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.

Issue Section:
Technical Papers
Topics:
Boundary-value problems, Constitutive equations, Displacement, Elasticity, Potential energy
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