LAUSR

The present study deals with a problem of modeling a surface growth process. Governing principles for mechanics of growing solids have been formulated. Within the framework of the surface growth theory, different variants of boundary value problems are discussed. A human blood vessel under pathological growth processes has been considered as an example of a surface growth process. Vessels are simulated by a long thick‐walled circular cylinder. The boundary value problem of a surface growth for elastic thick‐walled vessels is solved. The analytical solution in terms of velocities for parameters of stress‐strain state has been obtained. Condition of thickness has allowed us to study strain‐stress state of cylinder surfaces using approximation of infinitesimal deformations. The stress‐strain state characteristics are numerically computed and graphically analyzed using various mechanical parameters of the surface growth processes. Two cases of boundary value problems, namely, deformation of two‐ and multilayer cylinder have been considered. General analytical solution for thick multilayer cylinder deformation has been obtained. Analytical solution is based on the Lamé problem for elastic material. Comparison of multilayer and single‐layer solutions is performed.