[en] An electrically permeable elliptical nano-hole or nano-crack embedded in an infinite piezoelectric material with surface effect is investigated based on the Gurtin–Murdoch surface/interface model, which is subjected to far-field anti-plane mechanical and in-plane electrical loads. The electric field inside the elliptical nano-hole has been taken into consideration, and exact electroelastic fields near the elliptical nano-hole are obtained by using the technique of conformal mapping. The size-dependent stress and electric displacement intensity factors at the crack tip are derived exactly for both electrically permeable and impermeable boundary conditions when the elliptical nano-hole reduces to the nano-crack. Numerical examples are illustrated to show the surface effects on the stress and electric displacement intensity factors of electrically permeable and impermeable cracks, and on the stress and electric field concentrations around the electrically permeable and impermeable holes. The results indicate that the size dependence of an electrically permeable nano-hole or nano-crack is entirely different from that of the electrically impermeable case.

[en] The aim of this study is to gain a detailed understanding of the behavior of a liquid drop in AC electric fields at finite Reynolds number. A front-tracking/finite difference method, in conjunction with Taylor–Melcher leaky dielectric model, is used to solve the governing electrohydrodynamic equations. The evolution of the flow field and the drop deformation are studied for three representative fluid systems, corresponding to the three regions of the deformation–circulation map. It is shown that for the range of the physical parameters used here, the relaxation time during which the drop settles to its quasi-steady-state deformation is essentially the same as that predicted by the creeping flow solution. Furthermore, the mean (time-independent) deformation is well represented by its steady-state deformation in the corresponding DC field in a root-mean-square sense. The evolution of the flow field shows formation of closed vortices that cross the drop surface and move toward the ambient fluid or the drop, in line with the motion of the drop surface. The evolution of the kinetic energy of the flow field with time is investigated, and the correlations between the minimum and the maximum kinetic energy and the state of the drop deformation are explored.

[en] In this study, a thermodynamically consistent constitutive relation is developed for ferroelectric materials. The present model is developed in such a way that an intermediate variable is introduced as a stored variable which accounts for calculating the internal variable. Due to this approach, simulations can be performed without an iterative procedure. Thus, this model improves the computational efficiency. The algorithmic procedure can also handle the evolution of ferroelastic strain as well as the evolution of polarisation simultaneously, without getting into convergence issues. In this work, simulations have been performed to capture various behaviours such as ferroelectric hysteresis with prestress, mechanical depolarisation, ferroelastic hysteresis, and creep behaviour. The simulated results have been compared with the experimental results, and it is observed that the model is good enough to capture various nonlinear hysteresis behaviours.

[en] A micromechanics model for predicting the mechanical properties of a particulate composite is developed. The reinforcing particles are assumed to be rigid and spherical in shape, while the matrix is elastic–perfectly plastic. The interactions among the inclusions are taken into consideration by Mori–Tanaka’s approach. The elastic modulus, Poisson’s ratio and yield strength of the composite can be conveniently predicted and systematically investigated. The predictions of the model are discussed and compared with other theories. It is concluded that the yield strength of the composite can be improved by increasing the volume fraction of inclusions for most of loading conditions but not for certain loading paths such as spherical (hydrostatic) stress loading. The open-ended circular cylinder of v. Mises yield surface about the spherical stress axis in the principal stress space for the pure matrix changes to a more complicate yield surface ending at two apexes in the spherical stress axis for the composite.

[en] In this paper we consider the non-isothermal flow of a Bingham fluid with rheological parameters depending on pressure and temperature. The governing equations are scaled in order to evaluate the relevance of the various kinematical and thermodynamical effects represented by some non-dimensional groups such as the Reynolds, second Froude, Brinkman, Péclet and Bingham numbers. We consider a perturbative approach in which the small parameter is the product of the reference temperature and the thermal expansion coefficient. In a recent paper (Fusi in Meccanica, 2017. doi: 10.1007/s11012-017-0655-8 ) this problem has been investigated under the hypothesis that the Reynolds number is of order one. Here we study the case in which the Reynolds number is small (creeping flow). The differences with Fusi (Meccanica, 2017. doi: 10.1007/s11012-017-0655-8 ) are far from trivial. In particular we show that in the situation studied here we can obtain a non-isothermal Stokes Oberbeck approximation in which the buoyancy and frictional effects are taken into account.

[en] Soft membranous materials widely exist in engineering and nature, and the determination of their constitutive parameters is of both scientific and engineering significance. In this paper, the bulge test method is extended to determine the hyperelastic parameters of soft membranes with or without initial stresses. Two extensively applied models—neo-Hookean model and Arruda–Boyce model—are employed to characterize the nonlinear behavior of the membrane under test. The hyperelastic parameters are then extracted from the pressure–deflection curve of the membrane recorded in the bulge tests. Our method is finally validated by both finite element simulations and uniaxial tension experiments. The proposed method can be used to evaluate various soft membranes and tissues and hold promise for numerous applications in such fields as biomedical engineering and bionic engineering.

[en] The similarity equations that arise when there is a power-law outer flow, characterized by the parameter $\mathrm{\beta <!--\; ??\; -->}$, over a surface moving with the same power-law speed, described by the dimensionless parameter $\mathrm{\lambda <!--\; ??\; -->}$, are considered. The critical values ${\mathrm{\lambda <!--\; ??\; -->}}_c$ of $\mathrm{\lambda <!--\; ??\; -->}$ are calculated in terms of $\mathrm{\beta <!--\; ??\; -->}$, except in a range $0.139\lesssim <!--\; ???\; -->\mathrm{\beta <!--\; ??\; -->}\lesssim <!--\; ???\; -->0.5$ where there are no critical points. The behaviour of the solution with $\mathrm{\lambda <!--\; ??\; -->}$ for representative values of $\mathrm{\beta <!--\; ??\; -->}$ is examined, including cases where there are no critical points and one or two critical points leading to two and three solution branches. The asymptotic behaviour for large $\mathrm{\lambda <!--\; ??\; -->}$ is derived. For $-<!--\; ???\; -->2<\mathrm{\beta <!--\; ??\; -->}<-<!--\; ???\; -->1$, the solution proceeds to large negative values of $\mathrm{\lambda <!--\; ??\; -->}$ with this asymptotic limit derived. Aiding flow, $\mathrm{\lambda <!--\; ??\; -->}>0$, shows the existence of additional critical points, with a range $-<!--\; ???\; -->2.6583<\mathrm{\beta <!--\; ??\; -->}<-<!--\; ???\; -->2$ over which ${\mathrm{\lambda <!--\; ??\; -->}}_c$ takes all values both positive and negative. Relatively weak, $\mathrm{\lambda <!--\; ??\; -->}=-<!--\; ???\; -->0.5$, and stronger, $\mathrm{\lambda <!--\; ??\; -->}=-<!--\; ???\; -->5.0$, cases of opposing are treated. The weak case shows two disjoint sections of the solution. For the larger value of $|\mathrm{\lambda <!--\; ??\; -->}|$, one section of the solution in which $f^{″}(0)$ decreases monotonically as $\mathrm{\beta <!--\; ??\; -->}$ is increased and another section where there is a critical point with two solution branches is seen. In all the cases considered, the solution became singular as $\mathrm{\beta <!--\; ??\; -->}\to <!--\; ???\; -->-<!--\; ???\; -->2$, this limit being discussed.

[en] Piezoelectric materials like bulk PZT are often subjected to mechanical creep loads. But being brittle, these undergo premature failure. Hence, piezocomposites are used instead of bulk PZT. Piezocomposites are viscoelastic in nature owing to the presence of a ductile epoxy matrix. In this paper, mechanical creep is studied for 1–3 piezocomposites of different fiber volume fractions under various levels of compressive prestress. Experiments are performed to understand the difference in their electromechanical response. The creep strain is found to increase with the increase in matrix volume fraction and stress level. The creep polarization is observed to decrease with the decrease in fiber volume fraction and stress level. The degradation in the piezocoupling coefficient is observed to be the maximum for the piezocomposite 35% fiber volume fraction and the least for the bulk PZT. This is attributed to the time-dependent permanent re-orientation of ferroelastic domains by 90${}^{\circ <!--\; ???\; -->}$ during the mechanical creep phenomenon. Finally, a viscoelastic model comprising of two parallel Kelvin–Voigt elements is proposed to capture the creep strain. The creep strain is decomposed into the ferroelastic strain and anelastic strain. Creep polarization is computed from the ferroelastic strain. The model predictions are found to be in agreement with the experimental results.

[en] The article presents the dynamic process of a single water droplet impinging on a hot oil surface with various temperatures ranging from 205 to 260 ${}^{\circ <!--\; ???\; -->}\text{C}$. Distilled water is used to produce water droplets with different diameters. The impact behavior is recorded by using a high-speed digital camera with the speed of 2000 fps. The result shows that two typical phenomena, including crater–jet–bubble and vapor explosion, can be observed. The vapor explosion occurs when the oil temperature is higher than 210 ${}^{\circ <!--\; ???\; -->}\text{C}$. The oil temperature, the droplet size, and the Weber number are found to have significant influence on the vapor explosion time. The higher the oil pool temperature is, the earlier the vapor explosion occurs. Vapor explosion time increases with the droplet size, while decreases as the droplet Weber number increases. Moreover, the maximum heat absorption for a single water droplet immersing into the hot oil is calculated considering the changes of the droplet size. Both dimensionless maximum crater depth and maximum jet height increase with the pool temperature due to the surface tension, viscous force and decreasing density of the hot oil.

[en] We investigate the magnetoelectric effect and potential fields of functionally graded multiferroic fibrous composites under anti-plane shear deformation coupled to in-plane electric and magnetic fields. The cylinders are exponentially graded along the radial direction. Rayleigh’s formalism and composite cylinder assemblage model are generalized to account for the configuration. We find that the grading parameter has a dramatic effect on the potential field of the inclusion and the effective property of the composite. We adopt this approach to numerically study the exponentially graded ${\text{BaTiO}}_3{\text{--CoFe}}_2{\text{O}}_4$ composite and provide insights into developing new multiferroic fibrous media with high magnetoelectric coupling.