Plastic spin: necessity or redundancy?

The plastic spin concept in large deformation anisotropic elastoplasticity theories with tensorial internal variables, is proved to be a necessary constitutive ingredient. Different inaccurate notions about the plastic spin are dispelled, and its presence in the theory is demystified as something very simple and straightforward. To this extent it is necessary to disassociate the plastic spin concept and the conjugate notion of constitutive spin from the foundation of kinematics, which caused confusion in the past, and define it only in relation to the constitutive equations of evolution of the tensorial internal variables. There, the plastic spin is related to the orientation aspect of such constitutive equations, and the multiplicity of the different internal variables suggests the necessity to have a different spin for each variable. In the process, a straightforward constitutive framework is developed which is based on classical hyperelasticity, yield criteria and invariance requirements of the constitutive functions under superposed rigid body rotation. Ad-hoc assumptions about stress corotational or convected rates and other fuzzy suggestions for different spins are not part of this development. Other topics such as the concept and simplifying effect of the spinless unstressed configuration and its comparison with the isoclinic configuration, some computational aspects, and the effect of small elastic strains are discussed, and all along the significance of plastic spin in the different equations is evaluated.     

Genetic counseling for the public?

The widespread availability of diagnostic tools for numerous inherited diseases requires diligent decision-making regarding the risks and benefits, not only for the individual but also at the population level. Should therefore genetic counseling be offered to the entire population at risk for genetic diseases? In our opinion, the goals of public health may only be reached by serving primarily the individual at risk and his/her family. Efforts in public health genetics should be focused on appropriate genetic counseling, especially regarding common diseases with complex genetic components in the near future.     

Polymeric liquids in extension: fluid mechanics or rheometry?

We use a transient 3D free surface finite element method to simulate flow of entangled polymer fluids in the dual cylinder wind-up extensional rheometer. The constitutive equations are K-BKZ integral representations of the Doi–Edwards models with and without the independent alignment approximation (IA). It is demonstrated that the actual kinematics in this rheometer is a mixture of planar and uniaxial extension. Moreover, the ratio of planar to uniaxial deformation is highly dependent upon whether IA is invoked. Without IA, the flow has a tendency toward planar extension, while it tends to be more uniaxial with IA invoked. As a second illustration of the techniques, we simulate the phenomenon of delayed rupture after rapid extension of entangled polymer systems. It is demonstrated that this phenomenon can be explained on the basis of the Doi–Edwards model in terms of a Considere-type instability after chain stretch relaxation.     

Fourier-BEM: or What To Do if No Fundamental Solution is Available?

The application of boundary element methods (BEM) to soil-structure interaction problems is still restricted to cases where fundamental solutions are known. Hence, a large number of engineering problems cannot be solved by the BEM. Therefore, an alternative approach is presented here which establishes new boundary integral equations (BIEs) for the computation of the entries of the BEM matrices by means of the spatial Fourier transform.For these alternative BIEs, we need only the transform of the fundamental solution and not the fundamental solution itself. The former is always available as long as the underlying differential operator is linear and has constant coefficients. The approach is possible for all variants of the BEM. For Galerkin approaches, the double integrations over the boundary panels are replaced by single integrations over the infinite domain.     

Slow flows of yield stress fluids: yielding liquids or flowing solids?

Yield stress fluids (YSF) exhibit strongly non-linear rheological characteristics. As a consequence, they develop original flow features (as compared to simple fluids) under various boundary conditions. This paper reviews and analyzes the characteristics of a series of slow flows (just beyond yielding) under more or less complex conditions (simple shear flow, flow through a cavity, dip-coating, blade-coating, Rayleigh-Taylor instability, Saffman-Taylor instability) and highlights some of their common original characteristics: (i) a transition from a solid regime to a flowing regime which does not correspond to a true “liquid state,” the flow in this regime may rather be seen as a succession of solid states during very large deformation; (ii) a strong tendency to localization of the yielded regions in some small region of the material while the rest of the material undergoes some deformation in its solid state; (iii) the deformation of YSF interface with another fluid, in the form of fingers tending to penetrate the material via a local liquefaction process. Finally, these observations suggest that slow flows of YSF are a kind of extension of plastic flows for very large deformations and without irreversible changes of the structure. This suggests that the field of plasticity and the field of slow flows of YSF could benefit from each other.     

A non-smooth-contact-dynamics analysis of Brunelleschi’s cupola: an octagonal vault or a circular dome?

Meccanica - The cupola (dome) of Santa Maria del Fiore in Florence was ingeniously constructed by Brunelleschi using a conical bricklaying, radial-oriented toward a focus point on the central axis....     

Collective sustained oscillations in excitable small-world networks: the moderate fundamental loop or the minimum Winfree loop?

Nonlinear Dynamics - The problem of self-sustained oscillations in excitable complex networks is the central issue under investigation, among which the exploration of the key factors in determining...     

On the Optimal Pattern for Displacement Field Measurement: Random Speckle and DIC,or Checkerboard and LSA?

Experimental Mechanics - This paper deals with the optimal pattern that can be used to retrieve displacement fields by minimizing the optical residual calculated over small regions of contrasted...     

On the detachment of step-tapered doublers: Part 2—evolution of pressure loaded structures

One-dimensional edge debonding of layerwise step-tapered patches from both flat and cylindrical structures subjected to applied pressure is studied in the context of the general formulation presented in Part 1. Numerical simulations based on analytical solutions of the problems of interest are performed and intricate results presented in the form of threshold curves/delamination paths for various taper angles and support conditions. Configurations corresponding to full contact of the debonded segments, edge contact of the debonded segments and no contact of the debonded segments of the evolving composite structure are included in the model and found to significantly affect the predicted behavior of the debonding structure as does the manner of support. The degree of taper is generally found to influence the onset and characteristics of debonding in a nontrivial manner. It is seen that in many instances, the introduction of edge taper within a wide range of angles often enhances the structures propensity for debonding, rather than diminishing it, both with regard to the critical load level and with regard to the stability and extent of debond propagation.     

Hydromagnetic stagnation point flow of a viscous fluid over?a?stretching or shrinking sheet

We establish the existence and uniqueness results over the semi-infinite interval [0,∞) for a class of nonlinear third order ordinary differential equations of the form

Microstructural effects on yield surface evolution in cubic metals using the viscoplastic ?-model

Polycrystalline yield surfaces of metals are a good way to characterize the anisotropy of plastic deformation. The evolution of these surfaces is impossible to accurately reproduce without taking into account the evolution of the material microstructure such as texture development. In this paper, a numerical computation of yield surfaces using the viscoplastic ?-model is proposed. Results concerning face-centered cubic metals subjected to a plane strain compression test are presented. The influence of several mechanical parameters (strain hardening, strain rate sensitivity coefficient and accumulated deformation) on subsequent yield surfaces evolution is studied. The analysis of the change in the shape and size of the yield surfaces shows that the results depend strongly on the parameter ? which controls the strength of the interactions in the polycrystal. In addition, the predictions are compared to the widely used viscoplastic self-consistent model as well as to experimental yield loci taken from the literature for various aluminum alloy sheets. A fairly good qualitative agreement between our ?-model results and the experimental ones is found. The probable links between the parameter ? and the microstructural features such as the stacking fault energy and the grain size of the polycrystal are also briefly discussed.     

Strength or toughness? A criterion for crack onset at a notch

Both energy and stress criteria are necessary conditions for fracture but neither one nor the other are sufficient. Experiments by Parvizi et al. on transverse cracking in cross-ply laminates corroborate this assumption. Thanks to the singularity at the tip of the notch, the incremental form of the energy criterion gives a lower bound of admissible crack lengths. On the contrary, the stress criterion leads to an upper bound. The consistency between these two conditions provides a general form of a criterion for crack nucleation. It enjoys the desirable property of coinciding with the usual Griffith criterion to study the crack growth and with the stress criterion for the uniform traction along a straight edge. Comparisons with experiments carried out on homogeneous notched materials and on bimaterial structures show a good agreement.     

Adiabatic shear localization in α-titanium: experiments, modeling and microstructural evolution

The localization of dynamic shearing deformations in α-titanium is examined using a novel experimental technique (the compression-torsion Kolsky bar) that allows the recovery of specimens within which an adiabatic shear band has been grown as the result of a single torsional pulse. The specimens are circumferentially notched thick-walled cylinders that are subjected to simultaneous, independently controlled, dynamic compression and torsion. Explicit finite element computations are performed to obtain the stress, strain, temperature and pressure distributions within the specimens under the measured boundary conditions. The constitutive behavior input to the computational simulations is obtained from independent high-strain-rate experiments (involving only homogeneous deformations) on the same material. Shear band growth and microstructural evolution in the specimens are investigated by sectioning the specimens at different depths from the outer radial surface. TEM observations across the shear bands reveal the following microstructural evolution: (a) planar dislocation motion and twinning; (b) grouping of dislocations into cells; (c) formation of elongated subgrains along the shear direction, and (d) development of equiaxed nanocrystalline grains 50- in diameter. The microstructures observed are analogous to those reported for severely cold-rolled metals.     

Does N 1 or N 2 control the onset of edge fracture?

The edge fracture instability which occurs at the air/liquid interface in a cone-and-plate rheometer is studied for six elastic polymer solutions. Theoretical models for the onset of edge fracture are evaluated in light of the experimental data. The data are well-described by the Tanner-Keentok model, which predicts that fracture will occur whenever a critical value of the second normal stress difference is exceeded in magnitude.     

Tsallis entropy: how unique?

It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability, and the axiomatic foundations.Received: 6 May 2003, Accepted: 7 July 2003, Published online: 9 December 2003PACS: 05.20.-y, 05.70.-a, 05.90. + m, 65.40.Gr