Applicability Indicators and Identification Techniques for a Nonlinear Maxwell-Type Elasto-Viscoplastic Model using Multi-Step Creep Curves

A physically non-linear Maxwell-type constitutive relation with two material functions for non-aging rheonomous materials is studied analytically in order to elucidate the set of basic rheological phenomena that it simulates, to enclose its application field, to obtain necessary phenomenological restrictions which should be imposed on its material functions and to develop identification techniques. General properties and characteristic features of creep curves produced by the relation with arbitrary material functions under arbitrary multi-step uni-axial loadings are analyzed. The analysis reveals several attributes of the theoretic creep curves that can be employed as the relation feasibility indicators which are convenient for check using test data of a material. Three effective general identification techniques are developed. The first one is based on a set of creep and recovery tests at various stress levels and implies measurement of two strain magnitudes in each test. The second one is based on a single creep test under multi-step loading with growing stress levels. The third one is based on a single creep test under multi-step loading with growing stress levels alternated with unloading to zero stress and rest periods. The explicit expressions are derived in each case to determine the material functions values at arbitrarily chosen points in stress domain via minimal number of measured strain magnitudes. The identification techniques proposed herein enable separate and direct evaluation of the material functions values at a chosen points via test data escaping error accumulation. The techniques don't require any prescribed form of approximation and any kind of least square deviation minimization to determine its parameters; they don't require to solve a set of non-linear equations (its solution we have constructed analytically) and to involve iterative procedures or recurrent formulas. A number of the identification technique versions are considered and their advantages and shortcomings are discussed

The work was carried out with the state financial support of the RFBR (grant no. 17-08-01146_а)

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