Identification and verification of visco-hyperelastic constants of defining relations for shock absorbing rubber

Dmitry A. Boyarshinov, Oleg Yu. Smetannikov

Author details

Dmitry A. Boyarshinov
Perm Scientific-Industrial Instrument Making Company, Perm, Russian Federation
Oleg Yu. Smetannikov
Perm National Research Polytechnic University, Perm, Russian Federation

https://doi.org/10.15593/perm.mech/2025.4.02

Nowadays, highly elastic materials showing pronounced rheological properties that contribute to the reduction of peak amplitudes of vibrations in resonance modes are widely used in the designs of vibration-protective devices. The design of such structures in modern conditions requires the construction of a mathematical model, the most important part of which are the defining relations for the description of viscoelastic and hyperelastic behavior of the material and an adequate methodology for the identification of material constants. The purpose of this study is to construct a methodology for determining the visco-hyperelastic properties of a material based on quasi-static test data. In describing the hyperelastic behavior of the material, the Mooney – Rivlin strain energy potential with two constants and Neo-Hookean potential with consideration of compressibility were used, and when viscoelasticity was taken into account, the relaxation function was expanded into Prony series. Semi-analytical expressions of stress dependence on principal strains and time with account of visco-hyperelastic behavior of the material in cases of uniaxial stressed and uniaxial deformed states are obtained. To select the optimum distribution of approximation parameters of relative shear moduli and range of relaxation times, the effect of changing viscoelastic parameters on the magnitude of hysteresis and maximum stresses in the cycle at different strain rates was evaluated. The results of full-scale cyclic tests in free tension and compression and constrained compression were used to calculate material constants. A procedure for determining the visco-hyperelastic properties of the material has been developed, which consists in minimizing the difference between the results of mechanical tests and the response values calculated using the constructed semi-analytical expressions using the Nelder – Mead method. As a result, the hyperelastic and viscoelastic material properties were determined, which agree with the experimental curves with reasonable accuracy. It is shown that the Neo-Hookean potential with its simpler form allows describing the data of mechanical tests on a par with the Mooney – Rivlin potential with two constants. The calculated material properties were verified by comparing the shock absorber test data and the results of numerical simulation of the shock absorber deformation.

Keywords

hyperelasticityviscoelasticityMooney – Rivlin potentialNeo-Hookean potentialmaterial propertiesrubbercyclic deformation

ИДЕНТИФИКАЦИЯ И ВЕРИФИКАЦИЯ ВЯЗКОГИПЕРУРГИХ КОНСТАНТ ОПРЕДЕЛЯЮЩИХ СООТНОШЕНИЙ ДЛЯ АМОРТИЗАЦИОННОЙ РЕЗИНЫ

В настоящее время в конструкциях виброзащитных устройств широкое применение нашли высокоэластические материалы, проявляющие ярко выраженные реологические свойства, способствующие снижению пиковых амплитуд колебаний в резонансных режимах. Проектирование подобных конструкций в современных условиях требует построения математической модели, наиболее ответственной частью которой являются определяющие соотношения для описания вязкоупругого и гиперупругого поведения материала и адекватная методика идентификации материальных констант. Цель данного исследования заключается в построении методики определения вязкогиперпунктурих свойств материала на основании данных квазистатических испытаний. При описании гиперупругого поведения материала использовались потенциалы энергии деформации Муни – Ривлина с двумя константами и Нео-Гука с учетом сжимаемости, а при учете вязкоупругости функция релаксации раскладывалась в ряды Прони. Получены полуаналитические выражения зависимости напряжений от главных растяжений и времени с учетом вязкогиперупругого поведения материала в случаях одноосного напряженного и одноосного деформированного состояний. Для выбора оптимального распределения параметров аппроксимации относительных модулей сдвига и диапазона времен релаксации было оценено влияние изменения вязкоупругих параметров на величину гистерезиса и максимальных напряжений в цикле при различной скорости деформирования. Для вычисления параметров аппроксимации материальных свойств рассматривались результаты натурных циклических испытаний на свободное растяжение и сжатие, а также стесненное сжатие. Разработана процедура определения вязкогиперпунктурих свойств материала, которая заключается в минимизации разницы между результатами натурных испытаний и вычисленного с помощью построенных полуаналитических выражений значений отклика с использованием метода Нелдера – Мида. В результате были определены гиперупругие и вязкоупругие свойства материала, которые с достаточной точностью согласуются с экспериментальными кривыми. Показано, что потенциал Нео-Гука при своей более простой форме позволяет описать данные натурных испытаний наравне с потенциалом Муни – Ривлина с двумя константами. Вычисленные свойства материала были верифицированы на основании сравнения данных испытаний амортизатора и результатов численного моделирования деформирования демпфера.

Ключевые слова

гиперупругостьвязкоупругость. потенциал Муни – Ривлинапотенциал Нео-Гукасвойства материаларезинациклическое деформирование

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Article information

Published: 8 December 2025
Issue date: 8 December 2025
Issue: No. 4 (2025)