On the response of Burgers' fluid and its generalizations with pressure dependent moduli
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This manuscript presents a systematic investigation of the response of a Burgers' viscoelastic fluid model with stress-dependent material parameters. Such a model has been used extensively in geomechanics as well as to describe the response of materials like asphalt. The stress, strain, and time relation of Burgers' fluid model is expressed with second order differential operators applied to the stress and strain. The nonlinearity is due to the stress dependence of the material parameters, i.e., the fluid viscosity and the parameter related to the characteristic time. We impose discontinuity conditions, whose necessity was not recognized until the recent work of Prusa and Rajagopal (2011), for the stress and strain and also for the stress- and strain rates such that we satisfy the following assumptions: if there is a jump discontinuity in strain there should be a jump discontinuity in the corresponding stress, and if there is a small change in strain there ought to be a small change in the corresponding stress. These assumptions are also applied when a stress history is considered as input. We present constraints on the stress-dependent material functions in order to obtain a physically meaningful solution that describes the viscoelastic response of materials. We also allow different responses for tension and compression and perform parametric studies geared towards obtaining an understanding of the effect of nonlinear stress-dependent functions on the stress-relaxation and creep deformation under various loading histories. It is important to recognize that methods such as time-temperature superposition or the use of Laplace transforms that are useful in the case of the classical linear viscoelastic material will not work in the case of the non-linear model considered in this paper. 2012 Springer Science+Business Media, B. V.
