3D-Printing, surface growth, stress, constitutive equation, rational invariant, differential constraint, complete system

The present work is devoted to an approaches to derivation of constitutive equations on the propagating growing surface. The proposed approach is based on notion known from the algebra of rational invariants. The arguments of tensor functionals are elucidated taking account of their invariance with respect to rotational transformations of the coordinate frame. A complete system of joint rational invariants of the stress tensor and the unit normal vector to growing surface is discussed. The geometric visualization of the considered rational invariants is given. A number of variants of constitutive equations on PGS of different complexity levels are derived and discussed. The derivation of the transformation formulae for the directional derivatives on the tangent plane element to growing surface for transition from a given orthogonal frame to an arbitrary curvilinear one are obtained. The obtained boundary conditions on growing surface are geometrically and mechanically consistent. The formulated differential constraints imply an experimental identification of consitutive functions.

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.