S. Syngellakis

A two‐dimensional theory for high‐frequency vibrations of piezoelectric crystal plates with or without electrodes

Two‐dimensional equations of motion of successively higher‐order approximations for piezoelectric crystal plates with triclinic symmetry are deduced from the three‐dimensional equations of linear piezoelectricity by expansion in series of trigonometric functions of the thickness coordinate of the plate. These equations, complemented by two additional relations: one, the usual relation of face tractions to the mass of electrodes, and the other relating face charges to face potentials and face displacements, can accommodate either the traction and charge boundary conditions at the faces of the plate without electrodes or the traction and potential boundary conditions at the faces of the plate with electrodes. Dispersion curves are obtained from the first‐ to fourth‐order approximate plate equations for a rotated 45° Y‐cut lithium tantalate plate without electrodes, and these curves are compared with those from the frequency equation of the three‐dimensional equations with close agreement. Solutions of force...

Pressure sensitivity of side-hole optical fiber sensors

The dependency of the pressure-induced birefringence of a side-hole fiber on its geometry has been numerically investigated using the finite element method. We demonstrate that the pressure sensitivity of such a fiber shows a linear dependence on /spl phi//sup 2/, where /spl phi/ is the angle between the side hole center and core center axis and the core center to side-hole tangent. Experimental data obtained with two different side-hole fiber sensors are shown to agree extremely well (to within 10%) with theoretical predictions.

Numerical modelling of combined roughness and plasticity induced crack closure effects in fatigue

The incidence of roughness induced fatigue crack closure has been studied by finite element modelling. Closure analyses in the literature have been reviewed and been shown to lack a reasonable treatment of: (a) propagating elastic-plastic cracks, and (b) the influence of the characteristically inhomogeneous plastic deformation associated with near-threshold crack growth in many materials. Based on an analysis of both overall specimen compliance and node behaviour along the crack path, the present modelling shows: (a) an increasing effect of crack path angle on roughness induced closure levels in keeping with the simple analytical model of Suresh and Ritchie; (b) the mechanism by which closure occurs is more strongly dependent on residual plastic strains in the wake than global shear displacements of the fracture surfaces due to mixed-mode behaviour at the crack tip; and (c) the closure levels are relatively low compared to experimental data, consistent with the absence of environmental irreversibility in the finite element models and the idealised crack path morphologies that were studied. Slip band simulations show a significant increasing effect of inhomogeneous deformation on closure levels, improving the apparent accuracy of the modelling results.

Shear lag models for discontinuous composites: fibre end stresses and weak interface layers

A new shear lag (SL) type model for stress transfer in a composite with cylindrical fibres is derived. It accounts for fibre end stresses in an approximate yet realistic manner, and leads to a new formula for predicting the Young’s modulus of the composites. The predictions of this model were found to agree well with data for metal matrix composites (MMCs) with fibres of various aspect ratios. The accuracy and relative simplicity of the new model have been exploited in the development of an approximate analytical model for the stress transfer and macroscopic yield stress of a composite that contains a weak layer in the matrix adjacent to the reinforcement. With the aid of the latter model, the proof stress of MMCs which contain a precipitate free zone (PFZ) around the reinforcement, can be studied; experimental data obtained for aged 8090 MMCs is consistent with the model predictions.

Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method

Abstract The stiffness characteristics of plastic ankle foot orthoses (AFOs) are studied through finite element modelling and stress analysis. Particular attention is given to the modelling and prediction of non-linear AFO behaviour, which has been frequently observed in previous experimental studies but not fully addressed analytically. Both large deformation effects and material non-linearity are included in the formulation and their individual influence on results assessed. The finite element program is subsequently applied to the simulation of a series of tests designed to investigate the relation between AFO trimline location and stiffness for moderate and large rotations. Through careful consideration and identification of key modelling parameters, the developed finite element solution proves to be a reliable and effective alternative means of assessing variations of a typical plastic AFO design so that particular patient requirements could be met, in the long term.

Nanoindentation of CVD diamond: comparison of an FE model with analytical and experimental data

This paper describes an experimental procedure for the determination of the hardness and the elastic modulus through nanoindentation of a CVD diamond coating using simple analytical formulae. Such tests, performed with a Berkovich indenter, were simulated by finite element analysis. Through the numerical analysis, it was possible to reproduce the load-penetration depth curves and thus, confirm the validity or correct the property calculations. Results show that the predicted property values can be affected by the assumed material strain hardening. By comparing the numerical values with the experimental results, it is possible to characterise, with sufficient accuracy, the material behaviour.

Piezoelectric wave dispersion curves for infinite anisotropic plates

Plane‐wave propagation in an infinite plate is analyzed by the linear three‐dimensional theory of piezoelectricity. The general dispersion relation, valid for any degree of anisotropy and for the commonly applicable electrical boundary conditions, is formulated. The general equation yielding the surface wave velocities is also derived. A numerical algorithm, potentially applicable to piezoelectric plates of any material symmetry, is developed. Results are obtained for particular crystal cuts of practical interest and waves propagating in the coordinate directions. Comparison with corresponding predictions by the purely elastic theory allows assessment of the effect of electromechanical coupling as well as of the accuracy of the computed dispersion relationships.

Boundary element methods for polymer analysis

The application of the boundary element method (BEM) to the stress analysis of polymers is reviewed. Since polymers are most often modelled as viscoelastic materials, formulations specifically developed for other such materials are also discussed. Essentially, only linear viscoelasticity has been considered for which the correspondence principle applies. Two main BEM approaches are encountered in the literature. The first solves the problem in either Laplace or Fourier transformed domain and relies on numerical inversion for the determination for the time-dependent response. The second solves directly in the time domain using appropriate fundamental solutions each depending on the viscoelastic model used. The developed algorithms have been validated through their application to a range of benchmark problems. Scope for enhancing the potential of the method is identified by increasing the generality of material modelling and expanding its application to complex, industry-oriented problems.

Second-order theories for extensional vibrations of piezoelectric crystal plates and strips

An infinite system of two-dimensional (2-D) equations for piezoelectric plates with general symmetry and faces in contact with vacuum is derived from the 3-D equations of linear piezoelectricity in a manner similar to that of previous work, in which an infinite system of 2-D equations for plates with electroded faces was derived. By using a new truncation procedure, second-order equations for piezoelectric plates with faces in contact with either vacuums or electrodes are extracted from the aforementioned infinite systems of equations, respectively. The second-order equations for plates with or without electrodes are shown to predict accurate dispersion curves by comparing to the corresponding curves from the 3-D equations in a range up to the cut-off frequencies of the first symmetric thickness-stretch and the second symmetric thickness-shear modes without introducing any correction factors. Furthermore, a system of 1-D second-order equations for strips with rectangular cross section is deduced from the 2-D second-order equations by averaging variables across the narrow width of the plate. The present 1-D equations are used to study the extensional vibrations of barium titanate strips of finite length and narrow rectangular cross section. Predicted frequency spectra are compared with previously calculated results and experimental data.

Numerical modelling of crack shielding and deflection in a multi-layered material system

Finite element analysis has been used to investigate the fatigue behaviour observed in testing a layered structure (representative of an automotive journal bearing). The aim of the analysis was to explain the deflection or bifurcation observed as a fatigue crack propagates through the multi-layered structure of a bearing. A fracture mechanics approach was adopted using detailed evaluations of the J-integral to assess and monitor both crack tip driving force and directional propensity with crack growth. Crack shielding or anti-shielding as well as deflection or bifurcation were conclusively linked to the difference between the fundamental elasto-plastic properties of the various constituent materials.