The boundary value problem of the theory of viscoelastic plasticity of a growing body subject to aging

• Published in: Journal of applied mathematics and mechanics Vol. 48; no. 1; pp. 1 - 10
• Main Authors: Arutyunyan, N.Kh, Naumov, V.E.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 1984
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/0021-8928(84)90099-6

The formulation of the boundary value problem for a visco-elastic-plastic growing body taking into account its increasing inhomogeneity caused by the sequence and speed of accretion is considered. The presence of two changing boundaries, namely, the external surface of the body and the boundary of the material plastic state, is characteristic for this formulation. The complete system of equations and conditions of the boundary value problem for a continuously growing body is presented. As an example of the application, a model problem is given of a non-uniformly aging hollow sphere with a shifting outer surface. Conclusions are drawn regarding the substantial effect of the accretion speed and the preliminary stress of the growing elements on the stress-strain state of the body.