Mechanics of Growing Deformable Solids: A Review
Growing deformable solids increase their mass during the deformation process by way of the gradual addition of material onto the external surface of the solids. Only the processes of continuous growth (accretion) are under consideration in this paper. The mathematical formulation of the boundary‐value problem for continuously growing solids has some general distinctive features, which differentiate it from the formulation for solids of constant mass. First, the full strains within the growing body are incompatible due to arbitrary straining of each material element before its attachment to the body. Second, the boundary conditions on the surface of growth must prescribe the total stress state of the surface element, i.e., the full stress tensor on this part of the external boundary of the body. The writer undertakes an attempt to display such features and to present a brief historical sketch of the topic.