On the natural formulation and analysis of large deformation coupled thermomechanical problems

Abstract

The paper extends previous research on the natural methodology [1], [2] to the domain of coupled thermomechanical problems under the combined action of large inelastic and elastic deformations as well as of heat exchange. Some fundamental properties of redundant natural coordinate systems of reference are studied, and the local description of the coupled thermomechanical problem is developed a priori in natural terms. Following the transition from the local to the finite element level the numerical solution of the equations governing the coupled thermomechanical problem for the discretised body undergoing finite inelastic deformations is discussed. A number of applications conclude the paper. First a purely thermal problem is investigated which is followed by the study of various physical effects on the thermomechanical response of an expanding hollow cylinder assuming plastic and viscoplastic inelastic properties of the material. Two examples taken from the metal forming practice - the heading of a steel bolt and the extrusion of an aluminium billet - are treated under the aspect of thermomechanical coupling. The paper confirms in the authors' opinion the luminous clarity of the natural approach.