Modeling Transient Pipe Flow in Plastic Pipes with Modified Discrete Bubble Cavitation Model

Most of today’s water supply systems are based on plastic pipes. They are characterized by the retarded strain (RS) that takes place in the walls of these pipes. The occurrence of RS increases energy losses and leads to a different form of the basic equations describing the transient pipe flow. In this paper, the RS is calculated with the use of convolution integral of the local derivative of pressure and creep function that describes the viscoelastic behavior of the pipe-wall material. The main equations of a discrete bubble cavity model (DBCM) are based on a momentum equation of two-phase vaporous cavitating flow and continuity equations written initially separately for the gas and liquid phase. In transient flows, another important source of pressure damping is skin friction. Accordingly, the wall shear stress model also required necessary modifications. The final partial derivative set of equations was solved with the use of the method of characteristics (MOC), which transforms the original set of partial differential equations (PDE) into a set of ordinary differential equations (ODE). The developed numerical solutions along with the appropriate boundary conditions formed a basis to write a computer program that was used in comparison analysis. The comparisons between computed and measured results showed that the novel modified DBCM predicts pressure and velocity waveforms including cavitation and retarded strain effects with an acceptable accuracy. It was noticed that the influence of unsteady friction on damping of pressure waves was much smaller than the influence of retarded strain.

Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction

We suggest a detachment criterion for a viscoelastic elastomer contact based on Griffith's idea about the energy balance at an infinitesimal advancement of the boundary of an adhesive crack. At the moment of detachment of a surface element at the boundary of an adhesive contact, there is some quick (instant) relaxation of stored elastic energy which can be expressed in terms of the creep function of the material. We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and thus it is only this part of energy relaxation that must be used in Griffith's energy balance. The described idea has several restrictions. Firstly, in this pure form, it is only valid for adhesive forces having an infinitely small range of action (which we call the JKR-limit). Secondly, it is only applicable to non-entropic (energetic) interfaces, which detach "at once" and do not possess their own kinetics of detachment.

CREEP OF A THICKWALLED QUASILINEAR VISCOELASTIC TUBE UNDER A CONSTANT EXTERNAL AND INTERNAL PRESSURE

We consider the creep problem for a quasilinear viscoelastic model of a thickwalled tube, loaded with constant internal and external pressure; the material is supposed to be incompressible. An exact solution to this problem was received by one of the authors in previous papers, assuming the state of a tube to be plain deformation; hereby we study properties of this solution for arbitrary material functions of quasilinear viscoelasticity constitutive relation. A criterion of stress stationarity is derived; the stress field of a thickwalled tube under a constant pressure evolves in time in the case of unbounded creep function and arbitrary nonlinearity function, except some particular types. The monotonicity of stress field components is studied: the radial stress monotonicity depends only on internal and external pressure values (for internal pressure, greater than an external one, it is negative and increases in radii). For other stress components, there are derived sufficient conditions of monotonicity. For an exponential nonlinearity function and unbounded creep function, a creep curve is determined to be concave up at the initial moment, and concave down during prolonged observation; the creep curve of a bipower nonlinearity function model may change its convexity. The stressstrain state of a model with a bounded creep function is proved to be bounded.

Analysis of Viscoelastic Behavior of Polypropylene/Carbon Nanotube Nanocomposites by Instrumented Indentation

In this work, the viscoelastic behavior of polypropylene (PP)/multi-walled carbon nanotube (MWCNT) nanocomposites was investigated by indentation testing and phenomenological modeling. Firstly, indentation tests including two-cycle indentation were carried out on PP/MWCNT nanocomposite with three MWCNT loadings (1, 3 and 5 wt %). Next, the Maxwell–Voigt–Kelvin model coupled with two-cycle indentation tests was used to predict the shear creep compliance function and the equivalent indentation modulus. The indentation hardness and elastic modulus of the PP/MWCNT nanocomposites extracted based on the Oliver and Pharr method were compared with the equivalent indentation modulus predicted based on the Maxwell–Voigt–Kelvin mode. The experimental results indicated that the addition of nanotubes into the polypropylene has a positive effect on the micro-mechanical properties of PP/MWCNT nanocomposites. Indentation hardness and elastic modulus increased significantly with increasing MWCNT loading. The creep resistance at the micro-scale of the PP/MWCNT nanocomposites improved with the addition of MWCNTs, with creep displacement reduced by up to 20% by increasing the carbon nanotube loading from 1 to 5 wt %. The Maxwell–Voigt–Kelvin model with three and five Voigt–Kelvin units accurately predicted the shear creep function and its change with increasing MWCNT loading. However, the equivalent indentation modulus was found to be sensitive to the number of Voigt–Kelvin units: the more Voigt–Kelvin units, the better the model predicts the equivalent indentation modulus.

On the thermodynamical restrictions in isothermal deformations of fractional Burgers model

We investigate, in the distributional setting, the restrictions on the constitutive equation for a fractional Burgers model of viscoelastic fluid that follow from the weak form of the entropy inequality under isothermal conditions. The results are generalized, from the Burgers model, to an arbitrary class of linear constitutive equations with fractional derivatives. Our results show that the restrictions obtained here on the coefficients of constitutive equations are weaker when compared with the restrictions obtained by Bagley–Torvik method. We show the precise relation between restrictions derived here and those derived by Bagley–Torvik. We deal with the creep test, for the case when Bagley–Torvik conditions are violated, and new conditions obtained in this work are satisfied. The results show a qualitative difference in the form of creep function. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

Rigorous Estimates for Effective Creep-coefficients of Microcracked Masonry Accounting for Cracks Interactions

Based on the association of finite elements homogenization method and a rigorous homogenization scheme accounting for crack interactions, this paper provides rigorous predictions for the local and effective properties of microcracked viscoelastic masonry with or without creep of bricks. For the sake of simplicity, viscoelastic brick and mortar are assumed to follow the Generalized Maxwell rheological model and to be respectively safe and microcracked. In the mortar, the distribution of microcracks orientations is assumed to be random. Two steps are followed. The first one is based on the identification at the short and long terms of an approximate analytical creep function for the mortar. This step relies on the coupling between the Griffith’s brittle fracture theory and a rigorous homogenization scheme - the Ponte Castañeda & Willis model - accounting for crack interaction instead of the dilute scheme adopted previously in Rekik et al. Two cases are considered: open and closed cracks. The first step allows to avoid recourse to 'heavy' numerical inversion of the Laplace-Carson transform. The second one provides overall creep coefficients of masonry by means of periodic homogenization carried out by finite elements method. For open cracks state, time-dependent crack density is investigated. The proposed model is validated by comparison with an analytical one available for a compressed masonry wall with "standard" viscoelastic mortar joints. Effect induced by microcracks is also highlighted by comparison with uncracked masonry. At last, results provided by the proposed model can be considered to be rigorous solution improving on dilute estimates for the creep behavior of microcracked mortar and demonstrating the interest to not neglect both cracks interactions and creep of bricks units.

Low-frequency seismic properties of olivine-orthopyroxene mixtures

<p>Although the seismic properties of polycrystalline olivine have been the subject of systematic and comprehensive study at seismic frequencies, the role of orthopyroxene as the major secondary phase in the shallow parts of the Earth’s upper mantle has so far received little attention. Accordingly, we have newly prepared synthetic melt-free polycrystalline specimens containing different proportions of olivine (Ol, Fo<sub>90</sub>) and orthopyroxene (Opx, En<sub>90</sub>) by the solution-gelation method. The resulting specimens, ranging in composition between Ol<sub>95</sub>Opx<sub>5</sub> and Ol<sub>5</sub>Opx<sub>95</sub> composition, were mechanically tested by torsional forced oscillation at temperatures of 1200 ºC to 400 ºC accessed during staged cooling under a confining pressure of 200 MPa. The microstructures of tested specimens were evaluated by BSE, EBSD and TEM. The forced-oscillation data, i.e. shear modulus and associated strain-energy dissipation at 1-1000 s period, were closely fitted by a model based on an extended Burgers-type creep function. This model was also required to fit data from previous ultrasonic and Brillouin spectroscopic measurements at ns-µs periods. Within the observational window (1-1000 s), the shear modulus and dissipation vary monotonically with period and temperature for each of the tested specimens, which is broadly comparable with that previously reported for olivine-only samples. There is no evidence of the superimposed dissipation peak reported by Sundberg and Cooper (2010) for an Ol<sub>60</sub>Opx<sub>40</sub> specimen prepared from natural precursor materials and containing a melt fraction of 1.5%. The higher orthopyroxene concentrations are associated with systematically somewhat lower levels of dissipation and corresponding weaker modulus dispersion. The new findings suggest that the olivine-based model for high-temperature viscoelasticity in upper-mantle olivine requires only modest modification to accommodate the role of orthopyroxene, including appropriate compositional dependence of the unrelaxed modulus and its temperature derivative.</p>

Viscoelastic Behaviour from Complementary Forced-Oscillation and Microcreep Tests

There is an important complementarity between experimental methods for the study of high-temperature viscoelasticity in the time and frequency domains that has not always been fully exploited. Here, we show that the parallel processing of forced-oscillation data and microcreep records, involving the consistent use of either Andrade or extended Burgers creep function models, yields a robust composite modulus-dissipation dataset spanning a broader range of periods than either technique alone. In fitting this dataset, the alternative Andrade and extended Burgers models differ in their partitioning of strain between the anelastic and viscous contributions. The extended Burgers model is preferred because it involves a finite range of anelastic relaxation times and, accordingly, a well-defined anelastic relaxation strength. The new strategy offers the prospect of better constraining the transition between transient and steady-state creep or, equivalently, between anelastic and viscous behaviour.

Developing viscoelastic contact models and selecting suitable creep function for spherical biological cells

In most contact theories, the most popular of which are the three models of Hertz, Derjaguin, Muller and Toporov (DMT) and Johnson, Kendall and Roberts (JKR), biological cells were considered as an elastic material which is not a proper assumption. The elastic assumption in the case of biological cells could lead to neglecting the loading history as a result of which the stresses and strains applied to the material would not be studied accurately. In this paper, developing the three mentioned elastic models into viscoelastic models, simulating and comparing them with empirical data obtained through the indentation test of the MCF-7 cancer cell showed that the viscoelastic state presents a better prediction of biological cell behavior compared to that of an elastic state. The selection of the suitable creep function for objects in contact is another issue that has a significant importance in the viscoelastic case and this was investigated. Different mechanical models of a cell were studied and simulated for all three named theories among which the creep function obtained from the Kelvin model, a parallel combination of spring-damper, simplified the simulation and gave more precise results for modeling due to the fact that the obtained results from this model are closer to experimental ones and simpler than other models. On the other hand, for a more exact prediction of cell behavior, this model was modified by an equivalent elasticity module which considered cell components instead of the cell cortex only. The results of the simulation confirmed that a new elasticity module can improve the accuracy of cell models. After choosing the suitable mechanical model for the cell, we scrutinized the capability of the developed theories in predicting the results for biological liquid environments. Although the results of the Hertz and DMT viscoelastic models are closer to experimental ones in comparison with viscoelastic JKR, neglecting adhesion makes their prediction in biological liquid environments weak and erroneous. Therefore, it can be concluded that the developed viscoelastic model of JKR is more accurate and has a better performance in different environments than the other mentioned models.