The conditions of minimum potential energy and Castigliano's functional in a non-linear media

Oshhkunov M., Ozden S.

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, vol.38, no.1, pp.71-77, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 1
  • Publication Date: 2003
  • Doi Number: 10.1016/s0020-7462(01)00044-0
  • Page Numbers: pp.71-77


The behaviour of many polymeric materials under an external load may be described by a general form of non-linear relationship between stress and strain. In order to investigate such models, for example by a finite element method, it is necessary to construct the functional of energy (Castigliano or Lagrange's functional) and to find the extremum of the functional. Therefore, it is important to find the conditions under which functionals have a minimum. In this paper, the conditions when the functionals have a minimum for general stress-strain relations were investigated and an iterative method for the solution of the non-linear problems was proposed. The numerical results of the convergence speed of various iterative methods were discussed. This work is the continuation of the research presented in the literature by Oshhkunov and Ozden (The general stress and strain relationship in non-linear materials, Int. J. Non-Linear Mech. 35 (2000) 763-767.) (C) 2002 Elsevier Science Ltd. All rights reserved.