A Nonlinear Maxwell-Type Model for Rheonomic Materials: Stability under Symmetric Cyclic Loadings / A. V. Khokhlov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. № 2. P. 59-63 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 39-42].

The analytic study of the nonlinear Maxwell-type constitutive relation for rheonomic materials with two material solutions is continued to reveal the capabilities of this relation to model rheological effects, its applicability scope, and the techniques of identification. The properties of the response to an arbitrary periodic loading program are considered. A criterion of its periodicity is obtained. A condition is found when the nonlinear Maxwell-type model adequately describes the stability effect as well as the hysteresis loop closure under symmetric cyclic loadings. It is shown that this condition is dependent on a single material function and is consistent with the simulation of resistance capabilities of materials.

Key words: nonlinear viscoelasticity, rate sensitivity, symmetric cyclic loadings, plastic strain, cyclic stability, ratcheting.

№ 2/2018