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A Note on Existence Result for Viscoplastic Models with Nonlinear Hardening

In the recent work of H.-D. Alber and K. Chelminski (Mathematical Models and Methods in the Applied Sciences, 17, 189—213, 2007) the existence of the solutions to a model of inelastic (viscoplastic) behavior of materials at small strain is derived. In this work we show that the conditions of the existence theorem of Alber and Chelminski can be relaxed and the same result can be proved under less restrictive assumptions. The relaxation of the conditions of the existence theorem of Alber and Chelminski (2007) makes it possible to answer the question raised by them concerning the solvability of the model of nonlinear kinematic hardening without assuming a higher exponent in the constitutive law for one of the internal variables than the exponent in the constitutive law for the other one.