The first theoretical estimate of the shear strength of a perfect
crystal was given by Frenkel [Z. Phys. 37, 572 (1926)]. By assuming
that two rigid atomic rows in the crystal would move over each other
along a slip plane, he derived the ultimate shear strength to be about
one-tenth of the shear modulus. Here we present a theoretical study
showing that catastrophic failure of viscoelastic materials may occur
below Frenkel's ultimate limit as a result of thermal runaway. The
thermal runaway failure mechanism exhibits progressive localization of
the strain and temperature profiles in space, thereby producing a narrow
region of highly deformed material, i.e., a shear band. We calculate the
maximum shear strength sigma(c) of materials and then demonstrate the
relevance of this new concept for material failure known to occur at
scales ranging from nanometers to kilometers.