Turns out some flexible materials are basically forced to grow tiny holes just to keep from falling apart.
March 25, 2026
Original Paper
A Lavrentiev phenomenon in the neo-Hookean model
arXiv · 2603.22873
The Takeaway
Under the 'neo-Hookean' model of elasticity, it was long assumed materials could stretch smoothly. This paper proves a 'Lavrentiev gap' where a smooth stretch is mathematically impossible; instead, the material must create a microscopic 'dipole' defect to reach its lowest energy state, meaning some materials must break slightly to exist in their most efficient form.
From the abstract
We exhibit a Lavrentiev gap phenomenon for the neo-Hookean energy in three-dimensional nonlinear elasticity. More precisely, we construct boundary data for which the infimum of the neo-Hookean energy over deformations satisfying a natural regularity and invertibility condition is strictly larger than the infimum over the weak $H^1$-closure of that class. The mechanism underlying the gap is a deformation with a dipole-type singularity.