A material force method for inelastic fracture mechanics

A material force method is proposed for evaluating the energy release rate and work rate of dissipation for fracture in inelastic materials. The inelastic material response is characterized by an internal variable model with an explicitly defined free energy density and dissipation potential. Expressions for the global material and dissipation forces are obtained from a global balance of energy-momentum that incorporates dissipation from inelastic material behavior. It is shown that in the special case of steady-state growth, the global dissipation force equals the work rate of dissipation, and the global material force and J-integral methods are equivalent. For implementation in finite element computations, an equivalent domain expression of the global material force is developed from the weak form of the energy-momentum balance. The method is applied to model problems of cohesive fracture in a remote K-field for viscoelasticity and elastoplasticity. The viscoelastic problem is used to compare various element discretizations in combination with different schemes for computing strain gradients. For the elastoplastic problem, the effects of cohesive and bulk properties on the plastic dissipation are examined using calculations of the global dissipation force.     

Instability and friction

A review on the stability analysis of solids in unilateral and frictional contact is given. The presentation is focussed on the stability of an equilibrium position of an elastic solid in frictional contact with a fixed or moving obstacle. The problem of divergence instability and the obtention of a criterion of static stability are discussed first for the case of a fixed obstacle. The possibility of flutter instability is then considered for a steady sliding equilibrium with a moving obstacle. The steady sliding solution is generically unstable by flutter and leads to a dynamic response which can be chaotic or periodic. This dynamic response leads to the generation of stick–slip–separation waves on the contact surface in a similar way as Schallamach waves in statics. Illustrating examples and principal results recently obtained in the literature are reported. Some problems of friction-induced vibration and noise emittence, such as brake squeal for example, can be interpreted in this spirit. To cite this article: Q.S. Nguyen, C. R. Mecanique 331 (2003).     

Spin gapless semiconductor like Ti2MnAl film as a new candidate for spintronics application

A novel Heusler ferrimagnet Ti₂MnAl film has been grown on Si(001) substrate using magnetron sputtering. Characteristics of its magnetic and transport properties reveal the spin‐gapless‐semiconductor (SGS) nature of the stoichiometric Ti₂MnAl, in agreement with theoretical prediction. The as‐grown SGS‐like Ti₂MnAl film demonstrated high Curie temperature, nearly compensated ferrimagnetic properties with small coercivity and low magnetization. It also showed semiconductor‐like behavior at room temperature allowing good compatibility with commercial Si‐based semiconductor. In this regards, Ti₂MnAl film is a potential candidate material for spintronics application, especially for the minimization of energy consumption of device. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

On a convex set with nondifferentiable metric projection

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with \(C^{1,1}\) boundary which possesses the same property.     

Dynamics of a powered disk in clay soil

Experiments were conducted with a single powered disk in a laboratory soil bin containing Bangkok clay soil with an average moisture content of 18% (db) and 1100 kPa cone index. The disk was 510 cm in diameter and 560 mm in radius of concavity. During the tests the disk angle was varied from 20° to 35°, ground speed from 1 to 3 km/h and rotational speed from 60 to 140 rpm. The working depth was kept constant at 12 cm. The vertical, horizontal and lateral reactions of the soil were measured by force transducers. The forward and rotational speeds were recorded. It was observed that disk angle, rotational speed and ground speed had significant effects on soil reactive forces and power requirement. With a small disk angle, low ground speed, and high rotational speed, the soil longitudinal reactive force was a pushing force and became a resistive one at larger disk angles and ground speeds. The soil transverse reactive force increased with an increase of rotational and ground speed but decreased with the increase of disk angle, whereas the vertical relative force increased only with the increase of ground speed but decreased with the increase of rotational speed and disk angle. It was found that the powered disk required the least power at a disk angle of 30° and rotational speed between 80 and 100 rpm. Increase in ground speed from 1 to 3 km/h increased the total power requirement by 31.8%. Upon driving the disk forward, the draft reduced considerably compared to that of the free-rolling disk. By driving the disk in the reverse direction, the draft reduced slightly. At a disk angle of 30°, rotational speed of 100 rpm, and ground speed of 3 km/h, the total power requirement of the forward-driven disk was 65% higher than that of the free-rolling disk. The predicted engine power of the forward-driven disk, however, was only 21% higher than that of the free-rolling one owing to the more efficient power transmission through the PTO, as opposed to the drawbar. The effects of reverse driving and free rolling of the disk were also studied.     

Ondes adhérence–glissement–décollement sous contact unilatéral frottantStick–slip–separation waves in unilateral and frictional contact

A numerical study on the dynamic response of a mechanical system composed of two coaxial cylinders in relative rotation and unilateral contact with Coulomb friction is presented. This discussion complements the semi-analytical results on stick–slip waves given in Moirot, Nguyen, C. R. Acad. Sci. Paris Sér. IIb 328 (2000) 663–669, by some numerical simulations on the dynamic transition of the system from a given initial state to a surface wave. The case of stick–slip–separation waves is considered. To cite this article: A. Oueslati et al., C. R. Mecanique 331 (2003).     

Nouvelle approche numerique des solutions de la couche limite laminaire incompressible en regime non-stationnaire autour d'une paroi cylindrique elliptique mise en impulsion brutale

The equations of the unsteady incompressible laminar boundary layers about circular and elliptic cylinders started impulsively from rest are solved, after an original coordinate transformation, with the help of a semi-implicit difference scheme linearly stable without conditions. The knowledge of the phenomenon results only from that of the flow characteristics at the initial time; this makes mandatory the use of an analytical method of the Blasius type. When the ratio of the semi-axes of the elliptic cylinder becomes infinite, the present method gives the solution of the stagnation flow.When the flow presents a separation point in the steady state (circular cylinder), a criterion for stopping computation is proposed. It may be noted that to obtain the stagnation flow, we can continue the computations as far as possible and a steady solution is found with excellent accuracy.     

Unsteadiness of Flow Separation and End-Effects Regime in a Thrust-Optimized Contour Rocket Nozzle

Turbulent flow separation in over-expanded rocket nozzles is investigated experimentally in a sub-scale model nozzle fed with cold air and having a thrust-optimized contour. Depending upon the pressure ratio either a free shock separation (FSS) or a restricted shock separation (RSS) is observed with a significant hysteresis between these two flow regimes. It is shown that the RSS configuration may involve several separated regions. Analysis of wall pressure fluctuations give quantitative information on the fluctuating pressure field directly connected with the occurrence of significant side loads. Direct measurements of the evolution of the side loads with respect to the pressure ratio show the occurrence of three distinct peaks which are explained by the wall pressure fluctuations measurements.