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Papers by Oliver O'Reilly

International Journal of Non-Linear Mechanics, 2006

ASME 2009 Summer Bioengineering Conference, Parts A and B, 2009

ABSTRACT Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Associat... more ABSTRACT Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

International Journal of Non-Linear Mechanics, 2005

ABSTRACT As attractive alternatives to a set of three Euler angles, the rotation of a rigidly def... more ABSTRACT As attractive alternatives to a set of three Euler angles, the rotation of a rigidly deforming body is often represented using four or more parameters. The accompanying parameter constraints introduce generalized constraint forces in the equations of motion which can often negate the benefits of a particular parameterization. In this paper, we discuss situations where the parameter constraints are not imposed. Thus, although the body no longer deforms rigidly, it does deform homogeneously. This allows the theory of a Cosserat point (or, equivalently, the theory of a pseudo-rigid body) to be used to establish equations governing its motion. Earlier work on this topic by O’Reilly and Varadi considered the four Euler parameters and the single Euler parameter constraint. Here, we consider Poincaré's six parameter representation of a rotation tensor, and, complementing earlier work, discuss numerical implementation and representative simulations. One of the contributions of this paper is the development of a viscoelastic Cosserat point, whose equations of motion are free from parameter constraints and singularities, that can be used to approximate the motion of a rigid body.

International Journal of Solids and Structures, 2005

Numerous systems can be described using masses and rods in transverse vibration. Motivated by the... more Numerous systems can be described using masses and rods in transverse vibration. Motivated by the desire to model the effects of axial strain and temperature on systems of this type, we develop a procedure to determine the frequencies of transverse vibration of devices composed of rods and rigid masses as functions of these effects. Our models allow for the rods

Regular and Chaotic Dynamics, 2008

In the 1950s and 1960s, Charles F. Taylor designed and tested various prototype one-wheeled vehic... more In the 1950s and 1960s, Charles F. Taylor designed and tested various prototype one-wheeled vehicles. These machines were stabilized and steered using gyroscopes. In this paper, a simple model of a one-wheeled vehicle is presented and analyzed. This analysis explains the ability of these machines to exhibit stable steady motions.

Physical Review Letters, 2007

Multibody System Dynamics, 2010

Mathematics and Mechanics of Solids, 2002

Mathematics and Mechanics of Solids, 2011

Abstract Motivated by studies on a type of brain injury known as diffuse axonal injury, the dynam... more Abstract Motivated by studies on a type of brain injury known as diffuse axonal injury, the dynamic azimuthal shearing of a mixture of a transversely isotropic viscoelastic material which is surrounded by a softer isotropic viscoelastic material is considered. It is ...

Journal of Elasticity, 2006

The influences of transverse and rotational symmetries on the strain-energy functions of elastic ... more The influences of transverse and rotational symmetries on the strain-energy functions of elastic rods are discussed. Complete function bases are presented and, for some constrained theories, these bases are also proven to be irreducible. The treatment of symmetry is based on a reformulation of a recent work by Luo and O’Reilly. It is also shown how this work relates to existing treatments by Antman and Healey for a particular constrained rod theory.

Journal of Applied Mechanics, 2001

Journal of Applied Mechanics, 2004

ABSTRACT We consider the dynamics of a closed loop of inextensible string which is undergoing an ... more ABSTRACT We consider the dynamics of a closed loop of inextensible string which is undergoing an axial motion. At each instant, one material point of the string is in contact with a singular supply of linear momentum (also known as an external constraint). Several peculiar features of this problem which have not been previously discussed are presented. These include the possible presence of an arbitrary number of kinks, the vanishing nature of the singular supply of momentum, and the critical nature of the tension in the string. When the linear momentum is supplied by a mass-spring-dashpot system, we are also able to establish an exact expression for the frequency of the resulting vibrations, prove that dissipation cannot be present, show that these vibrations only occur for discrete speeds of axial motion, and establish that Coulomb friction is absent.

International Journal of Engineering Science, 2004

International Journal of Engineering Science, 2011

Structures featuring rod-like bodies connected in a branched ensemble are ubiquitous. They appear... more Structures featuring rod-like bodies connected in a branched ensemble are ubiquitous. They appear in antennae, replicating DNA strands, and, most visibly, in the plant kingdom. In spite of this, modeling these branched structures using rod theories have received little attention in the literature. With the help of a general rod theory, which was originally developed by Green and Naghdi, balance laws for these structures are discussed. The governing equations established are then shown to be equivalent to variational principles for tree-like structures. These principles are adopted from works by Ivanov and Tuzhilin and may lead to the development of nonlinear stability criteria for these structures. It is also shown how the conditions at a branching point in these structures can be understood using recent interpretations of Eshelby’s work on material (configurational) forces in adhesion problems. The static configurations are illuminated for several structures using Euler’s theory of the elastica. Instances of multiple possible configurations and novel extensions to the classical problem of the tallest column are also discussed.

European Journal of Mechanics - A/Solids, 2007

Biomechanics and Modeling in Mechanobiology, 2012

ABSTRACT In many applications of rod theories as models for plant stem growth and development, it... more ABSTRACT In many applications of rod theories as models for plant stem growth and development, it is necessary to allow the intrinsic curvature and flexural stiffness of the rod to evolve. In the present paper, the application of evolution equations for these quantities is examined and a new evolution equation for the intrinsic curvature is proposed. To illustrate the new evolution equation, several examples of the evolution of rods in the presence of external forces and tip growth are presented. Growth in plants frequently results in residual stresses and the compatibility of rod models with these fields is also discussed.

Acta Mechanica, 2003

Summary. This paper discusses the dynamics of strings which are subject to the presence of singul... more Summary. This paper discusses the dynamics of strings which are subject to the presence of singular sources of momentum and energy. Such sources arise naturally in many problems featuring axially moving strings and have been the subject of several recent works. The contribution of the present paper is to present new results pertaining to the time rate of change of

Acta Mechanica, 1995

Summary The equations of motion describing the non-linear behavior of a perfectly flexible travel... more Summary The equations of motion describing the non-linear behavior of a perfectly flexible travelling cable are derived from first principles. Influences due to changes in the cross-sectional area of the cable and mass conservation are included. A homogenous isotropic non-linearly elastic cable material is assumed and the qualitative nature of a class of its equilibria is analyzed. The dependence of