Свойства диаграмм нагружения и разгрузки, порождаемых нелинейным определяющим соотношением типа Максвелла для реономных материаловстатья
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Аннотация:A. V. Khokhlov. Properties of stress-strain curves generated by the nonlinear Maxwell-type iscoelastoplastic model under loading and unloading at constant stress rates
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Abstract
A physically nonlinear Maxwell-type constitutive relation for non-aging
rheonomic materials is studied analytically to find out the set of basic rheological
phenomena that it simulates, to indicate its application field and
to develop identification techniques and ways of tuning and further modifications.
Under minimal primary restrictions on two material functions
of the relation, the general equation of theoretic stress-strain curves family
produced by the model under loading and unloading at constant stress
rates is derived and analyzed in uni-axial case. Intervals of monotonicity
and convexity of loading and unloading curves, conditions for existence of
extremum and inflection points, magnitudes of maximal strain, strain rate
jumps and plastic strain arising as a result of loading- unloading cycle are
considered and their dependences on material functions and on stress rate
and maximal stress are examined. The main qualitative properties of stressstrain
curves and unloading responses generated by the constitutive equation
are compared to typical properties of test loading-unloading curves of viscoelastoplastic
materials in order to elucidate capabilities of the model, to
obtain necessary phenomenological restrictions which should be imposed on
the material functions and to find convenient indicators of applicability (or
non-applicability) that can (and should) be checked examining test data of
a material. ***************************
Keywords: elastoviscoplasticity, stress-strain curves, stress rate, unloading
response, rate sensitivity, instantaneous modulus, equilibrium stress-strain
curve, tension compression asymmetry, superplasticity, polymers