Incubation time based testing of materials

Some principal features of the behavior of materials subjected to pulsed actions are common for a number of seemingly quite different physical processes, such as dynamic fracture (starting cracks and scabbing), cavitation in liquids, and electrical breakdown in solids. In this paper, we analyze examples illustrating typical dynamic effects inherent in these processes. We propose a unified interpretation for the fracture of solids and liquids and electrical breakdown in insulators using the structural-time approach based on the concept of the fracture incubation time. The examples of different physical processes considered in the paper show the fundamental importance of investigating incubation processes preparing abrupt structural changes (fracture and phase transitions) in continua under intense pulsed actions. The fracture incubation time is evidently a universal basic characteristic of the dynamic strength and must become one of the main material parameters to be experimentally determined (measured).     

Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.     

Vibrations of a solid sphere or shell of Functionally Graded Materials

We have solved the equation of equilibrium for torsional vibrations of a sphere in which the density and rigidity are functions of the radial distance and co-latitude. Making use of the particular forms of heterogeneity the exact frequency equations are derived. The work is motivated by the recent research activity on functionally graded materials (FGM), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications.     

Optimally designed renewal reward processes: General framework and applications

For physical and organizational systems which are regenerative in nature, certain mechanisms may be utilized to effect the time between regenerations. Those scenarios give rise to renewal processes with renewal distributions that are controllable at cost. We provide a unifying framework for optimal design of such processes in situations where certain parameter(s) of the renewal distributions can be manipulated at cost. Following the formulation of the general problem and discussion of some of its properties, we discuss three application areas where such situations arise. Those involve stochastic dispatching, labour turnover control, and design of repairable systems.     

The shortest path problem with two objective functions

We present methods to find the shortest path in a network where each path is associated with two objectives. We describe how to obtain the nondominated paths and the extreme nondominated paths, and compare the expected complexity of the methods. An improvement in efficiency can be obtained when quasiconcave or quasiconvex utility functions are assumed. In the first case, we describe how to find the optimal extreme nondominated path and bounds for the optimal path value. Then the optimal path can be located by calculating the k-th shortest path. In the second case we suggest a branch and bound method to solve the problem.     

Multiple target pattern creation and synchronization phenomena

It is shown how a random system of coupled nonlinear oscillators can synchronize due to multiple formation of target patterns. The time dependence of the averaged oscillation frequency in the system is estimated.     

The polarized absorption spectrum of 5-methyl indole in polyethylene and polyvinylalcohol films

The stretched film technique has been used to resolve the two overlapping ¹L_a and ¹L_b transitions of indole. 5-Methyl indole was studied as a model compound in two polymer matrices, polyethylene (PE) and polyvinylalcohol (PVA). The directions of the transition moments with respect to the long molecular axis are found to be in PE − 10° and +22° for ¹L_a and ¹L_b, respectively. These angles are found to be −25° and +29° in PVA. ¹L_a has two prominent vibrations in PE at 2040 and 2895 cm⁻¹ from the origin. ¹L_b has four prominent vibrations in PE at 761, 1308, 1937 and 3196 cm⁻¹ from the origin. In PVA, ¹L_a has two prominent vibrations at 2149 and 2874 cm⁻¹ from the origin and ¹L_b has four prominent vibrations at 1049, 1352, 2229 and 3196 cm⁻¹ from the origin.