The Yield-Strain in Shear Banding Amorphous Solids
Abstract
In recent research it was found that the fundamental shear-localizing instability of amorphous solids under external strain, which eventually results in a shear band and failure, consists of a highly correlated array of Eshelby quadrupoles all having the same orientation and some density
ρ
. In this paper we calculate analytically the energy
E(ρ,γ)
associated with such highly correlated structures as a function of the density
ρ
and the external strain
γ
. We show that for strains smaller than a characteristic strain
γ
Y
the total strain energy initially increases as the quadrupole density increases, but that for strains larger than
γ
Y
the energy monotonically decreases with quadrupole density. We identify
γ
Y
as the yield strain. Its value, derived from values of the qudrupole strength based on the atomistic model, agrees with that from the computed stress-strain curves and broadly with experimental results.