The mechanics of growth in a solid continuum has been the subject of intense interest in the last few years, with particular reference to mass growth in biological tissue. In this talk, we review the general theory for a single-component continuum, point out some differences between the various contributions published in the literature, and attempt to reconcile these differences. We then apply the theory with the aim of relating growth to the development of evolving residual stresses in the material. The general balance equations for a growing continuum are coupled with suitable mechanical constitutive laws. At any instant of the evolution (which is on a relatively long time scale) the material response is taken to be elastic, but the elastic constitutive law changes (slowly) with the growth. As is well known, an unloaded isotropic material cannot support residual stress, so it is necessary to take the material to be anisotropic, and we consider both transversely isotropic and orthotropic responses, which may be associated with the directional preferences engendered by, respectively, one or two families of fibers (collagen fibers in soft tissue, for example). Additionally, suitable growth laws (which may also be anisotropic) that couple the growth to changes in the mechanical response are introduced. The theory is illustrated by a prototype example for the modeling of an artery, that of a circular cylindrical tube subject to extension and internal pressure when the wall thickness changes as a result of persistent high pressure.
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