Finite layer analysis of layered elastic materials using a flexibility approach. Part 1—Strip loadings

It is well known that the analysis of a horizontally layered elastic material can be considerably simplified by the introduction of a Fourier or Hankel transform and the application of the finite layer approach. The conventional finite layer (and finite element) stiffness approach breaks down when applied to incompressible materials. In this paper these difficulties are overcome by the introduction of an exact finite layer flexibility matrix. This flexibility matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite for an incompressible material. The method is illustrated by a series of examples drawn from the geotechnical area, where it is observed that many natural and man-made deposits are horizontally layered and where it is necessary to consider incompressible behaviour for undrained conditions.     

Finite layer analysis of layered viscoelastic materials under three-dimensional loading conditions

A method is presented which enables the calculation of the settlement behaviour of circular or general loadings on horizontally layered soils which undergo secondary or ‘creep’ consolidation. The method of analysis involves the use of Hankel or double Fourier transforms to simplify the equations governing the consolidation process. This leads to great savings in the preparation of data and the amount of computer storage needed to solve problems involving three-dimensional loadings since such problems are essentially reduced to that of one spatial dimension: Solutions are then obtained by a ‘forward marching’ process where solutions at a particular time are found from those at a previous time. A method is presented which eliminates the need to store the solutions at all previous time steps, and is therefore very efficient. The theory is illustrated by examples of the behaviour of rectangular and circular loadings on layered soil profiles.     

On the overall elastic moduli of polymer-clay nanocomposite materials using a self-consistent approach. Part I: Theory

Although few investigations recently proposed to describe the overall elastic response of polymer-clay nanocomposite materials using micromechanical-based models, the applicability of such models for nanocomposites is far from being fully established. The main point of criticism to mention is the shelving of crucial physical phenomena, such as interactions and length scale effects, generally associated by material scientists, in addition to the nanofiller aspect ratio, to the remarkable mechanical property enhancement of polymer-clay nanocomposites. In this Part I of two-part paper, we present a micromechanical approach for the prediction of the overall moduli of polymer-clay nanocomposites using a self-consistent scheme based on the double-inclusion model. This approach is used to account for the inter-inclusion and inclusion-matrix interactions. Although neglected in the models presented in the literature, the active interaction between the nanofillers should play a key role in the reinforcing effect of nano-objects dispersed in a polymer matrix. The present micromechanical model incorporates the nanostructure of clay stacks, modeled as transversely isotropic spheroids, and the so-called constrained region, modeled as an interphase around reinforcements. This latter is linked to the interfacial interaction between matrix and reinforcements that forms a region where the polymer chain mobility is reduced. To account for length scale effects, interphase thickness and particle dimensions are taken as explicit model parameters. Instead of solving iteratively the basic homogenization equation of the self-consistent scheme, our formulation yields to a pair of equations that can be solved simultaneously for the overall elastic moduli of composite materials. When the interphase is disregarded for spheroids with zero aspect ratio, our formulation coincides with the Walpole solution (J Mech Phys Solids 1969;17:235-251). Using the proposed general form, a parametric study is presented to analyze the respective influence of aspect ratio, number of silicate layers, interlayer spacing and nanoscopic size of the transversely isotropic spheroids on the overall elastic moduli of nanocomposite materials.     

Stresses and displacements of a transversely isotropic elastic halfspace due to rectangular loadings

Analytical solutions in exact closed-forms are obtained for stresses and displacements in an solid due to rectangular loading. The stresses and displacements are induced in the solid due to the vertical and horizontal loadings uniformly distributed on a rectangular area. The rectangular area is horizontally embedded in or on the solid. The solid occupies a space of semi-infinite extent and has a linear elastic property with transverse isotropy. The classical integral transforms are used in the solution formulation. The solutions are systematically presented in matrix forms and in terms of elementary harmonic functions. The solutions are easily implemented for numerical calculations and applied to problems encountered in engineering. Comparisons of the present solution with existing similar solutions are presented for the stresses and displacements induced by the vertical load. In addition, the numerical results of the stresses and displacements in the solid induced by the horizontal and vertical loads are also presented. These results illustrate the effect of different elastic constants of transversely isotropic solids on the stress and displacement fields.     

On the overall elastic moduli of polymer-clay nanocomposite materials using a self-consistent approach. Part II: Experimental verification

Polyamide-6 (PA6) based nanocomposites were prepared using a modified montmorillonite (MMT) Cloisite 20A as nanofillers. The silicate weight fraction of the prepared nanocomposites, determined by burning off the PA6 matrix, was ranged from 0.2 wt% up to 7.5 wt%. The thermomechanical properties of both the neat PA6 and the PA6 filled with MMT nanoclay were measured by means of uniaxial tension tests and dynamic mechanical thermoanalysis, their crystallinity analyzed by differential scanning calorimetry and their morphology observed by transmission electron microscopy. The elastic stiffness of PA6-clay nanocomposites was examined under two moisture levels and was analyzed with the theory formulated in the Part I of this work. Predicted results are found in good agreement with our experiments. The model capabilities are also critically discussed by comparisons with both experiments issued from the literature and the Mori-Tanaka approach widely used in recent literature. It is demonstrated that the proposed micromechanical model is more efficient than the Mori-Tanaka approach. Moreover, the obtained results support the idea that the elastic stiffness of polymer-clay nanocomposites is governed by the same mechanisms as microcomposites, the effects of particle dimension or constrained region being of a second order.     

Finite strain numerical analysis of elastomeric bushings under multi-axial loadings: a compressible visco-hyperelastic approach

Elastomers have wide and ever increasing applications in several industries. In this work a compressible visco-hyperelastic approach is employed to investigate the behavior of elastomeric materials. The time-discrete form of the material model is developed to be used in numerical simulations. This formulation provides a recursive relation to update the stress in any time step regarding the deformation history. By means of analytical solutions derived for pure torsion of a solid circular cylinder, the numerical implementation is validated and then, the response of an elastomeric bushing is investigated in torsional, axial and combined deformations. These bushings are used in suspension systems to reduce amplitude of vibrations as well as shocks. It is shown that, the numerical model well simulates the non-linear time dependent response of the bushing in different deformation rates. Also, a multi-step relaxation test is simulated to identify the hysteretic behavior. Finally, fully relaxed response of the bushing for torsional and combined torsional–axial deformations is predicted and compared with those of experiment as well as three other constitutive models. The comparisons reveal that, the proposed approach well predicts the coupling effect of axial displacement on torsional moment where it is not the case for other compared models.     

Visco-plasticity—plasticity and creep in elastic solids—a unified numerical solution approach

The visco-plastic model of material behaviour is of much practical interest in its own right and initial strain techniques for its solution have been developed and proved efficient. More important however is the fact that the visco-plastic model can be used to generate plasticity solutions in a simple manner when stationary conditions are reached and, at the other extreme, can reproduce standard creep phenomena. Used in this sense it allows the treatment of non-associated plasticity and strain softening situations which present difficulties in conventional plasticity approaches. A standard programme thus allows the treatment of a wide range of materially non-linear problems. The paper discusses various applications of the new general formulation and introduces certain numerical information on solution stability.     

The behaviour of Kevlar fibre-epoxy laminates under static and fatigue loadings. Part I—experimental

Kevlar 49 fibre and unidirectional Kevlar fibre reinforced plastic (KFRP) laminates both show an increase in stiffness under monotonic tensile loading. This stiffening effect is time-dependent and is reversible once the load is removed. In contrast, the modulus of a cross-ply KFRP laminate is affected primarily by matrix cracking of the transverse (90°) ply, and is sensitive to strain-rate and temperature. In cyclic (tensile) loading, however, the modulus of the cross-ply laminate depends on a combination of the fibre stiffening effect and transverse matrix cracking.     

Finite elements in space and time for the analysis of generalised visco‐elastic materials

Numerical analysis of linear visco‐elastic materials requires robust and stable methods to integrate partial differential equations in both space and time. In this paper, symmetric space–time finite element operators are derived for the first time for elementary linear elastic spring and linear viscous dashpot. These can thereafter be assembled in parallel and in series to simulate an arbitrarily complex linear visco‐elastic behaviour. The flexibility of the proposed method allows the formulation of the behaviour, which closely reflects physical processes. An efficient algorithm is proposed to use the generated elementary matrices in a way that is comparable with finite difference schemes, in terms of both processor and memory costs. This unconditionally stable and convergent procedure is equally valid for space domains in which geometry or material properties evolve with time. Copyright © 2013 John Wiley & Sons, Ltd.     

The CNPM thermal heat pump. Part 1 — general description and thermodynamic analysis

A research programme, funded by CNR (National Research Council), has been undertaken by CNPM since 1973. The aim of the programme is the construction and testing of a prototype thermal heat pump. The most significant component is an organic Rankine cycle engine, driving the compressor of a heat pump. Since the heat rejected by the engine is supplied to the user — water for domestic heating — the whole system performs as a ‘heat multiplier’, converting the high temperature heat given to the engine into a larger amount of low temperature heat, to be used for domestic heating.In this paper, the selection criteria for the working fluid — a completely fluoro-substituted hydrocarbon — and the main thermodynamic data of both power and heat pump cycles, are discussed; the finally adopted plant configuration is described, with particular emphasis on the influence exterted by the working fluid nature on the heat exchangers and turbo-machinery dimensions and performance. A discussion on the merits of the single fluid solution (ie the same working fluid in the power and the heat pump cycle) and dual fluid solution is also carried out. The feasibility of a low-temperature heat distribution, based on compact-surface, natural-draft convectors, with the relevant advantages on the Rankine and heat-pump cycles, is also investigated.Finally, the expected overal; system performance is given, both at design and part-load conditions. As a premium for the rather complex but efficient thermodynamicscv of the system, significant energy savings are obtained in all situations.     

Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory: Part II—Buckling and free vibration

Using the higher-order plate theory developed in the first part of this paper, as well as the technique based on the state space concept, the free vibration and buckling problems of rectangular cross-ply laminated plates are analyzed. In this context a variety of boundary conditions is considered and comparisons with the existing literature are made.     

Numerical analysis of elastic contact problems using the boundary integral equation method. Part 2: Results

This paper gives solutions to various frictionless and frictional contact problems using the boundary integral formulation developed in Part 1. A range of problems is considered in order to demonstrate the applicability of the approach. In most cases equal size linear elements are found to give best results. In the case of frictional problems the arrangement of strick-slip zones is affected by the node locations and a relatively large number of elements may be required to produce satisfactory results. In all cases, the boundary integral equation method yields numerical solutions that are in very good agreement with the analytical solutions to which they are compared.     

Mechanics of three-dimensional braided structures for composite materials – Part II: prediction of the elastic moduli

In the first part of this series of paper [Z.X. Zang, R. Postle, Mechanics of three-dimensional braided structures for composite materials – Part I: fabric structure and fibre volume fraction, Comp. Struct. 49 (2000) 451–459], it was demonstrated that the braiding angles and fibre volume fraction can be represented as functions of the normalized pitch length introduced as a key parameter of three-dimensional braided reinforced composite materials. In the present paper, the models for the prediction of the tensile and shear moduli of three-dimensional braided composites are established by numerical simulation and mathematical modelling. Three-dimensional braided preforms are produced from the material system comprising glass/polypropylene and their moduli are measured. The results predicted from the braided composite models are supported by the experimental data.     

Durability analysis of carburized components using a local approach based on elastic stresses

The carburizing of non‐homogeneously stressed components is often used to improve the fatigue properties. In order to predict fatigue life curves the local behavior has to be analyzed. Therefore, cyclic material properties of the carburized surface layer and the core were investigated. In general it is challenging to obtain the input data necessary for a durability analysis of carburized components with the local strain approach. Therefore, a simple method is proposed to estimate the life curve of carburized components under proportional constant‐ and variable‐amplitude loading. With a S‐N curve for a similar component as input local elastic stresses can be back‐calculated. Experimental results show a strong influence of the highly stressed volume on the fatigue properties of the carburized surface layer. This effect can be taken into account with a size correction factor calculated on the basis of a weakest link model. Based on an appropriate local elastic stress‐life curve and regarding the size effect, durability analysis can be improved in an early stage of design. Fatigue tests on notched specimens and components of vehicle transmission cases were used to compare experimental and numerical results.     

Modeling of uncertainties in reliability centered maintenance — a probabilistic approach

Uncertainties in the decision making of reliability centered maintenance (RCM) are discussed. These uncertainties might be unacceptable in many practical applications, leading to non-optimum maintenance strategies. An alternative approach, opening for specified uncertainties is shown to correct this defect. Exemplifying the approach, a simple fire detection system is discussed.     

Finite element analysis of the buckling and mode jumping of a rectangular plate

This paper presents the construction, validation and application of a toolkit which allows the combination of the well-understood theoretical analysis of the post-buck- ling behavior of a rectangular plate and of the numerical treatment of general boundary conditions. The construction is based on appropriate mixed finite element discretizations of both the spectral and nonlinear problems, with which one can obtain reliable approximations of the relevant parameters.     

Synthesis of nanostructured materials using supercritical CO<Subscript>2</Subscript>: Part II. Chemical transformations

This article, the second part of our review series on the use of supercritical carbon dioxide (scCO₂) for synthesis of nanostructured material deals with the production techniques that involve chemical transformations. Taking advantage of both solvent and anti-solvent tunable properties of scCO₂, many nanostructured materials including supported/unsupported nanoparticles, quantum nanodots, nanofilms, nanorods, nanofoams, and nanowires can be prepared. Furthermore, material surfaces can be functionalized using scCO₂. scCO₂ can also be used as a carbon source for the controlled synthesis of carbon nanotubes and fullerenes or as an oxygen source for metal oxide nanostructures. Moreover, materials produced using scCO₂ does not usually need additional purification or drying steps. Depending on surface properties, the morphology of the final material can be adjusted by tuning the process conditions and the reactant concentrations.     

Synthesis of nanostructured materials using supercritical CO<Subscript>2</Subscript>: Part I. Physical transformations

Nanostructured materials have been attracting increased attention for a wide variety of applications due to their superior properties compared to their bulk counterparts. Current methods to synthesize nanostructured materials have various drawbacks such as difficulties in control of the nanostructure and morphology, excessive use of solvents, abundant energy consumption, and costly purification steps. Supercritical fluids especially supercritical carbon dioxide (scCO₂) is an attractive medium for the synthesis of nanostructured materials due to its favorable properties such as being abundant, inexpensive, non-flammable, non-toxic, and environmentally benign. Furthermore, the thermophysical properties of scCO₂ can be adjusted by changing the processing temperature and pressure. The synthesis of nanostructured materials in scCO₂ can be classified as physical and chemical transformations. In this article, Part I of our review series, synthesis of nanostructured materials using physical transformations is described where scCO₂ functions as a solvent, an anti-solvent or as a solute. The nanostructured materials, which can be synthesized by these techniques include nanoparticles, nanowires, nanofibers, foams, aerogels, and polymer nanocomposites. scCO₂ based processes can also be utilized in the intensification of the conventional processes by elimination of some of the costly purification or separation steps. The fundamental aspects of the processes, which would be beneficial for further development of the technologies, are also reviewed.     

The spectral element method for elastic wave equations—application to 2‐D and 3‐D seismic problems

A spectral element method for the approximate solution of linear elastodynamic equations, set in a weak form, is shown to provide an efficient tool for simulating elastic wave propagation in realistic geological structures in two‐ and three‐dimensional geometries. The computational domain is discretized into quadrangles, or hexahedra, defined with respect to a reference unit domain by an invertible local mapping. Inside each reference element, the numerical integration is based on the tensor‐product of a Gauss–Lobatto–Legendre 1‐D quadrature and the solution is expanded onto a discrete polynomial basis using Lagrange interpolants. As a result, the mass matrix is always diagonal, which drastically reduces the computational cost and allows an efficient parallel implementation. Absorbing boundary conditions are introduced in variational form to simulate unbounded physical domains. The time discretization is based on an energy‐momentum conserving scheme that can be put into a classical explicit‐implicit predictor/multicorrector format. Long term energy conservation and stability properties are illustrated as well as the efficiency of the absorbing conditions. The accuracy of the method is shown by comparing the spectral element results to numerical solutions of some classical two‐dimensional problems obtained by other methods. The potentiality of the method is then illustrated by studying a simple three‐dimensional model. Very accurate modelling of Rayleigh wave propagation and surface diffraction is obtained at a low computational cost. The method is shown to provide an efficient tool to study the diffraction of elastic waves and the large amplification of ground motion caused by three‐dimensional surface topographies. Copyright © 1999 John Wiley & Sons, Ltd.