Load-Rate Sensitivity in 1D Non-Linear Viscoelastic Model
Load-rate sensitivity of material is important in impact and other dynamic loadings. It is assumed that the strain-rate sensitivity is not a material property but comes out naturally from dynamic equilibrium equations. Material is assumed non-linear, similar as used in the microplane model for quasi-brittle materials, and viscoelastic arranged into Kelvin scheme. The scheme is the simplest possible and consists of two Kelvin bars in series with an optional mass between them (Maxwell bars are considered in our previous paper). Loading is uniaxial tension with changing intensity in time, asymptotic or harmonic. The resulting differential equation (equations when a mass is present) is non-linear and stiff. Equations have been solved numerically using adaptive and Radau integration. For equal parameters nonsymmetrical (together with symmetrical) results could be obtained, meaning localization is possible without the localization initiator. System response is strongly influenced with the presence of a mass. Phase diagram show that some combination of parameters and loading demonstrate chaotic behavior.
Z. Tonković and M.H. Aliabadi
I. Kožar et al., "Load-Rate Sensitivity in 1D Non-Linear Viscoelastic Model", Key Engineering Materials, Vols. 488-489, pp. 731-734, 2012