Holonomic constraints : an analytical result

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by using Lagrange multipliers. Finding the value of the Lagrange multipliers allows to compute the forces induced by the constraints and therefore, to integrate the equations of motions of the system. Computing analytically the Lagrange multipliers for a constrained system may be a difficult task that is depending on the complexity of systems. For complex systems, it is most of the time impossible to achieve. In computer simulations, some algorithms using iterative procedures estimate numerically Lagrange multipliers or constraint forces by correcting the unconstrained trajectory. In this work, we provide an analytical computation of the Lagrange multipliers for a set of linear holonomic constraints with an arbitrary number of bonds of constant length. In the appendix of the paper, one would find explicit formulas for Lagrange multipliers for systems having 1, 2, 3, 4 and 5 bonds of constant length, linearly connected.Comment: 13 pages, no figures. To appear in J. Phys. A : Math. The

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

Lekner summations and Ewald summations for quasi-two dimensional systems

Using the specific model of a bilayer of classical charged particles (bilayer Wigner crystal), we compare the predictions for energies and pair distribution functions obtained by Monte Carlo simulations using three different methods available to treat the long range Coulomb interactions in systems periodic in two directions but bound in the third one. The three methods compared are: the Ewald method for quasi-two dimensional systems [D.E. Parry, Surf. Sci. $\bm{49}$, 433 (1975); \it{ibid.}, $\bm{54}$, 195 (1976)], the Hautman-Klein method [J. Hautman and M.L. Klein, Mol. Phys. $\bm{75}$, 379 (1992)] and the Lekner summations method [J. Lekner, Physica A$\bm{176}$, 485 (1991)]. All of the three method studied in this paper may be applied to any quasi-two dimensional systems, including those having not the specific symmetry of slab systems. For the particular system used in this work, the Ewald method for quasi-two dimensional systems is exact and may be implemented with efficiency; results obtained with the other two methods are systematically compared to results found with the Ewald method. General recommendations to implement with accuracy, but not always with efficiency, the Lekner summations technique in Monte Carlo algorithms are given.Comment: 50 pages, 9 figures, 4 table

Damage model for FRP-confined concrete columns under cyclic loading

International audienceIn structural engineering, seismic vulnerability reduction of existing structures is a crucial issue. External reinforcement with fiber-reinforced polymer (FRP) holds interest in achieving this aim. Its use as a retrofitting method is limited, however, for a number of reasons, including the lack of numerical tools for predicting cyclic loading. This paper presents a simplified stress-strain model suitable for monotonic and cycling loading capable of predicting the FRP's effect on reinforced-concrete columns. The model was inspired by two well-known concrete constitutive laws: one based on damage mechanics (La Borderie's concrete-damage model, 1991); the other on extensive experimental studies (Eid and Paultre's confined-concrete model, 2008). Validation is provided using experimental results on reinforced concrete columns subjected to axial and flexural cyclic loading. The proposed approach also deals with steel-bar rupture, considering low-cycle fatigue effects. All the simulations were conducted with multifiber Timoshenko beam elements

Stress-strain model for FRP-confined concrete columns under cyclic and seismic loading

In structural engineering, seismic vulnerability reduction of existing structures is a crucial issue. External reinforcement with fiber-reinforced polymer (FRP) holds interest in achieving this aim. Its use as a retrofitting method is limited, however, for a number of reasons, including the lack of numerical tools for predicting cyclic loading. This paper presents a simplified stress-strain model suitable for monotonic and cycling loading capable of predicting the FRP's effect on reinforced-concrete col umns. The model is inspired by two well-known concrete constitutive laws: one based on damage mechanics (La Borderie's concrete-damage model, 1991); the other on extensive experimental studies (Eid & Paultre's confined-concrete model, 2008). Validation is provided using experimental results on reinforced concrete columns subjected to axial and flexural cyclic loading. All the simulations were conducted with multifiber Timoshenko beam elements

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)

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

Yukawa potentials are often used as effective potentials for systems as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential ; in this small screening limit, or Coulomb limit, the potential is long ranged. As it is well known in computer simulation, a simple truncation of the long ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of the space, has already been derived for Yukawa potential [cf. Y., Rosenfeld, {\it Mol. Phys.}, \bm{88}, 1357, (1996) and G., Salin and J.-M., Caillol, {\it J. Chem. Phys.}, \bm{113}, 10459, (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [M., Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. A special attention is paid to the Coulomb limit and its relation with the electroneutrality of systems.Comment: 40 pages, 5 figures and 4 table

Retrofitting reinforced concrete structures with FRP: Numerical simulations using multifiber beam elements

In structural engineering, seismic vulnerability reduction of existing structures is a crucial issue. External reinforcement by Polymer Reinforced Fibers (FRP) is an interesting tool in order to fulfill this aim. However, the use of FRP reinforcement as a retrofitting method is limited, one of the reasons being the lack of predicting numerical tools for cyclic loading. This paper presents a method to predict the behavior of beam-column structures considering the FRP reinforcement effect. It describes the construction of a 1D concrete constitutive model suitable for monotonic and cycling loadings. The model is inspired on two well-known concrete models, the first one based on the damage mechanics theory (La Borderie concrete damage model), and the second one based on experimental studies (Eid & Paultre's confined concrete model). Validation of the approach is done using experimental results on reinforced concrete beam and columns submitted to axial and flexural cyclic loading. The proposed method deals also with steel bar rupture considering low cycle fatigue effects. All the simulations are done using multifiber Timoshenko beam elements

Structure and thermodynamics of a ferrofluid bilayer

We present extensive Monte Carlo simulations for the thermodynamic and structural properties of a planar bilayer of dipolar hard spheres for a wide range of densities, dipole moments and layer separations. Expressions for the stress and pressure tensors of the bilayer system are derived. For all thermodynamic states considered the interlayer energy is shown to be attractive and much smaller than the intralayer contribution to the energy. It vanishes at layer separations of the order of two hard sphere diameters. The normal pressure is negative and decays as a function of layer separation $h$ as $-1/h^5$. Intralayer and interlayer pair distribution functions and angular correlation functions are presented. Despite the weak interlayer energy strong positional and orientational correlations exist between particles in the two layers.Comment: 45 pages, 4 Tables, 9 Figure