What triggers microbranching of fast cracks in brittle amorphous solids?
In plain words
A fast crack moving through glass or plastic becomes unstable and develops small side branches at a speed well below that predicted by classical fracture theory. The cause of this threshold in three-dimensional samples is not explained.
Precise statement
In brittle amorphous materials (silicate glass, PMMA, polyacrylamide gels), single cracks become unstable to microbranching at velocities of roughly $0.4 c_R$ ($c_R$ the Rayleigh wave speed), below the branching velocity predicted by linear elastic fracture mechanics. Determine the 3D mechanism and critical velocity from a theory including near-tip nonlinear elasticity and dissipation, and predict the branch length and spacing.
What would settle it
A theory and 3D simulations predicting the microbranching velocity and branch statistics that agree with measurements in at least two materials.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
In thin gel sheets an oscillatory crack instability near the Rayleigh speed was explained by weakly nonlinear elasticity in the 2010s; the 3D microbranching threshold lacks a first-principles explanation (2026).
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