d–operator, plastic flow, additive manufacturing, growing surface, differential constraint

The transformation formulae for differential d–operators are obtained. Such operators can be found in two-dimensional and three-dimensional problems of the mathematical theory of plasticity and the mechanics of growing solids. These transformations are caused by in the course of varying in the coordinate systems in order to simplify the differential equations (in particular, in the theory of plasticity) and the differential constraints imposed on the growing surface known in mechanics of growing solids. In the paper, the transformation formulae are derived and the corresponding examples are considered and discussed.

Yuri N. Radayev, D.Sc., PhD, MSc, Professor of Continuum Mechanics, Leading Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101, korp. 1, pr. Vernadskogo, Moscow, 119526, Russian Federation.

Evgenii V. Murashkin, Cand.Sc., PhD, MD, Senior Researcher, Ishlinsky Institute for Problems in

Mechanics of the Russian Academy of Sciences,

101, korp. 1, pr. Vernadskogo, Moscow, 119526, Russian Federation.