pseudotensor, growing surface, 3D woven material, micropolar medium, rational invariant

The article discusses the formulation of the defining differential constraints on the buildup surface in the case of modeling the processes of forming a 3D material characterized by additional characteristic directors (directions of laying fibers in woven materials, reinforcement in concrete structures). The general form of the tensor relation on the growing surface is derived, taking into account the additional selected directions. Determine the set of joint rational invariants of the stress tensor and characteristic directors. An invariant-complete formulation of the constitutive relations on the surface of the build-up is given. The results obtained can be used to formulate and solve boundary value problems that simulate the processes of synthesis of woven 3D materials.

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.