Гибридизация определяющего соотношения линейной вязкоупругости и нелинейной модели вязкоупругопластичности типа Максвелла и анализ сценариев эволюции коэффициента поперечной деформации при ползучести

Хохлов, А.В.

Автор: Хохлов А.В.
Журнал: Физическая мезомеханика
Том: 27
Номер: 1
Год издания: 2024
Первая страница: 20
Последняя страница: 48
DOI: 10.55652/1683-805X_2024_27_1_20-48
Аннотация: Crossbreeding the linear viscoelasticity constitutive equation with a Maxwell-type viscoelastoplasticity model and analysis of Poisson’s ratio evolution scenarios under creep ***We state a generalization for the physically nonlinear Maxwell-type constitutive equation with two material functions for non-aging rheonomic materials which have been studied analytically in previous articles to elucidate its properties and its application field. To extend the set of basic rheological phenomena that it simulates, we propose to add the third strain component expressed as the Boltzmann-Volterra linear integral operator governed by two arbitrary shear and bulk creep functions. For generality and convenient tuning of the constitutive equation, for its fitting to various materials and various phenomena lists (test data), we introduce a weight factor (i.e. nonlinearity factor) into the equation. It enables to combine primary physically nonlinear Maxwell-type model with the linear viscoelasticity equation in arbitrary proportion, to construct crossbred constitutive equation governed by six material functions and regulate prominence of different phenomena described by the two constitutive equations we crossbred. General expressions for volumetric, longitudinal and lateral creep curves under tensile loading and for the Poisson ratio evolution in time produced by the proposed constitutive equation are derived and analyzed, their basic properties are studied analytically assuming six material functions are arbitrary. Conditions for monotonicity and convexity of the curves or for existence of extrema, inflection points and sign changes are examined. New properties are found which enable the hybrid model to tune the form of creep and recovery curves and the Poisson ratio curve, and to simulate additional effects (in comparison with the primary Maxwell-type model) observed in creep and recovery tests of various materials at different stress levels. Taking into account compressibility and volumetric creep (governed by two material functions) is proved to affect strongly the qualitative behavior of lateral strain and the Poisson ratio. In particular, it is proved that the crossbred model can reproduce increasing, decreasing or non-monotone and convex up or down dependences of lateral strain and Poisson’s ratio on time under tension or compression at constant stress, it can provide existence of minimum, maximum or inflection points and sign changes from minus to plus and vice versa. It is shown, that the Poisson ratio at any moment of time is confined in the interval from -1 to 0.5 and the restriction on material functions is derived which provides negative values of the Poisson ratio. Criteria for the Poisson ratio increase or decrease and for extrema existence are obtained.In addition, we examine the specific properties of the simplified model which neglects bulk creep and simulates purely elastic volumetric strain dependence on a mean stress. This assumption is commonly (and very often) used for simplification of viscoelasticity problems solutions. It reduces the number of the model material functions by two. A number of restrictions and additional applicability indicators are found for this models. In particular, it is found that elastic bulk deformation assumption doesn’t cut the overall range of the Poisson ratio values and doesn’t demolish the model ability to describe non-monotonicity and sign changes of lateral strain and to produce negative values of the Poisson ratio. But neglecting bulk creep restricts this ability significantly and reduces drastically the variety of possible scenarios of Poisson’s ratio evolution and so contracts applicability field of the model. The model with purely elastic bulk strain dependence always generates the Poisson ratio which is an increasing convex-up function of time (without any extrema or inflection points which are possible in general case).***Ключевые слова: вязкоупругопластичность, ползучесть, физическая нелинейность, линейная вязкоупругость, кривые ползучести и восстановления, объемная ползучесть, кривые осевой и поперечной ползучести, параметр вида деформированного состояния, коэффициент Пуассона, ауксетики, индикаторы применимости, полимеры, композиты***Keywords: viscoplasticity, viscoelasticity, creep, physical non-linearity, linear viscoelasticity relation, tensile creep and recovery curves, volumetric creep, lateral strain-time curves, lateral contraction ratio, non-monotone Poisson’s ratio, negative Poisson’s ratio, viscoelastic auxetics, applicability indicators, polymers, composites
Добавил в систему: Хохлов Андрей Владимирович

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