Crack propagation in the power-law nonlinear viscoelastic material

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The creep incompressilility assumption is used. To simulate fracture behavior of craze region, it is assumed that in the fracture process zone near the crack tip, the cohesive stress sigma(f) acts upon the crack surfaces and resists crack opening. Through a perturbation method, i. e., by superposing the Mode-I applied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelastic problem is reduced to linear problem. For weak nonlinear materials, for which the power-law index n similar or equal to 1, the expressions of stress and crack surface displacement are derived. Then, the fracture process zone local energy criterion is proposed and based on which the formulas of cracking incubation time t

Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given. (C) 2002 Published by Elsevier Science Ltd.

Nonlinear fatigue damage model based on the residual strength degradation law

In this paper, a logarithmic expression to describe the residual strength degradation process is developed in order to fatigue test results for normalized carbon steel. The definition and expression of fatigue damage due to symmetrical stress with a constant amplitude are also given. The expression of fatigue damage can also explain the nonlinear properties of fatigue damage. Furthermore, the fatigue damage of structures under random stress is analyzed, and an iterative formula to describe the fatigue damage process is deduced. Finally, an approximate method for evaluating the fatigue life of structures under repeated random stress blocking is presented through various calculation examples.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Monte Carlo approaches to nonlinear optimal control

This paper explores the use of Monte Carlo techniques in deterministic nonlinear optimal control. Inter-dimensional population Markov Chain Monte Carlo (MCMC) techniques are proposed to solve the nonlinear optimal control problem. The linear quadratic and Acrobot problems are studied to demonstrate the successful application of the relevant techniques.