Generalized Continuum Mechanics
A continuum-mechanical theory is presented in which the deformation is described by a number of generalized coordinate fields. The applied force system is described by conjugate generalized force fields distributed throughout the volume of the body and on the surface. These arise as the coefficients of the rates of change of the generalized forces in an expression for the rate at which work is done by the force system acting on the body. The differential equations of the theories are obtained by the systematic use of the first and second laws of thermodynamics, together with invariant-theoretical considerations. The theory is motivated by a particle model in which each particle consists of a number of mass-points. It is seen that starting with a given model there is a considerable ambiguity in the choice of the generalized coordinates describing the deformation and hence in the form of the resulting theory.
KeywordsInternal Energy Generalize Force Director Theory Translational Velocity Classical Continuum Mechanic
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- Truesdell, C. A., and R. Toupin: The Classical Field Theories. Handbuch der Physik. Vol. III. Berlin-Göttingen-Heidelberg: Springer. 1960.Google Scholar