Homogenization of Rubber-Cord Layers at Moderately Large Deformations

Sheshenin, S. V.; Yikun, Du

doi:10.1007/s11029-021-09953-2

Cited by 7 publications

(7 citation statements)

References 11 publications

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“…Асимптотический подход развивался при анализе периодических сред как в трехмерном случае [21, 23-25], так и в случае неоднородных слоев [26][27]31]. В [28,29] двухслойный резинокордный ламинат был проанализирован в рамках линейной упругости.…”

Section: осреднение резинокордных слоевunclassified

“…Следует отметить, что в большинстве работ определяются двумерные эффективные определяющие соотношения в предположении плоского напряженного состояния слоя. К этому приводит асимптотический подход, так же, как и классическая ламинатная теория (КЛТ) (см., например, [26,27,30,31]). Последнее неудивительно, поскольку КЛТ является просто первым приближением асимптотического разложения [31].…”

Section: осреднение резинокордных слоевunclassified

“…К этому приводит асимптотический подход, так же, как и классическая ламинатная теория (КЛТ) (см., например, [26,27,30,31]). Последнее неудивительно, поскольку КЛТ является просто первым приближением асимптотического разложения [31].…”

Section: осреднение резинокордных слоевunclassified

“…Однородный слой с правильными двумерными модулями в плоскости слоя может обладать изгибными жесткостями, не соответствующими изгибным жесткостям осредняемого неоднородного слоя. Поэтому не случайно, что метод осреднения [27,31] одновременно понижает размерность задачи, сводя трехмерный слой к модели пластины, а также позволяет определять как жесткости в плане, так и изгибные и крутильную жесткости. В соответствие со сказанным, изгибные жесткости, вообще говоря, не могут быть получены из осредненных двумерных жесткостей в плане слоя.…”

Section: осреднение резинокордных слоевunclassified

“…Рассмотрим лишь его схему. Известно, что при применении второго приближения [31] для неоднородного линейного упругого слоя результатом является теория пластин, эквивалентная теории Миндлина -Рейснера. С другой стороны, согласно работе [33], применение первого приближения для однородного слоя, подчиняющегося линейной моментной теории упругости, приводит также к теории типа Миндлина -Рейснера.…”

Section: осреднение резинокордных слоевunclassified

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Modeling of rubber-cord layers under quasi-static loading

Sheshenin

Yikun

Chistyakov

et al. 2021

PNRPU Mechanics Bulletin

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Modeling a pneumatic tire with a strong change in shape causes the problem of choosing an adequate model for rubber-cord plies. Generally, the classical method of asymptotic homogenization is not suitable due to physical and geometrical nonlinearity for the strain up to 15 %. The known models used for simulation the entire tire as well as rubber-cord plies are analyzed. A choice is made in favor of modeling the plies using the stress anisotropic potential, which is an anisotropic function of the strain tensor invariants. The relationship of such a constitutive law with a quasi-linear constitutive equation in terms of stress and strain differentials is indicated. A convenience of these two types of constitutive equations in terms of numerical implementation is also given. A modification of the effective properties definition for an inhomogeneous layer is explained. The difference from the standard effective moduli definition is clarified. The arrangement of the cords is supposed to be approximately periodic and all cords to be equivalent to the effective fiber. Two models of a rubber-cord plies are described under such assumption. These are a model of an orthotropic material and a model of a transversely isotropic material. Computational experiments, which make it possible to determine the material parameters of anisotropic potentials, are pointed out. Real tests with a sample of rubber ply under slow quasi-static loading were conducted. Significant hysteresis was detected. It is shown that an additive model combining a hyper elastic material with Maxwell viscoelastic model provides good accuracy in stress dependence on the strain rate. The numerical procedure developed to calculate solution to the quasi-static problem of tire deformation is described. It is implemented in home-made computer code. A numerical example on the tire simulation is given. That is so-called breaking test, in which strong deformation is achieved and the developed model is applied to.

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Section: осреднение резинокордных слоевunclassified

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Modeling of rubber-cord layers under quasi-static loading

Sheshenin

Yikun

Chistyakov

et al. 2021

PNRPU Mechanics Bulletin

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Geometrically nonlinear topology and fiber orientation optimization of composite structures using membrane-embedded model

Zuo,

Xie,

Zhang

et al. 2024

Thin-Walled Structures

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Utilization of viscoelatic models with non-linear springs and dashpots in delamination study of multilayered beams

Rizov

2022

PNRPU Mechanics Bulletin

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This paper analyzes delamination of multilayered inhomogeneous beam structure by utilization a non-linear viscoelastic mechanical model. The non-linear time-dependent response is treated by a non-linear spring and a non-linear dashpot connected in series to a system of two linear springs and two linear dashpots. The model is under stress that is a linear function of time. The constitutive law of the model representing a non-linear dependence between stress, strain and time is derived. The main goal of the paper is to obtain a solution of the strain energy release rate for the delamination in the multilayered inhomogeneous beam by applying the nonlinear viscoelastic model. Solutions are derived by using the complementary strain energy and by analyzing the balance of the energy with taking into account the non-linear viscoelastic behaviour. For this purpose, the constitutive law of the non-linear viscoelastic mechanical model is used. The solutions are applied to obtain results for multilayered beams with non-linear variation of material properties in longitudinal direction. The influence of different parameters on the timedependent strain energy release rate is assessed. The study indicates the effectiveness of the viscoelastic mechanical models with non-linear springs and dashpots in time-dependent delamination analyses of multilayered inhomogeneous beam structures. © PNRPUФинансирование. Исследование не имело спонсорской поддержки. Конфликт интересов. Автор заявляет об отсутствии конфликта интересов.

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Homogenization of Rubber-Cord Layers at Moderately Large Deformations

Cited by 7 publications

References 11 publications

Modeling of rubber-cord layers under quasi-static loading

Modeling of rubber-cord layers under quasi-static loading

Geometrically nonlinear topology and fiber orientation optimization of composite structures using membrane-embedded model

Utilization of viscoelatic models with non-linear springs and dashpots in delamination study of multilayered beams

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