Tensor Nonlinear Viscoelastic Models of the Maxwell Type: Vibration Creep and Ratcheting

Abstract

Some effects of the stress-strain state, such as vibration creep, creep acceleration and ratcheting, observed and studied in the experimental mechanics of a deformable solid, are proposed to be modeled on the basis of constitutive relations implemented in tensor nonlinear viscoelastic models of the Maxwell type. The apparatus of isotropic tensor functions is used, depending on two symmetric tensor arguments. Examples are given of a complex stress state in a tubular sample, when there is a significant disproportionate increase in time of the axial component of deformation under the combined action of constant axial and oscillatory shear loads compared to the case of action of only axial load. The concepts of generalized and combined ratcheting under complex stress conditions are introduced.