure : ce travail est basé sur le concept de « macro-élément ». La particularité du macro-élément réside dans le fait qu'il est formulé en variables globales (forces et déplacements) décrites au centre de la fondation. Le comportement non-linéaire du sol est reproduit selon la théorie de plasticité. Cette Note propose une amélioration d'un macro-élément existant dans la littérature par la prise en compte du décollement de la fondation selon la théorie de la plasticité. Des comparaisons avec des résultats expérimentaux d'une fondation soumise à des chargements cycliques montrent la performance de cette approche

Seismic vulnerability of RC structures: Assessment before and after FRP retrofitting (case study)

In structural engineering, seismic assessment of existing structures is a crucial issue to provide adapted decisions in a vulnerability reduction context. Amongst the widely range of technical solutions for structural upgrading, external reinforcement by Fiber Reinforced Polymer (FRP) is an interesting tool. Nevertheless, the use of FRP as a retrofitting method is limited, one of the reasons being the lack of predictive numerical tools allowing the vulnerability assessment. Based on a case-study, this paper presents a simplified modeling strategy to assess the seismic vulnerability of an existing reinforced concrete building before and after FRP retrofitting. More specifically, the structure is simulated using multifiber beam elements, the model is validated with in-situ ambient vibrations records and a simplified method to consider FRP retrofitting is proposed. Non linear dynamic analysis studies are performed using a synthetic earthquake signal according to the Eurocode 8. Finally, local indicators, based on the European Macroseismic Scale (EMS 98), are adopted to quantify the damage level in the structure, before and after its FRP retrofitting.Keywords: earthquake; vulnerability; retrofitting; FRP; concrete; multifiber beam

Nonlocal damage based failure models, extraction of crack opening and transition to fracture

International audienceDamage models are capable to represent initiation and somehow crack propagation in a continuum framework. Thus crack openings are not explicitly described. However for concrete structures durability analysis, crack opening through transfer properties is a key issue. Therefore, in this contribution we present a new approach that is able from a continuum modelling to locate a crack from internal variable field and then to estimate crack opening along its path. Results compared to experimental measures for a three point bending test are in a good agreement with an error lower than 10% for widely opened crack (40μm)