Geodesic
Properties of a nonlinear Maxwell-type model of viscoelasticity with two material functions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 36-41

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General equations and qualitative properties of basic quasi-static theoretic curves (i.e., stress-strain curves at constant strain or stress rates, relaxation, creep and recovery curves) generated by the nonlinear Maxwell-type constitutive equation with two arbitrary material functions are studied analytically (in uniaxial case). The goal is to reveal the model abilities to describe the set of basic rheological phenomena pertaining to viscoelastoplastic materials (e.g., superplasticity effect) and to find out convenient indicators marking the field of applicability or non-applicability of the model. The minimal set of general restrictions that should be imposed on material functions to provide an adequate description of typical test curves of viscoelastoplastic materials is revealed. 
@article{VMUMM_2016_6_a5,
     author = {A. V. Khokhlov},
     title = {Properties of a nonlinear {Maxwell-type} model of viscoelasticity with two material functions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {36--41},
     publisher = {mathdoc},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a5/}
}
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A. V. Khokhlov. Properties of a nonlinear Maxwell-type model of viscoelasticity with two material functions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 36-41. http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a5/