Large Amplitude Oscillatory Shear

Deformation of Chemically Heterogeneous Interfacial Layers of Polymer Nanocomposites

“…, where T n is the nth order polynomial; e n is the corresponding elastic coefficient; and x = γ/γ 0 . 34,35 e 1 represents the average stored energy per unit volume within an oscillation cycle and equals G 1 ′, and e 3 represents the deviations from average response at large strains. The positive e 3 represents strain stiffening, and negative e 3 indicates softening within an oscillation cycle.…”

“…The relative intensity of the higher harmonics with respect to fundamental frequency, I n / I 1 , has been used to relate the nonlinearities to the materials’ properties. − Rogers et al , analyzed the nonlinear stress response and interpreted each harmonics as a sequence of physical processes in colloidal glasses such as linear stress increase, yielding, flow, and reformation. The measured total stress is decomposed into two constructions as known as elastic σ e and viscous σ v stresses using the MITLaos software. , The orthonormal decomposition of the elastic and viscous stresses is described with the Chebyshev polynomials of the first kind as σ e ( x , ω, γ) = , where T n is the n th order polynomial; e n is the corresponding elastic coefficient; and x = γ/γ 0 . , e 1 represents the average stored energy per unit volume within an oscillation cycle and equals G 1 ′ , and e 3 represents the deviations from average response at large strains. The positive e 3 represents strain stiffening, and negative e 3 indicates softening within an oscillation cycle.…”