Application of nonlinear continuum dislocation theory to antiplane shear

We apply the nonlinear dislocation theory to the problem of antiplane constrained shear in a single crystal with one slip system. By taking dissipation into account, the relaxed energy functional has to be minimized. We show that, up to a threshold strain, no dislocations are nucleated and therefore the plastic slip is zero. Since this threshold value depends on the width of the specimen, a size effect takes place. The stress strain curve turns out to be a hysteresis loop exhibiting the work hardening due to the dislocation pile-up. It is shown that the Bauschinger effect holds true. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces

In this paper, we introduce and study some low computational cost numerical methods for finding a solution of a variational inequality problem over the solution set of an equilibrium problem in a real Hilbert space. The strong convergence of the iterative sequences generated by the proposed algorithms is obtained by combining viscosity-type approximations with projected subgradient techniques. First a general scheme is proposed, and afterwards two practical realizations of it are studied depending on the characteristics of the feasible set. When this set is described by convex inequalities, the projections onto the feasible set are replaced by projections onto half-spaces with the consequence that most iterates are outside the feasible domain. On the other hand, when the projections onto the feasible set can be easily computed, the method generates feasible points and can be considered as a generalization of Maingé’s method to equilibrium problem constraints. In both cases, the strong convergence of the sequences generated by the proposed algorithms is proven.     

Generic Stability and Essential Components of Generalized KKM Points and Applications

We propose the definition of T-KKM points and consider generic stability of T-KKM mappings and essential components of sets of T-KKM points. As applications, using a unified approach, we derive from these results the existence of essential components of solution sets to various optimization-related problems. We do this in two steps. First, we deduce the corresponding results for variational inclusions, which are new. Then we obtain, as consequences, the existence of essential components of solutions to other problems, which are new or include recent ones in the literature.     

Temperature-responsive self-assembly of charged and uncharged hydroxyethylcellulose-<Emphasis Type="Italic">graft</Emphasis>-poly(<Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide) copolymer in aqueous solution

Temperature-induced interchain association and contraction of species in aqueous solutions of charged (MHEC(−)-g-PNIPAAM) and uncharged (MHEC-g-PNIPAAM) modified hydroxyethylcellulose-graft-poly(N-isopropylacrylamide) copolymer have been studied with the aid of turbidimetry and dynamic light scattering (DLS). It was shown that by attaching PNIPAAM chains to the backbone of a hydrophilic cellulose derivative, a strongly temperature-responsive copolymer could be prepared. The results show an intriguing interplay between interchain association and contraction of the multichain species. The transition zone for compression is narrow, and the compaction effect is promoted by a low polymer concentration and charges on the polymer moieties. The findings from DLS revealed two populations of species, namely molecularly dispersed molecules or small clusters and interchain complexes, which exhibit temperature-induced collapse. The magnitude of the cluster contraction can be modulated by changing the polymer concentration and charge density of the copolymer.     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

Boundary contour analysis for surface stress recovery in 2-D elasticity and Stokes flow

Summary A variant of the boundary element method, called the boundary contour method, offers a further reduction in dimensionality. Consequently, boundary contour analysis of 2-D problems does not require any numerical integration at all. In a boundary contour analysis, boundary stresses can be accurately computed using the approach proposed in Ref. [1]. However, due to singularity, this approach can be used only to calculate boundary stresses at points that do not lie at an end of a boundary element. Herein, it is shown that a technique based on the displacement/velocity shape functions can overcome this drawback. Further, the approach is much simpler to apply, requires less computational effort, and provides competitive accuracy. Numerical solutions and convergence study for some well-known problems in linear elasticity and Stokes flow are presented to show the effectiveness of the proposed approach. This research was supported in part by the 2004 Ralph E. Powe Junior Faculty Enhancement Award from Oak Ridge Associated Universities and by the University of South Alabama Research Council.     

Boundary element simulations of spheres settling in circular,square and triangular conduits

Numerical simulations of a spherical particle sedimenting in circular, triangular and square conduits containing a viscous, inertialess, Newtonian fluid were investigated using the Boundary Element Method (BEM). Settling velocities and pressure drops for spheres falling along the centre-lines of the conduits were computed for a definitive range of sphere sizes. The numerical simulations for the settling velocities showed good agreement with existing experimental data. The most accurate analytic solution for a sphere settling along the axis of a circular conduit produced results which were almost indistinguishable from the present BEM calculations. For a sphere falling along the centre-line of a square conduit, the BEM calculations for small spheres agreed well with analytic results. No analytic results for a sphere falling along the axis of a triangular conduit were available for comparison. Extrapolation of the BEM predictions for the pressure drops, to infinitely small spheres, showed remarkable agreement with analytic results. For the circular conduit, the sphere's settling velocity and angular velocity were computed as a function of drop position for small, medium and large spheres. Excellent agreement with a reflection solution was achieved for the small sphere. In addition, end effects were investigated for centre-line drops and compared where possible with available experimental data and analytic results.Los Alamos National Laboratory, Los Alamos, New Mexico, USA.     

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).