A.-V. Phan

Improved quarter-point crack tip element

We present a modification to the quarter-point crack tip element and employ this element in two-dimensional boundary integral fracture analysis. The standard singular element is adjusted so that the near-tip crack opening displacement satisfies a known constraint: the coefficient of the term which is linear in the distance to the tip must vanish. Stress intensity factors calculated with the displacement correlation technique are shown to be highly accurate, and significantly more accurate than with the standard element. The improvements are especially dramatic for mixedmode problems involving curved and interacting cracks. 2002 Published by Elsevier Science Ltd.

Viscoelastic studies of human subscapularis tendon: Relaxation test and a Wiechert model

Numerical techniques such as the finite element method employ the material constitutive laws for their analysis. With regards to finite element analysis involving viscoelastic solids, the Generalized Standard Linear Solid (Wiechert) model has been a popular choice among available constitutive laws. Although numerous models have been developed to specifically describe the viscoelastic behavior of tendons and ligaments, most of them have not been implemented in commercial finite element packages. This paper describes a stress relaxation test on the human subscapularis tendon, and then presents an approach for obtaining constitutive parameters of a Wiechert model for the human subscapularis tendon using experimental data from the aforementioned relaxation test. The approach is general and thus, can be applied to other tendons and ligaments, as well as any linear viscoelastic solid materials. The Wiechert model is required if finite element analysis using the commercial finite element package ANSYS is to be performed for a biomechanic structure composed of tendons and/or ligaments.

Interfacial roughening during solid phase epitaxy: Interaction of dopant, stress, and anisotropy effects

The effects of externally applied stress and rate-enhancing dopants on interfacial roughness during the solid phase epitaxial growth of ion-implantation-doped Si are investigated using cross-sectional transmission electron microscopy and time-resolved reflectivity. We find long-wavelength roughness in the absence of an applied stress that arises solely from the dopant-gradient. With the addition of a compressive stress, the interface roughens further with an enhanced magnitude and a dramatically reduced wavelength. We discuss the experimental results in the context of a simulation that includes our current understanding of stress, dopant-gradient, and interface anisotropy effects. We find a rich interplay between these effects in determining growth morphology evolution, and demonstrate the successes and current limitations of the model.

Boundary Integral Evaluation of Surface Derivatives

In boundary element analysis, first order function derivatives, e.g., boundary potential gradient or stress tensor, can be accurately computed by evaluating the hypersingular integral equation for these quantities. However, this approach requires a complete integration over the boundary and is therefore computationally quite expensive. Herein it is shown that this method can be significantly simplified: only local singular integrals need to be evaluated. The procedure is based upon defining the singular integrals as a limit to the boundary and exploiting the ability to use both interior and exterior boundary limits. Test calculations for two- and three-dimensional problems demonstrate the accuracy of the method.

Finite element and experimental studies of diametral errors in cantilever bar turning

Abstract An improved model for predicting diametral errors in turning cantilever multi-diameter bars is presented. This model uses the same geometric analysis of the elastic deflections of the machine–workpiece–tool system due to the cutting force as in Ref. [Appl. Math. Model. 24 (2000) 943]. However, an important improvement is made here toward the determination of workpiece deflections in which the part holder stiffnesses are directly included and shear deformation effect is taken into account. It is noted that in Ref. [Appl. Math. Model. 24 (2000) 943], the workpiece deflection is determined using the finite element method with the assumption that the part holders are rigid. Thus, the part holder deflections need to be calculated separately after obtaining the support reactions from the above finite element analysis (FEA). This post-processing step for calculating the part holder deflections is eliminated in this work by taking the stiffness of these part holders into account in the FEA of the workpiece deflection. Here, the part holder stiffnesses include both the transversal and rotational components. As in our previous work related to the workpiece deflections in turning, the same approach to deriving solutions in closed-form is also applied here. The effects of the part holder stiffnesses on the predicted diametral errors are investigated. An experimental validation supports the proposed model.

The hypersingular boundary contour method for two-dimensional linear elasticity

SummaryThis paper presents a novel method called the Hypersingular Boundary Contour Method (HBCM) for two-dimensional (2-D) linear elastostatics. This new method can be considered to be a variant of the standard Boundary Element Method (BEM) and the Boundary Contour Method (BCM) because: (a) a regularized form of the hypersingular boundary integral equation (HBIE) is employed as the starting point, and (b) the above regularized form is then converted to a boundary contour version based on the divergence free property of its integrand. Therefore, as in the 2-D BCM, numerical integrations are totally eliminated in the 2-D HBCM. Furthermore, the regularized HBIE can be collocated at any boundary point on a body where stresses are physically continuous. A full theoretical development for this new method is addressed in the present work. Selected examples are also included and the numerical results obtained are uniformly accurate.

On Some Benchmark Results for the Interaction of a Crack With a Circular Inclusion

Stress intensity factor calculations for crack-inclusion interaction problems are presented. The problems considered include the benchmark problems first discussed by Helsing and Jonsson, and subsequently by Wang, Mogilevskaya and Crouch. The numerical results are obtained using the symmetric-Galerkin boundary element method in conjunction with an improved quarter-point element for evaluating the stress intensity factors by means of the displacement correlation technique. The converged results confirm the accuracy of the previous simulations, and demonstrate that accurate solutions for these interaction problems can be obtained with numerical methods that are applicable in three dimensions.

Modelling a growth instability in a stressed solid

The growth of crystalline silicon from the amorphous phase in the presence of an applied stress is modelled using advanced numerical methods. The crystal region is modelled as a linear elastic solid and the amorphous as a viscous fluid with a time-dependent viscosity to reflect structural relaxation. Appropriate coupling conditions across the boundary are defined, and both problems are solved using a symmetric-Galerkin boundary integral method. The interface is advanced in time using the level set technique. The results match well with experiments and support the proposed kinetic mechanism for the observed interface growth instability.

A finite-element model with closed-form solutions to workpiece deflections in turning

Simulation models for workpiece deflections play an important role in determining conditions to maximize the part accuracy in machining processes as well as in analysing the dynamic response of the machining system. In this paper, the crosssectional deflection of the workpiece due to all cutting force components (radial, axial and tangential) is determined using the finite-element method. Three workpiece mounting types generally used in industrial practice are considered. The change in the workpiece diameter during machining can easily be taken into account with this model. Furthermore, the finite-element reponses are derived in closed form which enables rapid and continuous solutions along the part length. Numerical examples are treated for which the workpiece deflections calculated from this model are compared with those computed only from the radial cutting force component as usually done by several simplified models. From the results obtained, the proposed model is generally recommended to improve tur...

A non-singular boundary integral formula for frequency domain analysis of the dynamic T-stress

A non-singular 2-D boundary integral equation (BIE) in the Fourier-space frequency domain for determining the dynamic T-stress (DTS) is presented in this paper. This formulation, based upon the Fourier transform of the asymptotic expansion for the stress field in the vicinity of a crack tip, can be conveniently implemented as a post-processing step in a frequency-domain boundary element analysis of cracks. The proposed BIE is accurate as it can be directly collocated at the crack tip in question. The technique is also computationally effective as it simply requires a similar computing effort as that used in determining the dynamic stress components at an interior point of a domain. Five numerical examples involving both straight and curved cracks are studied to validate the proposed technique. For the frequency domain analysis of the DTS in these examples, the exponential window method is employed to obtain its time history.