stress tensor, principal stress, principal direction, asymptotic direction, asymptotic director, Lode parameter.

New general vector forms of three-dimensional equilibrium equations of continuum mechanics are obtained by representations of the symmetric stress tensor as symmetrized mixed diades of asymptotic directors. The present study employs notations and terminology known from the mathematical theory of plasticity. However all results remains valid for stress fields in an arbitrary continuum. The simplest and analytically most efficient stress tensor representations for full plastic (Haar—Karman hypothesis), semiplastic and nonplastic three-dimensional states given by mixed diades of asymptotic directors are discussed. Stress tensor transformation to the asymptotic directors involves the intermediate principal stress and the Lode parameter. The asymptotic directors provides a natural tensor basis for the symmetric stress tensor different from the spectral forms. The general vector forms of three-dimensional equilibrium equations are separately derived for the full plastic, semiplastic and nonplastic states. These forms are then analyzed from the viewpoint of their integrability.

Radayev Yuri Nickolaevich Dr. Sc. (Phys.&Math.), Prof. of Continuum Mechanics, Leading Researcher, Ishlinskii Institute for Problems in Mechanics of RAS, Moscow, Russia