A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers

We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material’s properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions.     

A variational constitutive framework for the nonlinear viscoelastic response of a dielectric elastomer

We formulate a variational constitutive framework that accounts for nonlinear viscous behavior of electrically sensitive polymers, specifically Dielectric Elastomers (DEs), under large deformation. DEs are highly viscoelastic and their actuation response is greatly affected in dynamic applications. We used the generalized Maxwell model to represent the viscoelastic response of DE allowing the material to relax with multiple mechanisms. The constitutive updates at each load increment are obtained by minimizing an objective function formulated using the free energy and electrostatic energy of the elastomer, in addition to the viscous dissipation potential of the dashpots in each Maxwell branch. The model is then used to predict the electromechanical instability (EMI) of DE. The electro-elastic response of the DE is verified with available analytical solutions in the literature and then the material parameters are calibrated using experimental data. The model is integrated with finite element software to perform a variety of simulations on different types of electrically driven actuators under various electromechanical loadings. The electromechanical response of the DE and the critical conditions at which EMI occurs were found to be greatly affected by the viscoelasticity. Our model predicts that under a dead load EMI can be avoided if the DE operates at a high voltage rate. Subjected to constant, ramp and cyclic voltage, our model qualitatively predicts responses similar to the ones obtained from the analytical solutions and experimental data available in the literature.     

The tricriteria flowshop scheduling problem

Multicriteria flowshop scheduling problems have been one of the most attractive subjects in recent years. In the multicriteria flowshop scheduling literature, a very limited number of studies have been performed on problems which include a tardiness criterion. In this paper a multicriteria (tricriteria) two-machine flowshop scheduling problem with a tardiness criterion is tackled. The objective is to minimise a weighted sum of total completion time, total tardiness and makespan. An integer programming model is proposed for the problem which belongs to NP-hard class. The modified NEH (Nawaz, Enscore and Ham) algorithm, a tabu search-based heuristic method, random search and the EDD rule (the earliest due date rule) are used to solve problems with up to 2,500 jobs. A computational analysis is conducted to evaluate the performance of the heuristics. The analysis shows that the heuristics are quite efficient, and the performance of the tabu search based heuristic is the best of all in terms of solution quality.     

Cube probe structures for integrated near-field scanner module

Two new miniature near-field 'cube probe' structures for EMC/EMI measurements are proposed. Their performances are compared to those of the classical H-field loop probe in two orthogonal planes. The single cube probe effectively replaces three conventional orthogonally oriented loops. An array of cube probes is also proposed to form a near-field scan module dedicated to the characterisation of integrated circuit radiated emissions.     

Thermal cycles effects on interlaminar shear strength (ILSS) and impact behaviour of carbon/PEI composites

In this paper, the effect of thermal cycle on the interlaminate shear strength (ILSS) and impact behaviour of unidirectional carbon fibre reinforced polyetherimide (PEI) matrix composites were studied. Samples were subjected to 100 thermal cycles (by immersing from boiling water (100°C) to ice water (0°C). The effects of thermal cycles were characterized by short beam shear and instrumented impact testers. Also Fractographic investigations were done using a scanning electron microscope (SEM). It is observed that the plastic deformations at the fibre/matrix and interlaminar interface as well as residual stresses lower the ILSS and flexural modulus of the material proportional with the number of thermal cycles. Up to the first 20 thermal cycles the material shows a brittle fracture with lower fracture energy, but after the 20th thermal cycles it is possible to observe that the material fractures with higher fracture energy at longer fracture time. A remarkable difference in the fracture morphology between the thermal cycled and un-treated materials has been observed. It is found that thermal cycles strictly affect the fracture morphology.     

Optimal Power Allocation in an Amplify-and-Forward Untrusted Relay Network with Imperfect Channel State Information

The characteristics of the wireless medium create difficulty to shield the data transmission from unauthorized recipients. In this paper, power optimization in an amplify-and-forward untrusted relay network is presented, using cooperative jamming transmission to prevent the untrusted relay from intercepting the confidential signals. Considering imperfect channel estimation error at the destination, an optimal power allocation (OPA) is designed to maximize the achievable secrecy rate for the network. Simplified OPA is derived for high signal-to-noise ratio regime with imperfect CSI and the ergodic secrecy rate is also analyzed to evaluate the achievable average secrecy rate for different scenarios as a common performance metric. The numerical results show that when the error of CSI is considered, the proposed OPA generates limited and acceptable degradation on the secrecy rate.     

Multi-time scale zero-sum differential games with perfect state measurements

We obtain necessary and sufficient conditions for the existence of approximate saddle-point solutions in linear-quadratic zero-sum differential games when the state dynamics are defined on multiple (three) time scales. These different time scales are characterized in terms of two small positive parameters ₁, and ₂, and the terminology approximate saddle-point solution is used to refer to saddle-point policies that do not depend on ₁ and ₂, while providing cost levels withinO(₁) of the full-order game. It is shown in the paper that, under perfect state measurements, the original game can be decomposed into three subgames-slow, fast and fastest, the composite saddle-point solution of which make up the approximate saddle-point solution of the original game. Specifically, for the minimizing player, it is necessary to use a composite policy that uses the solutions of all three subgames, whereas for the maximizing player, it is sufficient to use a slow policy. In the finite-horizon case this slow policy could be a feedback policy, whereas in the infinite-horizon case it has to be chosen as an open-loop policy that is generated from the solution and dynamics of the slow subgame. These results have direct applications in theH -optimal control of three-time scale singularly perturbed linear systems under perfect state measurements.Research supported in part by the National Science Foundation under Grant ECS 91-13153, and in part by the U.S. Department of Energy under Grant DE-FG-02-88-ER-13939. This paper is dedicated to the memory of John Breakwell.     

Robust mean field games for coupled Markov jump linear systems

We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents’ individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.