On the numerical approximation of a viscoelastodynamic problem with unilateral constraints

The present work is dedicated to the study of numerical schemes for a viscoelastic bar vibrating longitudinally and having its motion limited by rigid obstacles at the both ends. Finite elements and finite difference schemes are presented and their convergence is proved. Finally, some numerical examples are reported and analyzed

On slip pulses at a sheared frictional viscoelastic/ non deformable interface

We study the possibility for a semi-infinite block of linear viscoelastic material, in homogeneous frictional contact with a non-deformable one, to slide under shear via a periodic set of ``self-healing pulses'', i.e. a set of drifting slip regions separated by stick ones. We show that, contrary to existing experimental indications, such a mode of frictional sliding is impossible for an interface obeying a simple local Coulomb law of solid friction. We then discuss possible physical improvements of the friction model which might open the possibility of such dynamics, among which slip weakening of the friction coefficient, and stress the interest of developing systematic experimental investigations of this question.Comment: 23 pages, 3 figures. submitted to PR

Production of a non-stoichiometric Nb-Ti HSLA steel by thermomechanical processing on a steckel mill

Obtaining high levels of mechanical properties in steels is directly linked to the use of special mechanical forming processes and the addition of alloying elements during their manufacture. This work presents a study of a hot-rolled steel strip produced to achieve a yield strength above 600 MPa, using a niobium microalloyed HSLA steel with non-stoichiometric titanium (titanium/nitrogen ratio above 3.42), and rolled on a Steckel mill. A major challenge imposed by rolling on a Steckel mill is that the process is reversible, resulting in long interpass times, which facilitates recrystallization and grain growth kinetics. Rolling parameters whose aim was to obtain the maximum degree of microstructural refinement were determined by considering microstructural evolution simulations performed in MicroSim-SM (R) software and studying the alloy through physical simulations to obtain critical temperatures and determine the CCT diagram. Four ranges of coiling temperatures (525-550 degrees C/550-600 degrees C/600-650 degrees C/650-700 degrees C) were applied to evaluate their impact on microstructure, precipitation hardening, and mechanical properties, with the results showing a very refined microstructure, with the highest yield strength observed at coiling temperatures of 600-650 degrees C. This scenario is explained by the maximum precipitation of titanium carbide observed at this temperature, leading to a greater contribution of precipitation hardening provided by the presence of a large volume of small-sized precipitates. This paper shows that the combination of optimized industrial parameters based on metallurgical mechanisms and advanced modeling techniques opens up new possibilities for a robust production of high-strength steels using a Steckel mill. The microstructural base for a stable production of high-strength hot-rolled products relies on a consistent grain size refinement provided mainly by the effect of Nb together with appropriate rolling parameters, and the fine precipitation of TiC during cooling provides the additional increase to reach the requested yield strength values

Friction and instabilities

CISM Courses and Lectures Vol. 45

Arc-Length Method for Frictional Contact Problems by using Mathematical Program with Complementarity Constraints

A new formulation as well as a new solution technique is proposed for equilibrium path-following method in two-dimensional quasi-static frictional contact problems. We consider the classical Coulomb friction law as well as geometrical nonlinearity explicitly. Based on a criterion of maximum dissipation of energy, we propose a mathematical program with complementarity constraints (MPEC) formulation in order to avoid unloading solutions in which most contact candidate nodes become stuck. A regularization scheme for the MPEC is proposed, which can be solved by using the conventional nonlinear programming approach. The equilibrium paths of various structures are computed in cases such that there exist some limit points and/or infinite number of successive bifurcation points. Keywords: contact problem, Coulomb's friction; arc-length method, mathematical program with complementarity constraints (MPEC), maximum dissipation + Department of Urban and Environmental Engineering, Kyoto University e-mail: [email protected] # Instituto Superior Tecnico, Dep. Eng. Civil and ICIST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal e-mail: [email protected] 1