There are different viscoelastic materials such as polymer, rubbers, etc. How to calculate the complex stiffness (K*=K(1+i*eta)) for such viscoelastic material ?
Is there any calculation steps available for certain polymer materials ?
Dear Mukund A Patil, it is done via DMA. Please check the following attached files. My Regards
https://www.researchgate.net/publication/223306166_A_method_of_transmissibility_design_for_dual-chamber_pneumatic_vibration_isolator
Dear Abdelkader BOUAZIZ Sir,
Thank you for your suggestion and possible attachments.
Is there any open literature available where researchers/academicians had discussed about the different polymer materials with their experimentally evaluated complex stiffness values?
Dear sir , please read , may be useful to you
1. https://www.sciencedirect.com/topics/engineering/linear-viscoelasticity
2. https://web.mit.edu/course/3/3.11/www/modules/visco.pdf
3.http://homepages.engineering.auckland.ac.nz/~pkel015/SolidMechanicsBooks/Part_I/BookSM_Part_I/10_Viscoelasticity/10_Viscoelasticity_Complete.pdf
Please refer following: There are definitions and methods used to measure the stiffness are given. Good reading.
Dr. B R Gupta, Retd Prof., I I T Kharagpur
https://www.bksv.com/media/doc/bo0427.pdf
https://omnexus.specialchem.com/polymer-properties/properties/stiffness
Rakhi Gupta Madam,
Thank you for your reply. I went through the link and corresponding application note. Here, they mentioned about the flexural modulus of different plastic. Is this flexural modulus is the complex modulus for that particular plastic material?
Also, if this is not complex modulus, then how to get the loss factor for these all plastic materials?
Dear Mr. Patil,
Please note that the flexural modulus as referred is not the complex modulus.
Complex modulus is to be estimated from Voigt -Kelvin Model / Maxwell model as given in the second paper.Pl. follow the method given. The loss factor is calculated using equations: tan δ = G”/G’ = J”/J’ =1/ωψi = 1/ωθi
where G” = loss modulus; G’ = storage modulus and J”= storage compliance and J’ = loss compliance
θi = relaxation time and ψi = retardation time
The method is explained in the second paper. Hope it will clear you doubt. Any doubt pl. contact me by mail.
Thanks
B R Gupta
Complex stiffness = (complex elastic modulus/AL). Complex modulus is E(ω)= E’(ω) + jE”(ω)= dynamic storage modulus + dynamic loss modulus). Experimentally storage modulus can be measured using dynamic mechanical analyzer (DMA).The Dynamic Mechanical Analyzer (DMA) is a commercially available device that can be used to determine the dynamic modulus of viscoelastic materials. From dynamic modulus one can calculate the dynamic stiffness. Thanks
Dr. B R Gupta,
The complex stiffness, or dynamic modulus, of a viscoelastic material can be calculated by measuring the material's stress and strain response under oscillating conditions, such as under sinusoidal loading or unloading. The complex stiffness is a frequency-dependent property, and can be expressed as:
k* = E' + iE''
where E' is the storage modulus, or the elastic component of the material's stiffness, and E'' is the loss modulus, or the viscous component of the material's stiffness. i is the imaginary unit.
To measure the complex stiffness of a viscoelastic material, one option is to use a dynamic mechanical analysis (DMA) machine, which applies an oscillating stress or strain to the material and measures the corresponding response. The storage modulus and loss modulus can then be calculated from the amplitude and phase shift of the material's stress and strain response.
Alternatively, the complex stiffness can be calculated from the material's stress-strain response under sinusoidal loading or unloading conditions using the following equation:
k* = G* = G' + iG''
where G' is the storage modulus and G'' is the loss modulus, calculated from the material's stress and strain response under sinusoidal loading or unloading conditions.
It is also possible to calculate the complex stiffness from the material's viscoelastic constitutive equations, such as the Maxwell, Kelvin-Voigt, or standard linear solid model, by considering the frequency dependence of the material's stress and strain response.
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