Shingo Ozaki

Finite Element Analysis of Precursors to Macroscopic Stick–Slip Motion in Elastic Materials: Analysis of Friction Test as a Boundary Value Problem

AbstractIn this study, we apply the finite element method to investigate precursor to frictional sliding phenomena arising immediately prior to macroscopic stick–slip transitions in elastic bodies within the framework of a continuum theory. Using a numerical model that mimics an actual experimental system, we study the behavior of contact surface nodes to assess the influence of stiffness, driving velocity, initial conditions, and discretization conditions on the propagation characteristics of microscopic slips. In particular, we show that the initial distribution of frictional stress arising due to the Poisson effect has a significant effect on the propagation characteristics in slip regions. Next, based on the results of a finite element analysis of precursor phenomena that accounts for the influence of bulk compliance, we consider the determination of parameters in rate-dependent friction models. With regard to the behavior of sliding friction, we show that the relationship between friction tests and friction models is fundamentally different from the relationship between materialtests and constitutive models for material deformation. We conclude that a proper understanding and classification of friction tests, friction models, and the relationship between these tests and boundary value problems are crucial ingredients in the application of computer-aided engineering techniques to sliding-friction phenomena; indeed, friction tests must ultimately be treated as boundary value problems.

Finite element analysis of rate- and state-dependent frictional contact behavior

In the present study, the rate- and state-dependent friction model [Hashiguchi and Ozaki, 2008] is implemented in the dynamic finite element method. The typical rate- and state-dependent frictional contact problems, which are consisted by elastic and rigid bodies having simple shapes, are then analyzed by the present method. The validity of the present method for the microscopic sliding and stick-slip instability is examined under various dynamic characteristics of the system, such as contact load, elastic stiffness, driving velocity and frictional properties. It is shown that the present method can solve simultaneously not only rate- and state-dependent frictional behavior on the contact boundary but also coupling effects with internal deformations, whereas it cannot predicted by the conventional finite element analysis with the Coulomb’s friction law.

Elastoplastic analogy constitutive model for rate-dependent frictional sliding

The aim of this study is to propose a numerical approach for analyzing stick-slip motion; the approach is based on the finite element method implemented using an elastoplastic analogy constitutive model for rate-dependent frictional sliding. The present rate-dependent friction model can rationally describe the reciprocal transition between the static friction and the kinetic friction by a unified formulation. The rate-dependent friction model is implemented to FEM by using the user subroutine of the commercial software package. Then, the typical FE analysis of stick-slip motion is carried out. From the results of the FE analysis, we report that the present FE approach is applicable to the practical contact boundary value problems, including stick-slip motion.

PREDICTION OF MAXIMUM MOMENT OF CIRCULAR TUBES SUBJECTED TO PURE BENDING IN CONSIDERATION OF THE LENGTH EFFECT

In the present study, the bending collapse of an elastoplastic cylindrical tube subjected to static pure bending is investigated using the finite element method (FEM). The moment of the elastoplastic cylindrical tube is controlled by the flattening rate of the tube cross-section. For a long tube, the flattening rate can be expressed in terms of the axial and circumferential stresses that, in turn, depend on the material and geometrical properties and the curvature of the tube. On the other hand, for a short tube, the boundary condition of the fixed walls prevents the flattening rate. In order to account for the length effect of tubes, we propose a new method in which flattening is considered as a deflection problem of a fixed curved beam. The proposed method was able to predict the change in the flattening rate as the curvature was increased. A rational prediction method is proposed for estimating the maximum bending moment of cylindrical tubes that accounts for the length effect. Its validity is demonstrated by comparing it predictions with numerical results obtained using the finite element method.

Analysis of Stick-Slip Motion by the Rate-Dependent Friction Model

In this study, the rate-dependent subloading-friction model, which can rationally describe the reciprocal transition of static-kinetic frictions by the unified formulation, is proposed. Then, the one-dimensional model of spring-mass system is implemented by incorporating the present friction model, and is applied to simulations of stick-slip motion. Further, we verified the validity of the present approach for the stick-slip motion by numerical experiments under various dynamic conditions.