Lagrange multiplier method of the general variational principles of finite deformation theory of couple stress and its application in the strain gradient plasticity

Theory of couple stress was systematically studied by [A.C. Eringen, Basic Principles of Continuum Physics, Academic Press, 1975]. These theoretical results have many developments in the various areas of sciences. In this paper, one proposes a general variational principle of finite deformation theory of couple stress and uses it to the strain gradient plasticity. The general variational principle is a free variational principle. The variational functions need not satisfy any requirement (for example, when stress tensor is the variational function, it need not satisfy the requirements of equilibrium equation and boundary conditions); therefore, the variational functions are easy to choose. (C) 2004 Elsevier Ltd. All rights reserved.