A Comprehensive Energy Formulation for General Nonlinear Material Continua

[+] Author and Article Information
A. Carini

Department of Civil Engineering, University of Brescia, via Branze 38, 25123 Brescia, Italy

O. De Donato

Department of Structural Engineering, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy

J. Appl. Mech 64(2), 353-360 (Jun 01, 1997) (8 pages) doi:10.1115/1.2787314 History: Received June 19, 1995; Revised May 02, 1996; Online October 25, 2007


By specialization to the continuum problem of a general formulation of the initial/boundary value problem for every nonpotential operator (Tonti, 1984) and by virtue of a suitable choice of the “integrating operator,” a comprehensive energy formulation is established. Referring to the small strain and displacement case in the presence of any inelastic generally nonlinear constitutive law, provided that it is differentiable, this formulation allows us to derive extensions of well-known principles of elasticity (Hu-Washizu, Hellinger-Reissner, total potential energy, and complementary energy). An illustrative example is given. Peculiar properties of the formulation are the energy characterization of the functional and the use of Green functions of the same problem in the elastic range for every inelastic, generally nonlinear material considered.

Copyright © 1997 by The American Society of Mechanical Engineers
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