Small vibrations of a linearly elastic body surrounded by heavy,incompressible, non-Newtonian fluids with free surfaces

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity. To cite this article: C. Licht, Tran Thu Ha, C. R. Mecanique 333 (2005).     

A Binary Model of textile composites: III high failure strain and work of fracture in 3D weaves

Prior experiments have revealed exceptionally high values of the work of fracture (0.4-) in carbon/epoxy 3D interlock woven composites. Detailed destructive examination of specimens suggested that much of the work of fracture arose when the specimens were strained well beyond the failure of individual tows yet still carried loads . A mechanism of lockup amongst broken tows sliding across the final tensile fracture surface was suggested as the means by which high loads could still be transferred after tow failure. In this paper, the roles of weave architecture and the distribution of flaws in the mechanics of tow lockup are investigated by Monte Carlo simulations using the so-called Binary Model. The Binary Model was introduced previously as a finite element formulation specialised to the problem of simulating relatively large, three-dimensional segments of textile composites, without any assumption of periodicity or other symmetry, while preserving the architecture and topology of the tow arrangement. The simulations succeed in reproducing all qualitative aspects of measured stress-strain curves. They reveal that lockup can indeed account for high loads being sustained beyond tow failure, provided flaws in tows have certain spatial distributions. The importance of the interlock architecture in enhancing friction by holding asperities on sliding fibre tows into firm contact is highlighted.     

Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load

Summary  The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The problem is formulated as a system of integral equations with r ⁻³-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along the crack front is presented for various crack shapes and different Poisson's ratio. Received 5 March 2002; accepted for publication 2 July 2002     

Some surprising phenomena in weak-bond fracture of a triangular lattice

A semi-infinite crack growing along a straight line in an unbounded triangular-cell lattice and in lattice strips is under examination. Elastic and standard-material viscoelastic lattices are considered. Using the superposition similar to that used for a square-cell lattice (J. Mech. Phys. Solids 48 (2000) 927) an irregular stress distribution is revealed on the crack line in mode II: the strain of the crack-front bond is lower than that of the next bond. A further notable fact about mode II concerns the bonds on the crack line in the lattice strip deformed by a ‘rigid machine’. If the alternate bonds, such that are inclined differently than the crack-front bond, are removed, the stresses in the crack-front bond and in the other intact bonds decrease. These facts result in irregular quasi-static and dynamic crack growth. In particular, in a wide range of conditions for mode II, consecutive bond breaking becomes impossible. The most surprising phenomenon is the formation of a binary crack consisting of two branches propagating on the same line. It appears that the consecutive breaking of the right-slope bonds—as one branch of the crack—can proceed at a speed different from that for the left-slope bonds—as another branch. One of these branches can move faster than the other, but with time they can change places. Some irregularities are observed in mode I as well. Under the influence of viscosity, crack growth can be stabilized and crack speed can be low when viscosity is high; however, in mode II irregularities in the crack growth remain. It is found that crack speed is a discontinuous function of the creep and relaxation times.     

DISCUSSION ON TWO PROBLEMS OF THEORETICAL MECHANICS IN COLLEGE MECHANICS COMPETITION1)

针对两道力学竞赛试题,从欧拉动力学方程出发分别给出了更加简化的固连系选取方法,分别命名为"Serret-Andoyer近似固连系"和"虚固连系",在此基础上对第1届全国青年力学竞赛理论力学试题第9题,拓展讨论了大球同步旋转时,小球的稳 定性条件,结果表明后者的稳定临界转速要求更低,这将更有利于提高旋转结构的稳定性;对第12届全国周培源大学生力学 竞赛第3题,剖析了任一纬度的运动规律,发现当体系初始角动量为零时会出现一种简洁又优美的运动模式。     

Application de l'approximation polytropique à la Simulation Numérique Directe de gaz chaudsApplication of the polytropique approximation to Direct Numerical Simulation of heated gases

As alternative to the usual assumptions of Boussinesq, we propose, for heated gases, a new approximation called polytropic approximation. With this approximation the quantities of corresponding state are related by a polytropic law of exponent χ of which we neglect the variability in space-time derivations in the equations governing the flow considered. As application, we used this new proposition to solve numerically a heated gas flow in an annular cavity of rotor-stator type. We expose here the numerical method and some results of the polytropic approximation with comparison to results of Boussinesq approximations. To cite this article: S. Benjeddou et al., C. R. Mecanique 332 (2003).     

Hertz contact at finite friction and arbitrary profiles

Axisymmetric contact at finite Coulomb friction and arbitrary profiles is examined analytically and numerically for dissimilar linear elastic solids. Invariance and generality are aimed at and an incremental procedure is developed resulting in a reduced benchmark problem corresponding to a rigid flat indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, was solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, a tailored cumulative superposition procedure was developed to resolve the original problem to determine global and local field values. Save for the influence of the coefficients of friction and contraction ratio, it is shown that at partial slip the evolving relative stick-slip contour is independent of any convex and smooth contact profile at monotonic loading. For flat and conical profiles with rounded edges and apices, results are illustrated for relations between force, depth and contact contours together with surface stress distributions. The solution for dissimilar solids in a full space is transformed to a half-space problem and solved for a combination of material parameters in order to first determine interface traction distributions. Subsequently, full field values for the two solids were computed individually. In order to predict initiation of fracture and plastic flow, results are reported for the location and magnitude of maximum tensile stress and effective stress, respectively, for a range of geometrical and material parameters. In two illustrations, predicted results are compared with experimental findings related to initiation of brittle fracture and load-depth relations at nanoindentation.     

New trends in the analysis of masonry structures

The modern theory of masonry structures has been set up on the hypothesis of no-tension behaviour, with the aim of offering a reference model, independent of materials and building techniques employed. This hypothesis gives rise to inequalities which have to be satisfied by the stress tensor components and, as a dual aspect, to the kinematic behaviour characteristics of media which can be classified as lying between solids and fluids: the structure of the masonry material consists of particles reacting elastically only when in contact. An examination of the plane-stress problem leads us to define, within the prescribed domain under admissible loads, three different subdomains with null, regular, or non-regular principal stress tensors, respectively. As the boundaries of such subdomains are not known a priori, the problem can be classified as a free boundary value problem. The analysis concerns mainly the subdomains where the stress tensor is non-regular; and a non-regularity condition det =0 is added to the equilibrium equations. This condition makes the stress problem isostatic and leads to a violation of Saint-Venant's compliance conditions on strains. Hence there is a need to introduce a strain tensor, not related to the stress tensor, which can be decomposed into an extensional component and a shearing component; we prove that such strains, of the class ^c, are similar to those of the theory of plastic flow. From the point of view of computational analysis the anelastic strains are considered as given distortions; they are computed by means of the Haar-Kármán principle, modified for computational purposes by an idea of Prager and Hodge.

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Sommario La moderna teoria delle strutture murarie, fondata sulla rigorosa non reagenza a trazione del materiale, ha lo scopo di fornire un modello di riferimento indipendente sia dalle caratteristiche del materiale sia dalle techniche costruttive impiegate. L'ipotesi di non reagenza a trazione si traduce in disuguaglianze che le componenti del tensore di stress devono verificare; dualmente il comportamento caratteristico cinematico può esser classificato di confine, come del resto la stessa statica, tra solidi e fluidi: la struttura ipotizzata del materiale muratura consiste di particelle che reagiscono solo se sono in contatto. L'esame del problema piano porta a definire all'interno del dominio di definizione tre differenti tipi di sub-regioni in cui lo stress è nullo, canonico, o singolare. Poiché le frontiere di queste sub-regioni non sono note a priori il problema può anche essere classificato di frontiera libera. L'analisi concerne fondamentalmente la sub-regione in cui il tensore è non regolare, perché deve verificare anche la condizione det =0. Ciò rende isostatico il problema e conduce anche alla violazione della condizione di integrabilità delle deformazioni. Questo passaggio può essere superato introducendo un tensore di deformazioni a tensioni nulle che si può decomporre in una componente estensionale ed in una componente di scorrimento; si dimostra che queste deformazioni sono equivalenti a quelle che intervengono nella Teoria del flusso plastico. Dal punto di vista computazionale le deformazioni anelastiche sono considerate come distorsioni impresse determinate attraverso il principio di Haar-Kármán modificato, per le techniche computazionali, su idee di Prager e Hodge.

     

Experimental and numerical investigation of concrete properties effects on fracture toughness under complex loading

Abstract

This article is presenting the common experimental specimen for determining the fracture toughness of the first pure mode and second pure mode. The Notched beam is chosen from a presented common specimen in the form of three-point flexure beam and four-point flexure beam that were built in the concrete laboratory. For prevention of cracks growth, a critical load of first pure mode and the second pure mode of each specimen computed. Obtained results are used for computing the fracture toughness. For the purpose of investigating the effective fracture parameters in the suggested specimen, finite element analysis on the mentioned geometry is performed. Obtained results show that different parameters are effective on the fracture toughness including crack length, cement percentage, water and the thickness of biggest used aggregate in the sand. Also with changing each of these parameters, the fracture mechanic properties are changed. Each of these effects is examined separately in this article and the conclusions presented in tables and figures.

Communicated by Dumitru Caruntu.     

Identification of viscoelastic properties by means of nanoindentation taking the real tip geometry into account

Motivated by recent progress in viscoelastic indentation analysis, the identification of viscoelastic properties from nanoindentation test data taking the real tip geometry into account is presented in this paper. Based on the elastic solution of the indentation problem, the corresponding viscoelastic solution is obtained by the application of the method of functional equations. This general solution, which accounts for the real geometric properties of the indenter tip, is specialized for the case of a trapezoidal load history, commonly employed in nanoindentation testing. Three deviatoric creep models, the single dash-pot, the Maxwell, and the three-parameter model are considered. The so-obtained expressions allow us to determine viscoelastic model parameters via back calculation from the measured load–penetration history. The presented approach is illustrated by the identification of short-term viscoelastic properties of bitumen. Hereby, the influence of loading rate, maximum load, and temperature on the model parameters is investigated.