Nonconservative Nature of the Stresses Developed in a Continuum

Abstract

The stresses in an elastic continuum (i.e. a continuum with zero strains after unloading) are classically deemed to be conservative (i.e. their total work all over the continuum is a single-valued function of only the displacement distribution in the continuum). So, internal damping in an elastic continuum appears to be a contradiction in itself. Actually, the total work of the internal stresses all over a continuum does not coincide with the strain energy of the continuum, but also includes the work of the internal body forces formed by the stress derivatives, which only con-tributes to the kinetic energy of the continuum. Owing to this inclusion, the total work of the internal stresses cannot be a single-valued function of only the displacement distribution in the continuum, and hence, the internal stresses must be nonconservative, which indicates internal damping inherent in any continuum whether elastic or not. Only statically deforming continua may possess conservative internal stresses.