The Continual Mechanics of Frontally Growing Objects. Theory

Conditions for stresses and strains on the front of transformation of a material into a growing body are formulated. They allow one to solve problems on the stress–strain state of the material both ahead and on the rear of the front. As examples of such transformations, the solidification of great metal or polymer casts, the growth of bodies from a gas or liquid phase, growth of planets, and the formation of polycrystalline structures can be mentioned. The solutions of such problems are compared with those obtained by a discrete theory.