A finite element approach for the analysis of variable core dislocations

A finite element description of variable core edge dislocations in the context of linear elasticity is presented in this work. The approach followed is based on a thermal analogue and the integral representation of dislocations through stresses. The objective of a variable core defect concept is to eliminate the stress singularity experienced at the dislocation core. This is accomplished assuming that the displacement discontinuity is achieved gradually over some distance. To implement this concept in a finite element scheme, we first model purely rotational crystal defects considering an appropriate pseudo-temperature distribution, which produces a dislocation array of increasing width. Accordingly, we simulate a discrete edge dislocation of linearly increasing width. This description of dislocation core is closer to experimental observations and has a physically anticipated behaviour reproducing the Volterra dislocation away from the core. Further, interactions of variable core dislocations with free boundaries and coupled dislocation partials are investigated. In all cases, we recover the analytical solutions for the stress distributions and the total strain energ

Finite element analysis of Volterra dislocations in anisotropic crystals: A thermal analogue

The present work gives a systematic and rigorous implementation of Volterra dislocations in ordinary two-dimensional finite elements using the thermal analogue and the integral representation of dislocations through the stresses. The full fields are given for edge dislocations in anisotropic crystals, and the Peach-Koehler forces are found for some important examples

Influences of non-singular stresses on plane-stress near-tip fields for pressure-sensitive materials and applications to transformation toughened ceramics

In this paper, we investigate the effects of the non-singular stress ( T stress) on the mode I near-tip fields for elastic perfectly plastic pressure-sensitive materials under plane-stress and small-scale yielding conditions. The T stress is the normal stress parallel to the crack faces. The yield criterion for pressure-sensitive materials is described by a linear combination of the effective stress and the hydrostatic stress. Plastic dilatancy is introduced by the normality flow rule. The results of our finite element computations based on a two-parameter boundary layer formulation show that the total angular span of the plastic sectors of the near-tip fields increases with increasing T stress for materials with moderately large pressure sensitivity. The T stress also has significant effects on the sizes and shapes of the plastic zones. The height of the plastic zone increases substantially as the T stress increases, especially for materials with large pressure sensitivity. When the plastic strains are considered to be finite as for transformation toughened ceramics, the results of our finite element computations indicate that the phase transformation zones for strong transformation ceramics with large pressure sensitivity can be approximated by those for elastic-plastic materials with no limit on plastic strains. When the T stress and the stress intensity factor K are prescribed in the two-parameter boundary layer formulation to simulate the crack-tip constraint condition for a single-edge notch bend specimen of zirconia ceramics, our finite element computation shows a spear shape of the phase transformation zone which agrees well with the corresponding experimental observation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42782/1/10704_2004_Article_BF00018779.pd

An indentation methodology for measuring the elastic properties of biological patches used in human carotid endarterectomy

Carotid endarterectomy (CEA) is one of the approaches available for the treatment of atherosclerosis, a common carotid artery disease. Patch angioplasty is the pertinent technique mostly preferred by vascular surgeons. It entails an arteriotomy followed by closure with a textile, polymer or biological tissue patch. We propose a novel indentation methodology as a technique for mechanically characterizing biological patches used in carotid artery repair. The proposed methodology is a simple, yet accurate one, requiring only one initial experimental measurement to support the relevant calculations. Bovine pericardium patches are indented herein. Results, including material properties, are then obtained analytically. The experimental results indicate that indentation is a reliable method to assess the elastic properties of bovine patches. The modulus of elasticity and relevant indentation metrics are obtained for two commercial vascular bovine patches. © 2018 The Author(s)

A von Karman plate analogue for solving anti-plane problems in couple stress and dipolar gradient elasticity

The purpose of the present work is to present a direct analogy regarding the formulation and solution of anti-plane problems in the context of couple stress and dipolar gradient elasticity and the von Karman plate framework. We show aspects of boundary conditions in both theories of elasticity and propose a robust Finite Element methodology based on the von Karman plate theory in order to solve complex anti-plane (mode III) crack problems. Furthermore, we establish the equivalence between the anti-plane gradient elasticity J-Integral and the plate Ic-Integral (Sanders’ plate integral). In passing, we prove the path independency of the Ic-Integral. Finally we examine the near tip fields for both anti-plane and plate problems and establish possible strengthening effects due to the underlying microstructure. The proposed analogy is achieved through the von Karman plate theory where the plate is pre-stressed by a constant biaxial tension. The plate theory involves properties such as the plate thickness h, the Poisson's ratio ν and the bending stiffness D. This information, together with the pre-stress N transforms into properties required by the anti-plane couple stress and dipolar gradient elasticity problems: the shear modulus G, the internal length ℓ and the coefficient η. In both problems the two dimensional space remains the same, including the presence of cracks and other defects. The analogy permits numerical and analytical solutions of demanding anti-plane problems of gradient elasticity (couple stress and dipolar) utilizing the von Karman plate corresponding, and vice versa. © 201

Pretwisted beam subjected to thermal loads: A gradient thermoelastic analogue

It is well known from the classical torsion theory that the cross section of a prismatic beam subjected to end torsional moments will rotate and warp in the longitudinal direction. Rotation is depicted through the angle of twist per unit length and depends in general on the position along the length of the beam, while the warping function addresses the longitudinal distortion of the unrotated cross sections. In the present study, we consider a prismatic beam that possesses an initial twist which is constant along its length. A thermal field is present along the beam and its ends are loaded with axial forces and torsional moments. The governing equilibrium equations and the corresponding boundary conditions were obtained using an energy variational statement. A one-dimensional gradient thermoelastic analogue is developed. The advantageous aspect of the present study is that the additional (and peculiar) boundary conditions required by the gradient elasticity theory and the related microstructural lengths, analogous to micromechanical lengths, emerge in a natural way from the geometrical characteristics of the beam cross section and the material properties. We have examined various examples with different cross sections and loads to demonstrate the applicability of the model to the design of special yarns useful in smart textiles and thermally activated microdrilling actuators. © 2017 Taylor & Francis