Experimental method of dynamic caustics and its application in fracture mechanics

The equation of static and dynamic caustics, and the formulae determining the position of crack tip and stress intensity factor are given. It is proven that for the case of low speed of crack propagation the static formula is applicable in calculation. A simple method to measure the static stress-optical constants is proposed. An Optical system which is suitable for the experiments of dynamic caustics was set-up and used to study the fracture in beam and rings with initial crack under impact loading. A series of dynamic caustics' photographs and curves showing the variations of corresponding crack lengths and dynamic stress intensity factors with time, are presented.     

Violent societies: an application of orbital decomposition to the problem of human violence

This study uses orbital decomposition to analyze the patterns of how governments lose their monopolies on violence, therefore allowing those societies to descend into violent states from which it is difficult to recover. The nonlinear progression by which the governing body loses its monopoly is based on the work of criminologist Lonnie Athens and applied from the individual to the societal scale. Four different kinds of societies are considered: Those where the governing body is both unwilling and unable to assert its monopoly on violence (former Yugoslavia); where it is unwilling (Peru); where it is unable (South Africa); and a smaller pocket of violent society within a larger, more stable one (Gujarat). In each instance, orbital decomposition turns up insights not apparent in the qualitative data or through linear statistical analysis, both about the nature of the descent into violence and about the progression itself.     

Improvement of a pressure gradient method and its application to an unsteady flow problem

The pressure gradient method using velocity components and components of a pressure gradient as dependent variables has been modified to solve incompressible Newtonian fluid flow problems numerically. Applying this modified method to unsteady-state development of flow in a circular cavity shows that, at least for the case of a low Reynolds number flow, relative errors produced by the proposed method are smaller for most time intervals than those produced by the primitive velocity-pressure variable method and by the standard pressure gradient method. Also it is found that the modified and standard pressure gradient methods can be applied to the unsteady circular cavity flow at a moderate Reynolds number of at least up to 200.     

Revisit to the determination of stress-intensity factors and J-integrals using the caustics method

Applications of the optical (shadow) method of reflective caustics to measurement of the stress-intensity factor andJ integral in various specimens are investigated. The necessary experimental requirements to help determine accurate stress-intensity factor andJ integral are described. The ratios ofr _o (radius of initial curve)/r _p (plastic-zone size) andr _o/t(thickness of specimen) are found to be very important experimental parameters to obtain meaningful stress and/or strain intensities surrounding crack tips. The appropriate ranges to determine accurate values of stress-intensity factor andJ integral for polycarbonate (compact tension) and aluminum (c-shaped tension) specimens are presented. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Variational formulation of the equivalent eigenstrain method with an application to a problem with radial eigenstrains

In this paper a variational formulation of the equivalent eigenstrain method is established. A functional of the Hashin–Shtrikman type is proposed such that the solution of the equivalent eigenstrain equation is a unique minimizer of the functional. Moreover, it is also shown that the equivalent eigenstrain equation is the Euler–Lagrange equation of the potential energy of the inclusions. An approximate solution of the equivalent eigenstrain equation is then found as a minimizer of the functional on a finite dimensional span of basic eigenstrains. Special attention is paid to possible symmetries of the problem. The variational formulation is illustrated by determination of effective linear elastic properties. In particular, material with a simple cubic microstructure is considered in detail. A solution for the polynomial radial basic eigenstrains approximation is found. In particular, for the homogeneous eigenstrain approximation, the effective moduli are derived in an exact closed form.     

Analytical solution of the overdetermined inverse heat conduction problem with an application to monitoring thermal stresses

The paper presents a technique for determining the transient temperature distribution, when input data as thermocouple responses are known at several interior locations. If the temperature field is known, then the thermal stresses can be calculated. The problem is overdetermined and is solved using a least squares method that minimizes the error between the computed and measured thermocouple temperatures. The present method incorporates the advantages of simplicity and accuracy of analytical solutions. Several numerical examples and measurements are presented as an indication of the accuracy of the presented method. Received on 10 January 1997     

Multigrid method application to solve the tire rolling problem

The efficiency of a geometric multigrid method for solving the tire rolling problem is studied. The optimal components of this method are chosen. A good convergence of the method is shown for the systems that are large from the practical point of view. Its distinctive feature is a grid refinement in the circumferential direction only.     

Comparison of the techniques of transmitted caustics and photoelasticity as applied to fracture

A comparison of the optical techniques of photoelasticity and caustics as applied to fracture mechanics is presented. Static as well as dynamic experiments were conducted using the two methods with the same specimen geometry and under the same loading conditions. The results for the crack-tip stress-intensity factor as a function of crack length were obtained from both techniques in three different specimen geometries. A comparison of the results shows good agreement under static conditions but large differences for running cracks.     

The whiplash problem: an application of vector spherical harmonics

A brief discussion of an alternate method for finding the displacements of an elastic, homogeneous, isotropic sphere under a rotational loading is given. The method is shown to be applicable to nonconservative loadings and asymmetric geometry. Expressions for the strains and stresses are also given.     

The effects of surface topography on the method of caustics

An investigation was performed to establish the effects of surface topography on the determination of stress intensity factors of opaque components using the method of caustics. Theoretical predictions of caustics produced by curved surfaces were generated and validated by experiment. The errors introduced for stress intensity factors determined at various radii of curvature were assessed. It was found that relatively small surface curvatures caused significant errors in the stress intensity factor. These errors were affected by the initial radius, load and material properties.     

Some guidelines for an easier application of Popov's stability test

This paper compares the graphical and root-locus versions of Popov's stability test. The main purpose of the paper is to make possible the application of Popov's Method for a variety of non-linear elements.The various sectors of confinement are analyzed in detail for different non-linearities, and results are summarized in a table. The paper represents by itself a guide, permitting easier practical application of Popov's criterion, under different conditions.     

Analytical and numerical investigation on the tempered time-fractional operator with application to the Bloch equation and the two-layered problem

Nonlinear Dynamics - In the continuous-time random walk model, the time-fractional operator usually expresses an infinite waiting time probability density. Different from that usual setting, this...     

Experimental determination of the dynamic stress-intensity factor using caustics and photoelasticity

The methods of photoelasticity and caustics were used in conjunction with high-speed photography to determine the dynamic stress field near a moving crack. The photographs were analyzed to extract information on crack speed and the dynamic stress-intensity factor. The stress-intensity-factor histories obtained from both techniques were compared to determine the reliability of the two techniques.     

Magneto-electro-elastic coated inclusion problem and its application to magnetic-piezoelectric composite materials

In this work, a micromechanical model for the estimate of the magneto-electro-elastic behavior of the magnetic-piezoelectric composites with coated reinforcements is proposed. The coating is considered as a thin layer with properties different from those of the inclusion and the matrix. The micromechanical approach based on the Green’s functions techniques and on the interfacial operators is designed for solving the magneto-electro-elastic inhomogeneous coated inclusion problem. The effective magneto-electro-elastic properties of the composite containing thinly coated inclusions are obtained through the Mori–Tanaka’s model. Numerical investigations into magneto-electro-elastic moduli responsible for the magneto-electric coupling are presented as functions of the volume fraction and characteristics of the coated inclusions. Comparisons with existing models are presented for various shape and orientation of the coated inclusions.