Scaling in Cavity—Expansion Equations using the Isovector Method (original) (raw)

Cavity-expansion approximations are widely-used in the study of penetration mechanics and indentation phenomena. We apply the isovector method to a well-established model in the literature for elastic-plastic cavity-expansion to systematically demonstrate the existence of Lie symmetries corresponding to scale-invariant solutions. We use the symmetries obtained from the equations of motion to determine compatible auxiliary conditions describing the cavity wall trajectory and the elastic-plastic material interface. The admissible conditions are then compared with specific similarity solutions in the literature.