Handbook of Solid Mechanics by Bengt Sundström (ed.)

By Bengt Sundström (ed.)

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The most common methods are summarized in this chapter. They are often used for obtaining approximate solutions to boundary value problems. In applied mechanics, energy quantities are derived. These methods are therefore often named energy methods. The elastic energy per unit volume in a general case is defined as a function of sev­ eral strain measures and thermodynamic states. Discussions of these concepts may be found in the special literature. Energy expressions for structural components are treated in the specialized chapters as special versions of the theorems formulated first in their general form.

The model is treated among others in [7]. e. on deformation internal energy is stored and dissipation takes place (change of mechanical energy to heat). The characteristics o f this dissipation is that it is not devel­ oped momentarily, as in (time independent) plastic deformation, but that a certain limited time is needed. There are constitutive equations for linear and non-linear viscoelastic materials. The experimental base for determination of constitutive parameters is often sparse. It is usu­ ally limited to uniaxial situations.

Discussions of these concepts may be found in the special literature. Energy expressions for structural components are treated in the specialized chapters as special versions of the theorems formulated first in their general form. 1 Elastic energy In an elastic body, which is being deformed, the internal work per unit volume is com­ pletely transformed into strain energy. The strain energy density is denoted by W'(εij) . ) in their respective chapters below. 2 Linear isotropic elastic material For a linearly elastic material Hooke’s law corresponds, according to Eqn.

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