Buckling and Mechanical Failure of Viral Shells

We present a combined theoretical and experimental study of the structural failure of viral shells under mechanical stress due to indentation by atomic force microscopy. Modeling the indentation of icosahedral viruses with two-dimensional continuum shell elasticity theory, we find that the fivefold-symmetric disclinations precipitate geometric ``buckling'' instabilities, leading to structural collapse at indentation loads that are significantly lower than those which buckle perfectly spherical shells. Coincident with these instabilities, discontinuities in the force-indentation curve appear when the so-called F\"oppl-von K\'arm\'an (FvK) number exceeds a critical value. A nano-indentation study of a viral shell subject to a soft-mode instability, where the stiffness of the shell decreases with increasing pH, confirms the predicted onset of failure as a function of the FvK number.