T. A. Angelov

A SECANT-MODULUS METHOD FOR A RIGID-PLASTIC ROLLING PROBLEM

Abstract A steady-state rolling problem for rigid-plastic, strain-rate sensitive, slightly compressible materials is considered. A variational formulation in a variational inequality form is given. Existence and uniqueness results are obtained, and the convergence of a method of linearization, called the secant-modulus method by an analogy with Kachanovs (secant-modulus) method for elasto-plastic problems, is proved.

Infinite elements—theory and applications

Abstract The possibilities for solving numerically defined problems in infinite or semi-infinite domains by a combination of finite and infinite elements is considered. A review of the available infinite element formulations is made. A new infinite element technique is presented and tested for one- and two-dimensional problems.

A THERMOMECHANICALLY COUPLED ROLLING PROBLEM WITH DAMAGE

In hot metal-forming processes such as rolling, the material properties can vary considerably with the temperature. During the processes heat is generated due to the plastic deformation and friction and is lost due to radiation and convection to the environment and conduction to the rolls. Furthermore, at elevated temperatures, plastic deformations can lead to a material damage accumulation, due to microstructural changes. In ductile materials almost all material damage occurs as a consequence of nucleation and growth of microvoids. Thus the consideration of all these effects in the analysis of hot rolling processes is very important. This requires coupled thermomechanical rolling problems, incorporating adequate thermomechanical material damage and friction models, to be stated and studied and efficient numerical methods for computer simulation of the processes to be developed. Steady-state and transient thermomechanically coupled hot rolling problems for rigidplastic(viscoplastic), incompressible or slightly compressible, rate sensitive and or hardening materials, were considered in [1 - 4], as usually a constant Coulomb or Siebel friction law for the roll-workpiece interface was accepted. The computational experiments are usually based on the finite element method applied to the virtual power and the energy balance

Finite-element analysis of a hot-rolling problem with nonlinear friction

Abstract An isotermal, steady-state, hot-rolling problem of a workpiece with rectangular profile is considered. The workpiece material is assumed to be rigid-plastic, strain-rate sensitive and slightly compressible. The existence of a thin layer is supposed, where nonlinear Siebels type friction is assumed to hold. Several examples of rolling problems at different rolling conditions are solved numerically by an finite-element-secant-modulus method. Comparisons with experimental results are performed. The effect of the friction factor, workpiece reduction and rolling velocity on the relative contact velocity, roll pressure and effective strain rates is illustrated and discussed.

ANALYSIS OF A RIGID-PLASTIC ROLLING PROBLEM WITH SLIGHTLY COMPRESSIBLE MATERIAL MODEL

A steady-state rolling problem with rigid-plastic, strain-rate sensitive, slightly compressible material model and nonlinear Coulomb friction law is considered. For the corresponding variational problem, existence, uniqueness and convergence results, at compressibility parameter approaching zero, are obtained. A regularized variational problem is stated and studied and its finite element approximation is analyzed. Two computational algorithms are proposed and applied to solve an illustrative example.

SOLVABILITY OF A QUASI-STEADY ROLLING PROBLEM WITH SLIGHTLY COMPRESSIBLE MATERIAL MODEL

A quasi-steady rolling problem with slightly compressible, rigid-viscoplastic and isotropic hardening material model and nonlinear Coulomb friction law are studied. The problem is stated in the form of a nonlinear variational inequality coupled with an equivalent strain evolution equation. Under restrictions on the material characteristics, existence and uniqueness results are obtained and the convergence of a successive linearization method of solution is proved. An algorithm, combining this method with the finite element method, is proposed and applied to solve numerically an example problem.

A point-in-domain identification program

Abstract The present work describes a method for the determination of the position of a point with respect to a simple-connected domain. It is intended for application in the finite element mesh generation. The proposed method for identification of a point with respect to a domain appears as an extension of Sloans method, which is an improved version of Nordbecks and Rydsteadts one, for identification of a point with respect to a polygon. FORTRAN 77 computer programs are added implementing the proposed method.

Modelling and Solvability of a Rigid-Plastic Rolling Problem

A steady-state rolling problem with rigid—plastic, incompressible material model and with contact frictionless and friction boundary conditions is considered and studied. Existence and uniqueness of the solution of the corresponding penalty variational problem and its convergence to the solution of the primal variational problem is briefly presented. A regularization and the finite element approximation of the penalty problem are given and analysed. A convergent algorithm, combining the finite element method with the iterative secant-modulus method, is proposed and applied to solve an example problem and the obtained numerical results are illustrated.

The Kachanov Method for a Rigid-Plastic Rolling Problem

In this work, the method of successive linearization, proposed by L. M. Kachanov for solving nonlinear variational problems, arizing in the deformation theory of plasticity, is applied to a steady state, hot strip rolling problem. The material behaviour is described by a rigidplastic, incompressible, strain rate dependent material model and for the roll-workpiece interface a constant friction law is used. The problem is stated in the form of a variational inequality with strongly nonlinear and nondifferentiable terms. The equivalent minimization problem is also given. Under certain restrictions on the material characteristics, existence and uniqueness results are obtained and the convergence of the method is proved.

A Numerical Approach for a Hemivariational Inequality Concerning the Dynamic Interaction between Adjacent Elastic Bodies

A numerical treatment of an dynamic hemivariational inequality problem in structural mechanics is presented. This problem concerns the elastoplastic-fracturing unilateral contact with friction between neighboring civil engineering structures under second-order geometric effects during earthquakes. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the ?-Wilson method. The generally nonconvex constitutive contact laws are piece-wise linearized, and in each time-step a nonconvex linear complementarity problem is solved with a reduced number of unknowns.