Characterizing and modeling the non-linear viscoelastic tensile deformation of a glass fiber reinforced polypropylene

On the basis of comprehensive experimental investigations on a long glass fiber reinforced polypropylene (PP-LGF) a novel rheological material model is developed. It features a decomposition of the stress into a time independent quasi-static and a time and strain dependent viscous contribution. Furthermore it allows for plastic deformations starting from the very beginning of straining and is thereby able to reproduce the absence of a purely linear elastic domain going along with the nonexistence of a defined yield point, characteristic for many fiber reinforced thermoplastic polymers. In order to approach the true quasi-static material behavior, various tensile tests were carried out. The viscous material behavior was deduced from a series of stress relaxation experiments and is described by Eyring’s equation with strain dependent viscosity parameters.     

A finite element post-processed Galerkin method for dimensional reduction in the non-linear dynamics of solids. Applications to shells

In this paper we introduce the finite element version of the so-called post-processed Galerkin method into the field of solid mechanics and apply the new technique to the dynamics of shells. The proposed post-processed method provides low-cost means to lift low-dimensional solutions to high-dimensional solutions. It is the very fact that the kinematical fields are improved to higher orders which makes the method of great interest. Our shell theory is geometrically exact in the sense that all non-linearities are included in the formulation. For time integration an energy/momentum scheme is used to enhance integration stability. Two hierarchical enhanced finite elements are formulated, on the basis of which a specific post-processed method is then developed. With the help of some examples of non-linear shell vibrations, a critical examination and validation of the post-processed method is carried out.     

Variational bounds for the effective electroelastic moduli of piezoelectric composites with electromechanical coupling spring-type interfaces

The present work focuses on variational bounds for the effective electroelastic moduli of multiphase piezoelectric composites with thin piezoelectric interphase. Both the inhomogeneities and the matrix are assumed to be piezoelectric and transversely isotropic. The piezoelectric interphase is modeled as the spring-type interface with electromechanical coupling. The inhomogeneities are assumed to be spheroidal so that the reinforcement geometry is able to range from thin flake to continuous fiber. The effective properties of the piezoelectric composite with interfacial imperfection are defined and the principles of minimum internal energy and enthalpy are derived. These principles are applied to analytically obtain the upper and lower bounds for the effective electroelastic moduli. Unlike the Voigt–Reuss-type bounds for perfect interface, the present bounds depend not only on the material properties and volume fraction, but also on the interface parameters, inhomogeneity shape and orientation. An example of a two-phase composite is given for detailed discussion, where dependence of the electroelastic moduli and their bounds on the inhomogeneity shapes and orientations as well as the interface properties is provided and discussed. To qualitatively account for the dependence, analysis based on two possible mechanisms, i.e., the simple mixture rule of composite and the weakening effect by imperfect interface, are also provided.     

On the propagation of non-linear pressure waves in pipes with turbulent non-zero mean flow

The study deals with the propagation of small-amplitude finite-rate waves in gas filled pipes with non zero mean flow. Adopting the assumption of quasi-one-dimensional flow it is shown that the wave motion can be studied analytically provided the characteristic wave length is sufficiently small. The combined effects of stratification, nonlinearity and frictional attenuation are discussed in detail for left-running and rightrunning waves.     

A study on the effect of stiffeners on quasi-static crushing of stiffened square tube with non-linear finite element method

During ship collision and grounding, the crushing collapse of a thin-walled structure subjected to compressive loads is one of the important failure mechanisms. Non-linear finite element method (FEM) is a powerful tool for analyzing large deformation plasticity problems. In this paper, the effects of longitudinal and transverse stiffeners on the quasi-static crushing of stiffened square tubes, which have relatively light stiffeners, are studied with non-linear FE program LS-DYNA. Based on the experimental data and numerical simulation results, new formulas for equivalent plate thickness and the mean crushing load are developed. The prediction of the mean crushing load is in good agreement with the experimental data.     

On the electronic structure and equation of state in high pressure studies of solids

We discuss the high pressure behaviour of zinc as an interesting example of controversy, and of extensive interplay between theory and experiment. We present its room temperature electronic structure calculations to study the temperature effect on the occurrence of its controversial axial ratio (c/a) anomaly under pressure, and the related electronic topological transition (ETT). We have employed a dense 63 X 63 X 29 k-point sampling of the Brillouin zone and find that the small (c/a) anomaly near 10 GPa pressure persists at room temperature. A weak signature of the anomaly can be seen in the pressure-volume curve, which gets enhanced in the universal equation of state, along with that of K-point ETTs. We attribute the change of slope in the universal equation of state near 10 GPa pressure, mainly to hybridization effects. The temperature effect in fact enhances the possibility of L-point ETT. We find that the L-point ETT is very sensitive to exchange correlation terms, and hence we suggest that further refinements in the theoretical techniques are needed to resolve the controversies on the ETT in Zn.     

On the influence of membrane inertia and shear deformation on the geometrically non-linear vibrations of open,cylindrical, laminated clamped shells

It is the objective of this work to verify the validity of different approximations in the analysis of geometrically non-linear vibrations of open, cylindrical, laminated, fully clamped shells. Namely, it is intended to verify if membrane inertia and transverse shear deformation can be neglected and when. p-version finite elements with hierarchic basis functions are employed to define the models. A simple comparison of the different stiffness and mass terms is carried out first, to assess the relative importance of membrane inertia and shear deformation. Then a few numerical tests are carried out in non-linear vibrations by solving the ordinary differential equations of motion by Newmark’s method. It is found that what are usually considered to be thin panels actually require the consideration of shear deformation.     

On the numerical solution of non-linear reservoir flow models with gravity

Based on a two-phase fluid model for immiscible displacement in a porous medium, we develop and analyse numerical solution techniques for certain non-linear phenomena. Two different solution strategies for the treatment of gravity effects, which are non-trivial to model by existing solution techniques and may be of great influence in many practical flow situations, are presented. The solution procedures are based on an operator-splitting technique, combining the modified method of characteristics with finite element techniques and adaptive grid refinement.     

Effect of hydrostatic pressure on the electrical properties of blend vulcanizates loaded with paraffin wax

Blend vulcanizates from styrene butadiene rubber and natural rubber with equal proportions incorporated with the percolation concentration (40 phr) of High Abrasion Furnace carbon black and loaded with different concentrations of paraffin wax were prepared using the conventional two roll mill technique. With the application of different values of hydrostatic pressure on samples loaded with wax, a third jump non-linear region, obtained from I–V characteristics, clearly appears and was shifted to lower fields as the applied pressure increased. Furthermore, the non-linear coefficient were increased at a pressure of 0.6 kg/cm² and then decreased with further increase in pressure. On the other hand, the dc electrical conductivities were measured. At room temperature, it increased with increasing pressure for samples unloaded with wax while it has a minimum at a pressure of 0.4 kg/cm² for other samples. The positive and negative pressure of conductivity were calculated and found to increase with increasing wax contents. Hydrostatic pressures was found to highly affect the behavior of the temperature dependence of the dc conductivity. The maximum temperature coefficient of conductivity recorded a maximum value at a pressure of 0.4 kg/cm².     

On the effectiveness of porosity on unsteady flow between parallel plates of a viscoelastic fluid under constant pressure gradient with heat transfer

The unsteady flow in a porous medium of an incompressible non-Newtonian viscoelastic fluid between two parallel horizontal non-conducting porous plates is studied with heat transfer. A sudden uniform and constant pressure gradient and uniform suction and injection through the surface of the plates are applied. The two plates are kept at different but constant temperatures, while the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained using finite difference approximations. The effect of the porosity of the medium, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions is examined.     

Analysis of the flow in grooved pumps with specified pressure boundary conditions

In this study the numerical method is employed to examine the flow in pumps with spiral grooves. A methodology suitable for the use of unstructured grids is developed. In order to have the greatest feasibility, the governing equations are formulated in such a manner that the grids are allowed to rotate with the rotor. Different from common practices, pressures are specified on the inlet and the outlet boundaries. Therefore, special treatments are required to calculate the mass flow rate and the inlet and outlet velocities. The methodology developed here is assessed via comparison with existing measurements and good agreement is obtained. Examination of pump parameters reveals that in order to obtain maximum flow rate, both the spiral angle and the groove height need to be carefully determined. The force balance over the entire flow channel shows that for a fixed pressure rise across the pump, the pressure difference between side walls is proportional to tangent of the spiral angle and the groove width, but inversely proportional to the groove height and the rotor length. These relationships can roughly be seen in the calculated results.     

On the linear problem of swelling porous elastic soils with incompressible fluid

In this paper we consider the linear theory of swelling porous elastic soils in the case that the fluid is incompressible. The formulation belongs to the theory of mixtures for porous elastic solids filled with fluid and gas. It proposes some new mathematical difficulties. Continuous dependence results on initial conditions and supply terms are obtained in the general case. Logarithmic convexity method is used in case of fluid saturation. Structural stability with respect two constitutive coefficients is also obtained in the case of fluid saturation.     

On the slow motion of a sphere in fluids with non-constant viscosities

We study a slowly moving sphere in fluids where the viscosity depends upon factors such as shear-rate, temperature and pressure, with the flow field approximated by the Stokes flow past a sphere. We derive an expression for the stresses generated in the fluid due to these various factors. This gives us information about both, the force imposed by the fluid upon the sphere and also the reaction force due to the sphere upon the fluid, referred to as the stress density. The values of the force and stress density are numerically computed in each of the cases and analyzed for various values of the flow and material parameters. Our computations show interesting variations in the distribution of stress density in the fluid for the various cases and also give us valuable information about the effect of walls. Our calculations also indicate that particle heating or cooling can serve as a significant control parameter since the drag force upon the sphere increases dramatically for a cold particle and can be reduced considerably upon heating it.     

On the tensile behavior of an embedded carbon nanotube in polymer matrix with non-bonded interphase region

The longitudinal behavior of a carbon nanotube in a polymeric matrix is studied using a non-linear analysis on a full 3D multi-scale finite element model consisting of carbon nanotube, non-bonded interphase region and surrounding polymer. The bonding between carbon nanotube and its surrounding polymer is treated as van der Waals interactions. The results of simulation of carbon nanotube reinforced polymer implies on a non-linear stress–strain behavior. A comparison between finite element analysis results and the rule of mixture for conventional composites shows that the rule of mixture overestimates the result and cannot capture the scale difference between micro- and nano-scale. An equivalent fiber is developed to overcome this difficulty and corresponding longitudinal, transverse and shear moduli are calculated. The results reveal that the length of CNT affects the efficiency of reinforcement phenomenon.     

On the analysis of composite structures with material and geometric non-linearities

If major weight saving is to be realised it is essential that composites be used in “primary” structural components, i.e., wing and fuselage skins. To this end it is essential that analytical tools be developed to ensure that composite structures meet the FAA damage tolerance certification requirements. For stiffened composite panels one potential failure mechanism is the separation of the skin from the stiffeners; resulting from excessive “through the thickness” stresses. This failure mechanism is also present in bonded composite joints and composite repairs. Currently failure prediction due to in-plane loading appears to be relatively well handled. Unfortunately, this is not yet true for matrix-dominated failures. Consequently, it is essential that a valid analysis methodology capable of addressing all of the possible failure mechanisms, including failure due to interlaminar failure, be developed. To aid in achieving this objective the present paper outlines the results of a series of experimental, analytical and numerical studies into the matrix-dominated failures of rib stiffened structures.     

On the existence of periodic solution for equation of motion of thick beams having arbitrary cross section with tip mass under harmonic support motion

A cantilever beam having arbitrary cross section with a lumped mass attached to its free end while being excited harmonically at the base is fully investigated. The derived equation of vibrating motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. We have, therefore, established the sufficient conditions for the existence of periodic oscillatory behavior of the beam using Green’s function and employing Schauder’s fixed point theorem. The derived equation of vibration motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. To formulate a simple, physically correct dynamic model for stability and periodicity analysis, the general governing equations are truncated to only the first mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for periodic oscillatory behavior of the beam are established. Consequently, the phase domain of periodicity and stability for various values of physical characteristics of the beam-mass system and harmonic base excitation are presented.     

On the evaluation of the adhesion of electroplated Ni coatings upon steel substrate with extended microbridge technique

The interfacial adhesion of electroplated Ni coatings on steel substrate was assessed using an extended microbridge technique (eMBT), and the fracture path of interfacial cracks was examined through cross-sectional high-resolution SEM observation in loading condition. The results indicated that the magnitude of interfacial toughness increased ten to hundred times as the cleaning time of substrate surface was prolonged in a limited duration. The cross-sectional SEM examination revealed that the weak interface fracture was related to brittle mechanism, whereas the strong interface was a reflection of ductile one. In case of the duration time of substrate pre-cleaning, which was commonly adopted in applications of electroplate engineering, the over-erosion of substrate surface appeared and the steel surface became rough. In this case, the mechanical stick force, in addition to the physical bonding force across the interface, was observed to play a crucial role in the coatings integrity and bonding reliability.