Papers by Author: Peter B. Béda

Abstract: Gradient materials get more and more importance in both material science and numerical studies of technological processes. Their mathematical model is called the constitutive equation. The theoretical background of such model is presented on the basis of thermodynamics and continuum mechanics. The results show which is the quantity to measure to get constitutive equation for gradient dependent materials.

Abstract: A strange self-sustained oscillation in plastic uniaxial tension of various materials is called the Portevin Le Chatelier (PLC) effect. In modelling PLC dynamic strain aging is the common way of explanation. It is based mainly on dislocation dynamics. Experimental studies show the negative strain rate dependence (NRS) is always present at PLC. By using continuum mechanics and dynamical systems theory we find that NRS is the essential reason of it.

Abstract: There are several self-sustained oscillatory phenomena observed at plastic deformation of metals. One of them happens at the beginning of plastic behavior and leads to appearance of the famous Lüders-Hartmann bands. However, it can also be found self-sustained oscillations well beyond the yield stress like Portevin and Le Chatelier did in the early 20th century. This paper presents a simple model of that by using continuum approach and the theory of dynamical systems.

Abstract: This paper studies Portevin-Le Chatelier (PLC) effect as a form of dynamic material instability. In such phenomenon negative rate dependence is coupled with the appearance of a selfsustained oscillatory behavior in solid bodies. The tools of the investigation are of the theory of dynamical system. By selecting a proper form of the constitutive equation of the rate dependent material, a dynamical system will be constructed from the basic equations of continua. Then the birth of a self-sustained oscillation is detected at the conditions of a dynamic material instability mode. This results show an interpretation of PLC as a flutter type of loss of material stability.