Crack tip fields in a viscoplastic solid: monotonic and cyclic loading

The asymptotic stress and strain field near the tip of a plane strain Mode I stationary crack in a viscoplastic material are investigated in this work, using a unified viscoplastic model based on Chaboche (Int J Plast 5(3):247–302, 1989). Asymptotic analysis shows that the near tip stress field is governed by the Hutchinson–Rice–Rosengren (HRR) field (Hutchinson in J Mech Phys Solids 16(1):13–31, 1968; Rice and Rosengren in J Mech Phys Solids 16(1):1–12, 1968) with a time dependent amplitude that depends on the loading history. Finite element analysis is carried out for a single edge crack specimen subjected to a constant applied load and a simple class of cyclic loading history. The focus is on small scale creep where the region of inelasticity is small in comparison with typical specimen dimensions. For the case of constant load, the amplitude of the HRR field is found to vanish at long times and the elastic K field dominates. For the case of cyclic loading, we study the effect of stress ratio on inelastic strain and find that the strain accumulated per cycle decreases with stress ratio.     

Optimal pairing computation over families of pairing-friendly elliptic curves

Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log₂ r)/φ(k) + log₂ k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455–461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224–280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224–280, 2010) by taking the Ate or R-ate pairing approach.     

Sustainability metrics for eco-technologies assessment, part I: preliminary screening

This work presents a preliminary screening of eco-technologies for dimethyl carbonate (DMC) production. Through sustainability metrics, the assessment of six different chemical routes allows comparisons according to economical and environmental criteria, to determine the most sustainable route. CO₂ sequestration potential is also considered. The alternatives are scored according to the adopted metrics, leading to the decision of a suitable route based on economic and environmental grounds, prioritizing pollution-preventing technologies herein referred to as eco-technologies. Casting of technologies was based on alternatives available in the literature: Route 1 production of DMC from methanol and phosgene [Ono in Pure Appl Chem 68(2):367–375, 1996]; Route 2 production of DMC from methyl nitrite and CO [Ono in Pure Appl Chem 68(2):367–375, 1996]; Route 3 production of DMC from CO and methanol [Ono in Pure Appl Chem 68(2):367–375, 1996]; Route 4 production of DMC from urea and methanol (Wang et al. in Ind Eng Chem Res 46:8972–8979, 2007); Route 5 production of DMC from ethylene oxide and CO₂ [Ono in Pure Appl Chem 68(2):367–375, 1996]; Route 6 production of DMC from CO₂ and methanol (Choi et al. in Green Chem 4:230–234, 2002). The analysis shows that Routes 4 and 5 combine intermediate values of the total (sustainability) score, CO₂ sequestration potential and industrial feasibility, therefore entitled as eco-technologies, based on the adopted metrics. Although the two technologies are potentially ecological, they are recommended for a more rigorous analysis on the grounds of process simulation and life cycle analysis.     

A comment to the paper by Waltman et al., Scientometrics, 87, 467–481, 2011

In reaction to a previous critique (Opthof and Leydesdorff, J Informetr 4(3):423–430, 2010), the Center for Science and Technology Studies (CWTS) in Leiden proposed to change their old “crown” indicator in citation analysis into a new one. Waltman (Scientometrics 87:467–481, 2011a) argue that this change does not affect rankings at various aggregated levels. However, CWTS data is not publicly available for testing and criticism. Therefore, we comment by using previously published data of Van Raan (Scientometrics 67(3):491–502, 2006) to address the pivotal issue of how the results of citation analysis correlate with the results of peer review. A quality parameter based on peer review was neither significantly correlated with the two parameters developed by the CWTS in the past citations per paper/mean journal citation score (CPP/JCSm) or CPP/FCSm (citations per paper/mean field citation score) nor with the more recently proposed h-index (Hirsch, Proc Natl Acad Sci USA 102(46):16569–16572, 2005). Given the high correlations between the old and new “crown” indicators, one can expect that the lack of correlation with the peer-review based quality indicator applies equally to the newly developed ones.     

Another generalization of the geometric distribution

A new generalization of the geometric distribution with parameters α>0 and 0<θ<1 is obtained in this paper. This can be done either by using the Marshall and Olkin (Biometrika 84(3), 641–652, 1997) scheme and adding a parameter to the geometric distribution or by starting with the generalized exponential distribution in Marshall and Olkin (Biometrika 84(3), 641–652, 1997) and discretizing this continuous distribution. The particular case α=1 led us to the geometric distribution. After reviewing some of its properties, we investigated the question of parameter estimation. The new distribution is unimodal with a failure rate that is monotonically increasing or decreasing, depending on the value of the parameter α. Expected frequencies were calculated for two overdispersed and infradispersed examples, and the distribution was found to provide a very satisfactory fit.     

Magnetic Interaction Force and a Couple on a Superconducting Sphere in an Arbitrary Dipole Field

The calculation of the magnetostatic potential and levitation force due to a point magnetic dipole placed in front of a superconducting sphere in the Meissner state is readdressed. Closed-form analytical expression for the scalar potential function that yields the image system for an arbitrarily oriented magnetic dipole located in the vicinity of a superconducting sphere is given. Analytic expression for the lifting or levitation force acting on the sphere is extracted from the solution for a general dipole. A special case of our expression where the initial magnetic dipole makes an angle with the z-axis is derived. Our expression for the force in this particular case shows that a recently obtained result (J. Supercond. Nov. Magn. 21:93–96, 2008) for an arbitrary dipole is incorrect. A brief discussion of another erroneous result (J. Supercond. Nov. Magn. 15:257–262, 2002) for a transverse/tangential dipole–sphere configuration, corrected elsewhere recently, is reproduced. Correct expressions for the interaction energy with some limiting cases are also provided. The result derived here demonstrates that the value of the levitation force for a dipole that makes an angle with z-axis lies between the values for a radial dipole–sphere and transverse dipole–sphere configurations providing upper and lower bounds. It is found that for a magnetic dipole making an angle with z-axis, there exits a second force component along the negative y-direction, which influences a couple acting on the superconducting sphere. It is also shown that the couple is proportional to the second force component and that both the couple and second force components vanish for a radial dipole–sphere and transverse dipole–sphere configurations, respectively. These results appear to be new and have not had received due attention in the context of superconductivity.     

Micromechanics-based viscoelastic damage model for particle-reinforced polymeric composites

The objective of this study is to develop a micromechanics-based viscoelastic damage model that can predict the overall viscoelastic behavior of particle-reinforced polymeric composites undergoing damage. The emphasis here is that the present model successfully combines a rate-dependent viscoelastic constitutive model and a damage model. The Laplace transform based on the Boltzmann superposition principle and the ensemble-volume averaged method suggested by Ju and Chen (Acta Mech 103:103–121, 1994a; Acta Mech 103:123–144, 1994b) are extended toward effective viscoelastic properties. Further, the probability of the distribution function of Weibull (J Appl Mech 18:293–297, 1951) is adopted to describe a damage model that is dependent on damage parameters. A series of numerical simulations including parametric studies, and experimental comparisons are carried out to give insight into the potential capacity of the present micromechanics-based viscoelastic damage framework.     

Effect of Uniaxial Pressure on the Isotope Effect on the Spectrum of Hamiltonians with Electron–Phonon Coupling

We have studied the effect of a change in the equilibrium nearest neighbour distances on the dynamics of charge and ions on a three-site cluster, identified with an O–Cu–O cluster present in high temperature superconductors. We consider a model Hamiltonian that contains an electronic part represented by a single band Hubbard model with onsite electronic correlations and a phononic part consisting of non-interacting Raman and infrared active phonons. The electron–phonon coupling is introduced through the change in interatomic distances generated by Coulomb repulsion between charges at neighbouring sites. For intermediate and strong values of the electron–phonon coupling, this model generates correlated electron–ion motion, i.e., polaron formation. In order to simulate the effect of change in the equilibrium nearest neighbour distances, we assume that the main effect such a change is a variation of the intersite electron hopping probability, t. We, therefore, studied the excitation spectrum of this model and the local lattice distortion in the Cu–O bond length as a function of t. We also studied the effect of a change in t in the polaron tunnelling energy when we use different oxygen isotopic masses, i.e., O¹⁶ and O¹⁸. We find that as function of t, the isotopic shift does not show a monotonic behaviour, as it does as a function of the electron–phonon coupling constant. It exhibits a minimum for values of t for which the electron–phonon coupling generates local lattice distortions with magnitudes similar to those observed experimentally in high-temperature superconductors. This observation could be related with the observed maximum on T _c as a function of the microstrain of the Cu–O bonds (Sanna et al. in Int. J. Mod. Phys. B 14(29–31), 2000; Bianconi et al. in J. Phys.: Condens. Matter 12:10655, 2000; Agrestini et al. in J. Phys. A: Math. Gen. 36:9133, 2003).     

Stability analysis of undrained adiabatic shearing of a rock layer with Cosserat microstructure

Stability of undrained shearing in a classical Cauchy continuum has been first analyzed by Rice (J Geophys Res 80(11):1531–1536, 1975) who showed that instability occurs when the underlying drained deformation becomes unstable (i.e. in the softening regime of the corresponding drained stress-strain curve). However Vardoulakis (Int J Numer Anal Methods Geomech 9:339–414, 1985; Int J Numer Anal Methods Geomech 10:177–190, 1986) has shown that Rice’s linear stability analysis, if performed at the state of maximum deviator, leads to a sharp transition from infinitely stable to infinitely unstable behaviour, which indicates that the solution of the considered initial-value problem does not exist and consequently that the corresponding problem is mathematically ill-posed. Vardoulakis (Géotechnique 46(3):441–456, 1996; Géotechnique 46(3):457–472, 1996) proposed a regularization of the ill-posed problem in the softening regime by resorting to a second grade extension of plasticity theory. In this paper, the kinetics of a granular material is described by a Cosserat continuum as first suggested by Mühlhaus and Vardoulakis (Géotechnique 37:271–283, 1987) and we incorporate the effect of shear heating due to the dissipation of the frictional work. The undrained adiabatic limit is applicable as soon as the slip event is sufficiently rapid and the shear zone broad enough to effectively preclude heat or fluid transfer as it is the case during an earthquake or a landslide. It is shown that shear heating has a destabilizing effect and that instability can occur in the hardening regime if the amount of dilatant strengthening is not sufficient as compared to the effect of thermal pressurization of the pore fluid. It is shown that the linear stability analysis with macro and micro inertia terms leads to the selection of a preferred wave length of the instability mode corresponding to the instability mode with fastest (but finite) growth coefficient.     

A time-discrete model for dynamic fracture based on crack regularization

We propose a discrete time model for dynamic fracture based on crack regularization. The advantages of our approach are threefold: first, our regularization of the crack set has been rigorously shown to converge to the correct sharp-interface energy Ambrosio and Tortorelli (Comm. Pure Appl. Math., 43(8): 999–1036 (1990); Boll. Un. Mat. Ital. B (7), 6(1):105–123, 1992); second, our condition for crack growth, based on Griffith’s criterion, matches that of quasi-static settings Bourdin (Interfaces Free Bound 9(3): 411–430, 2007) where Griffith originally stated his criterion; third, solutions to our model converge, as the time-step tends to zero, to solutions of the correct continuous time model Larsen (Math Models Methods Appl Sci 20:1021–1048, 2010). Furthermore, in implementing this model, we naturally recover several features, such as the elastic wave speed as an upper bound on crack speed, and crack branching for sufficiently rapid boundary displacements. We conclude by comparing our approach to so-called “phase-field” ones. In particular, we explain why phase-field approaches are good for approximating free boundaries, but not the free discontinuity sets that model fracture.     

The secondary splitting of zero-gradient points in a scalar field

The mechanisms related to the secondary splitting of zero-gradient points of scalar fields are analyzed using the two-dimensional case of a scalar extreme point lying in a region of local strain. The velocity field is assumed to resemble a stagnation-point flow, cf. Gibson (Phys Fluids 11:2305–2315, 1968), which is approximated using a Taylor expansion up to third order. The temporal evolution of the scalar field in the vicinity of the stagnation point is derived using a series expansion, and it is found that the splitting can only be explained when the third-order terms of the Taylor expansion of the flow field are included. The non-dimensional splitting time turns out to depend on three parameters, namely the local Péclet number Pe _δ based on the initial size of the extreme point δ and two parameters which are measures of the rate of change of the local strain. For the limiting casePe _δ → 0, the splitting time is found to be finite but Péclet-number independent, while for the case of Pe _δ → ∞ it increases logarithmically with the Péclet number. The physical implications of the two-dimensional mathematical solution are discussed and compared with the splitting times obtained numerically from a Taylor–Green vortex.     

On the age-independent publication index

It is shown that the age-independent index based on h-type index per decade, called hereafter an α index instead of the a index, suggested by Kosmulski (Journal of Informetrics 3, 341–347, 2009) and Abt (Scientometrics 2012) is related to the square-root of the ratio of citation acceleration a to the Hirsch constant A.     

Dynamical theoretical model and variational principles for coupled temperature–diffusion–mechanics

In this paper, firstly, the acceleration of the temperature and concentration are assumed to need the extra increment of the heat and energy. The inertial entropy and the inertial chemical potential were proposed by Kuang (Acta Mech 203:1–11, 2009, Acta Mech 214:275–289, 2010). Secondly, the expressions of dissipative energy produced by the variation of the temperature and concentration are derived by using the second law of thermodynamics. Finally, several variational principles for coupled temperature–diffusion–mechanics are established, and their corresponding governing equations and boundary conditions are naturally presented. Meanwhile, some numerical simulations are carried out to describe the coupled reciprocity, which shows concentration diffusion with a finite velocity.     

The development of forced convection heat transfer near a forward stagnation point with Newtonian heating

A mathematical model for the unsteady forced convection boundary-layer flow near a forward stagnation point is considered when there is Newtonian heating on the surface whereby the heat transfer is proportional to the local surface temperature. In a previous paper (Salleh et al. J Eng Math 69:101–110, 2011), a critical value γ _c, dependent on the Prandtl number σ, of the heat transfer coefficient γ was identified, with solutions for the corresponding steady problem possible only for γ < γ _c. The unsteady problem considered here shows that these steady states are attained at large times when γ < γ _c. For γ > γ _c, the solution still continues to large time, now growing exponentially with time. This rate of growth is determined by an eigenvalue problem which we solve numerically for general values of γ and σ and asymptotically for large γ and both large and small σ.     

On Comparison of Experiment and Theory for Ultrasonic Attenuation in Polycrystalline Niobium

In this communication comparison of experimental attenuation results in polycrystalline niobium (Zeng et al., J. Nondestruct. Eval. 29:93–103, 2010) with scattering-induced attenuation models is reexamined. Reasonable agreement is found between those results and the standard Stanke and Kino model (in J. Acoust. Soc. Am. 75:665–681, 1984) contradicting the conclusions of Zeng et al.     

Influence diagnostics in a general class of beta regression models

In this article, we consider the issue of assessing influence of observations in the general class of beta regression models introduced by Simas et al. (Comput. Stat. Data Anal. 54:348–366, 2010), which is very useful in situations in which the response is restricted to the standard unit interval (0,1). Our results generalize those in Espinheira et al. (Comput. Stat. Data Anal. 52:4417–4431, 2008a; J. Appl. Stat. 35:407–419, 2008b), which only apply to linear beta regression models. We define some residuals, and a Portmanteau test for serial correlation. Further, some influence methods, such as the global, local, and total local influence of an individual and generalized leverage, are discussed. Moreover, we also derive the normal curvatures of local influence under various perturbation schemes. Finally, simulation results and an application to real data show the usefulness of our results.     

High density polyethylene (HDPE): Experiments and modeling

The uniaxial tension (loading and unloading), creep and relaxation experiments on high density polyethylene (HDPE) have been carried out at room temperature. The stress–strain behavior of HDPE under different strain rates, creep (relaxation) behavior at different stress (strain) levels have been investigated. These experimental results are used to compare the simulation results of a unified state variable theory, viscoplasticity theory based on overstress (VBO) and a macro-mechanical constitutive model for elasto-viscoplastic deformation of polymeric materials developed by Boyce et al. (Polymer 41:2183–2201, 2000). It is observed that elasto-viscoplasticity model by Boyce et al. (Polymer 41:2183–2201, 2000) is not good enough to simulate stress–strain, creep and relaxation behaviors of HDPE. However, the aforementioned behaviors can be modeled quantitatively by using VBO model.     

On the analogy between the evolution of thermodynamic and bibliometric systems: a breakthrough or just a bubble?

This paper presents an in depth study of an interesting analogy, recently proposed by Prathap (Scientometrics 87(3):515–524, 2011a), between the evolution of thermodynamic and bibliometric systems. The goal is to highlight some weaknesses and clarify some “dark sides” in the conceptual framework of this analogy, discussing the formal validity and practical meaning of the concepts of Energy, Exergy and Entropy in bibliometrics. Specifically, this analogy highlights the following major criticalities: (1) the definitions of E and X are controversial, (2) the equivalence classes of E and X are questionable, (3) the parallel between the evolution of thermodynamic and bibliometric systems is forced, (4) X is a non-monotonic performance indicator, and (5) in bibliometrics the condition of “thermodynamic perfection” is questionable. Argument is supported by many analytical demonstrations and practical examples.     

Role of Coexistence of Superconductivity and Paramagnetism in Magnetostriction of High-T c Superconductors

Total magnetostriction in the superconducting state for high T _c superconductors has been separated into critical state and paramagnetic components in terms of a H(x) dependent magnetic flux density. We show that the paramagnetic part is χ(2+χ)〈H(x)²〉, where χ is paramagnetic susceptibility. We have reproduced successfully ΔL/L−H _a curves measured by de la Fuente et al. (Phys. C 244:214, [1995]), in which they clearly observed coexistence of superconductivity and paramagnetism, employing the concepts presented in this work.