Solid Flow Fields and Growth of Soft Solid Mass

Recent work1,2 on growth of actin gel, and earlier studies3,4 on radial plastic forming processes, while seemingly distinct have in fact much in common by adopting the underlying view of source flow of solid materials. That conceptual framework, of Eulerian formulation of solid flow fields, is examined in the present contribution. We focus on radial patterns, with spherical symmetry in steady state conditions, to model kinematics of growth on a spherical bead. Constitutive response includes the Blatz-Ko hyperelastic solid, the Cauchy-Hookean elastic solid and a simple hypoelastic incompressible material. Useful analytical relations are derived for radial velocity profile, stretches and strains. High circumferential stresses at the external layer, in agreement with findings reported by Dafalias et al.1,2 using different constitutive models, can possibly induce symmetry breakdown. Growth driving parameters are discussed, including a thermodynamic growth driving force, and thin shell asymptotic formulae are given.