Rate-, state-, and pressure-dependent friction model based on the elastoplastic theory

Adhesion is one of essences with respect to rubber friction because the magnitude of the friction force is closely related to the magnitude of adhesion on a real contact area. However, the real contact area during sliding depends on the state and history of the contact surface. Therefore, the friction force occasionally exhibits rate-, state-, and pressure dependency. In this study, to rationally describe friction and simulate boundary value problems, a rate-, state-, and pressure-dependent friction model based on the elastoplastic theory was formulated. First, the evolution law for the friction coefficient was prescribed. Next, a nonlinear sliding surface (frictional criterion) was adopted, and several other evolution laws for internal state variables were prescribed. Subsequently, the typical response characteristics of the proposed friction model were demonstrated, and its validity was verified by comparing the obtained results with those of experiments conducted considering the contact surface between a rough rubber hemisphere and smooth acrylic plate.

CONTACT PROBLEMS AND DUAL VARIATIONAL INEQUALITY OF 2－D ELASTOPLASTIC BEAM THEORY

In Order to study the frictional contact problems of the elastoplastic beam theory,an extended two-dimensional beam model is established, and a second order nonlinear equilibrium problem with both internal and external complementarity conditions is proposed. The external complementarity condition provides the free boundary condition. while the internal complemententarity condition gives the interface of the elastic and plastic regions. We prove that this bicomplementarity problem is equivalent to a nonlinear variational inequality The dual variational inequality is also developed.It is shown that the dual variational inequality is much easier than the primalvariational problem. Application to limit analysis is illustrated.

A population-feedback control based algorithm for well trajectory optimization using proxy model

Wellbore instability is one of the concerns in the field of drilling engineering.This phenomenon is affected by several factors such as azimuth,inclination angle,in-situ stress,mud weight,and rock strength parameters.Among these factors,azimuth,inclination angle,and mud weight are controllable.The objective of this paper is to introduce a new procedure based on elastoplastic theory in wellbore stability solution to determine the optimum well trajectory and global minimum mud pressure required(GMMPR).Genetic algorithm(GA) was applied as a main optimization engine that employs proportional feedback controller to obtain the minimum mud pressure required(MMPR).The feedback function repeatedly calculated and updated the error between the simulated and set point of normalized yielded zone area(NYZA).To reduce computation expenses,an artificial neural network(ANN) was used as a proxy(surrogate model) to approximate the behavior of the actual wellbore model.The methodology was applied to a directional well in southwestern Iranian oilfield.The results demonstrated that the error between the predicted GMMPR and practical safe mud pressure was 4%for elastoplastic method,and 22%for conventional elastic solution.

A generalized dilatancy angle equation of granular soil

This paper presents a generalized dilatancy angle equation of granular soil to cover not only the drained tests but also the undrained tests by introducing a generalized structure of soil:soil skeleton formed by soil particles and the fluid in soil voids,under the assumptions of the incompressibility of soil particles and the compressibility of the fluid in soil voids.For the drained tests,the generalized dilatancy angle equation of granular soil would be degenerated to its current dilatancy angle equation.However,for the undrained tests,the generalized dilatancy angle equation of granular soil was derived with aλparameter that was related to the stress-strain state of soil and the nature of the fluid in soil voids.Theλparameter was determined by the initial dilatancy angles of granular soil at the onset of shearing on the same initial state of the soil in the drained and undrained tests.In addition,the generalized dilatancy angle equation of granular soil was verified for application in calculation of the dilatancy angles of sands in the drained and undrained tests.