Figure 1. Stress and energy across the yielding transition.

(a) Stress–strain plots of the two differently annealed glasses for various strain amplitudes in the steady states of oscillatory shear deformation. Maximum stress in the cycle for each amplitude is marked by filled and open circles for T=0.466 and T=1, respectively. (b) Averaged stress–strain curves for uniform strain (US) are shown as lines—thick (black) for N=4,000 and thin (magenta) for N=32,000 while solid and dashed lines represent T=0.466 and T=1, respectively. Maximum stress σ_max versus γ_max are shown for cyclic strain (CS) (circle and square denote N=4,000 and 32,000, respectively, with filled and open symbols corresponding to glasses from T=0.466 and T=1). The vertical line at γ_max=0.08 indicates the sharp yielding transition seen. (c) Energy versus strain in the steady states, displaying a bifurcation in the strain corresponding to minima in energy at the yielding transition between γ_max=0.07 and 0.08. (d) Strain values corresponding to energy minima (γ_Umin) and and zero stress are shown as open and filled symbols respectively, versus the number of cycles for different γ_max. For γ_max=0.08 an initial relaxation towards zero is reversed as the system evolves to a yielded steady state with finite γ_Umin and . (e) γ_Umin and as functions of strain amplitude γ_max, displaying a transition beyond γ_max=0.07. (f) Asymptotic energy per particle at γ=0 versus strain amplitude γ_max. Energies decrease with γ_max until the yield strain is reached, after which they increase with γ_max.