Lawrence Schovanec

The energy release rate for a quasi-static mode I crack in a nonhomogeneous linearly viscoelastic body

Abstract The Energy Release Rate (ERR) for the quasi-static problem of a semi-infinite mode I crack propagating through an inhomogeneous isotropic linearly viscoelastic body is examined. The shear modulus is assumed to have a power-law dependence on depth from the plane of the crack and a very general behavior in time. A Barenblatt type failure zone is introduced in order to cancel the singular stress and a formula for the ERR is derived which explicitly displays the combined influences of material viscoelasticity and inhomogeneity. The ERR is calculated for both power-law material and the standard linear solid and the qualitative features of the ERR are presented along with numerical illustrations.

The Control and Mechanics of Human Movement Systems

Issues that are central to the modeling and analysis of a human movement system include (1) musculotendon dynamics, (2) the kinetics and kinematics of the biomechanical system, and (3) the relationship between neurological control and the formulation of the system as an open or closed loop process. This paper will address these problems in the context of two particular movement systems. The first to be addressed is the human ocular system. Eye movement systems are ideal for studying human control of movement since they are of relatively low dimension and easier to control than other neuromuscular systems. By scrutinizing the trajectories of eye movements it is possible to infer the effects of motoneuronal activity, deduce the central nervous system’s control strategy, and systematically observe the effects of perturbations in the controls. An application of the locomotory-control system will also be presented in this paper. In particular, a model of human gait is developed for the purpose of relating neural controls to the state of stress in a skeletal member. This is achieved by modeling the human body as an ensemble of articulating rigid-body segments controlled by a minimal muscle set. Neurological signals act as the input into the musculotendon dynamics and from the resulting muscular forces, the joint moments and resulting motion of the segmental model are derived.

The quasi-static propagation of a plane strain crack in a power-law inhomogeneous linearly viscoelastic body

SummaryAn analysis is presented of the steady-state propagation of a semi-infinite mode I crack for an infinite inhomogeneous, linearly viscoelastic body. The shear modulus is assumed to have a power-law dependence on depth from the plane of the crack. Moreover, both a general and a power-law behavior in time for the shear modulus are considered. A simple closed form expression for the normal component of stress in front of the propagating crack is derived which exhibits explicitly the form of the stress singularity and its material dependency. The crack profile is examined and its dependence on the spatial and time behavior of the shear modulus is determined.

A dynamic 3-D model of ocular motion

Eye movement systems are ideal for studying human control of movement, since they are of relatively low dimension and easier to control than other neuromuscular systems. This paper presents a model for the dynamics of 3D eye rotation. The system that is presented incorporates muscle mass, general nonlinear musculotendon dynamics and activation dynamics that couple neural controls that are appropriate for saccadic movements to the muscle mechanics. The approach taken in this paper emphasizes a forward or direct dynamic approach that results in a natural flow of neural-to-muscular-to-movement events while utilizing physiologically realistic models of the musculotendon actuators. Numerical simulations illustrate that the model successfully simulates saccadic movements and accurately depicts eye position, velocity and muscle tension.

Quasi-static mode III fracture in a nonhomogeneous viscoelastic body

SummaryAn analysis is presented of the quasi-static propagation of a semi-infinite mode III crack in an inhomogeneous isotropic viscoelastic body. A shear modulus is assumed of the formG(t,y)=μ(t)η(y) where |y| denotes the distance measured from the plane of the crack and μ(t) is a positive, nonincreasing, convex function of time. A closed form expression is derived for the energy release rate (ERR) when a Barenblatt type failure zone is incorporated into the crack model. Numerical and asymptotic results illustrate the combined effects of viscoelastic properties, material inhomogeneity, and the failure zone at the crack tip upon the ERR.

A Griffith crack problem for an inhomogeneous elastic material

SummaryThis paper examines the problem of a Mode I crack in a nonhomogeneous elastic medium. It is assumed that the shear modulus varies exponentially with the coordinate perpendicular to the plane of the crack. The problem is reduced to a Fredholm integral equation and in terms of its solution the normal components of stress and displacement are described. Expressions are also derived for the stress intensity factor and the crack energy. The effect of the inhomogeneity is examined and comparisons made with the corresponding results for the homogeneous material.

A forward dynamic model of gait with application to stress analysis of bone

A model of human gait is developed for the purpose of relating neural controls to the state of stress in a skeletal member. This is achieved by implementing a forward dynamic model of gait in which the human body is modeled as an ensemble of articulating rigid-body segments controlled by a minimal muscle set. Neurological signals act as the input into musculotendon dynamics. Prom the muscular forces, the joint moments and resulting motion of the segmental model are derived. At fixed moments in the gait cycle, the joint torques and joint reaction forces are incorporated into an equilibrium analysis of the segmental elements, modeled as elastic bodies undergoing biaxial bending.

An anti-plane crack in a nonhomogeneous viscoelastic body

A quasi-static analysis of an anti-plane strain crack in a radially inhomogeneous viscoelastic material is carried out. Laplace and Mellin transform methods are used to construct explicit expressions for the stress and displacement fields. Results show that the stress field may exhibit both logarithmic and power-law type singularities and for special cases of material inhomogeneity the asymptotic behavior at the crack tip is determined by a logarithmic singularity. The effects of time and material inhomogeneity upon the stresses and displacements are numerically illustrated.

Dynamic steady-state mode III fracture in a nonhomogeneous viscoelastic body

SummaryThe problem of a propagating semi-infinite mode III crack in an infinite inhomogeneous viscoelastic body is analyzed. Inertial effects are included in the equation of motion while the crack is assumed to propagate with a fixed speed. Material inhomogeneity is introduced into the problem by assuming a shear modulus of the formG(t, y)=μ(t) η(y) where |y| denotes the distance measured from the plane of the crak and μ(t) is a positive, nonincreasing, convex function of time. Expressions for the stress and displacement are derived from the solution to the corresponding Riemann-Hilbert problem. A closed form expression is derived for the energy release rate (ERR) when a Barenblatt type failure zone is incorporated into the crack model. Numerical results illustrate the combined effects of viscoelastic properties, material inhomogeneity, and the crack tip failure zone upon the ERR.

A control model of eye movement

The model of the oculomotor system that presented concentrates upon the horizontal version eye tracking system. The major objective of the work here is to incorporate the known actuation and musculotendon dynamics into the plant model of the eye. In particular, the muscle model that is utilized is a two-component version of a Hill type model that consists of a passive and active contractile components. The approach presented allows for the inclusion of very general force-velocity and force-length characteristics in the active component. Furthermore, the model developed allows one to distinguish between the elastic and viscous effects in the muscle actuator that are neurologically controlled and those that are due to the passive structure of the actuator. In this paper, attention is focused upon saccadic eye movements. The eye model described includes activation dynamics that couple neural controls which are appropriate for saccadic movements to the muscle mechanics.