A Generalized Theory of Stress and Strain Measures in the Classical Continuum Mechanics / G. L. Brovko. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. № 5. P. 46-57 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 117-127].

A generalized theory of stress and strain tensor measures in the classical continuum mechanics is discussed: the main axioms of the theory are proposed, the general formulas for new tensor measures are derived, and an energy conjugate theorem is formulated to distinguish the complete Lagrangian class of measures. As a subclass, a simple Lagrangian class of energy conjugate measures of stresses and finite strains is constructed in which the families of holonomic and corotational measures are distinguished. The characteristics of holonomic and corotational measures are studied by comparing the tensor measures of the simple Lagrangian class with one another and with logarithmic measures. For the simple Lagrangian class and its families, their completeness and closure are shown with respect to the choice of a generating pair of energetically conjugate measures. The applications of the new tensor measures in modeling the properties of plasticity, viscoelasticity, and shape memory are mentioned.

Key words: classical continuum mechanics, tensor strain and stress measures, generalized theory, axioms of the theory, new tensor measures, Lagrangean classes, theorem of energy conjugation, families of holonomic and corotational measures, applications of new tensor measures.

№ 5/2018