Unbounded complex modulus of viscoelastic materials and the Kramers–Kronig relations

2005 ◽  
Vol 279 (3-5) ◽  
pp. 687-697 ◽  
Author(s):  
T. Pritz
Keyword(s):  
Complex Modulus ◽  
Viscoelastic Materials

scholarly journals A simplified transfer matrix approach for the determination of the complex modulus of viscoelastic materials

2016 ◽  
Vol 53 ◽  
pp. 180-187 ◽  
Author(s):  
Paolo Bonfiglio ◽  
Francesco Pompoli ◽  
Kirill V. Horoshenkov ◽  
Mahmud Iskandar B. Seth A. Rahim
Keyword(s):  
Transfer Matrix ◽  
Complex Modulus ◽  
Matrix Approach ◽  
Viscoelastic Materials ◽  
Transfer Matrix Approach

Finite‐difference modeling of viscoelastic materials with quality factors of arbitrary magnitude

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 817-824 ◽  
Author(s):  
Sergey Asvadurov ◽  
Leonid Knizhnerman ◽  
Jahir Pabon
Keyword(s):  
Finite Difference ◽  
Rational Approximation ◽  
Complex Modulus ◽  
Acoustic Noise ◽  
Viscoelastic Materials ◽  
Quality Factors ◽  
Frequency Dependent ◽  
High Attenuation ◽  
Constant Quality ◽  
The Time Domain

To minimize acoustic noise, designers of sonic logging tools often consider coatings of viscoelastic materials with very high attenuation properties. Efficient finite‐difference modeling of viscoelastic materials is a topic of current research. To model viscoelastic materials in the time domain through finite differences efficiently, one needs to replace the time convolution, which enters in the stress–strain relations, by a set of first‐order differential equations. This procedure is equivalent to computing a rational approximation of a certain form to the frequency‐dependent complex modulus of viscoelasticity. Known schemes for computing such approximations are designed to treat materials with low attenuation, such as underground formations, but fail to produce accurate or even physically meaningful results for highly attenuative materials. We propose a novel scheme that allows one to construct, for a given frequency range, a uniformly optimal rational approximation for the most widely used model of materials with constant quality (Q‐) factors of arbitrary magnitude. We present the proof of convergence and demonstrate it on numerical finite‐difference examples. These examples also demonstrate the effective transparency of a simple tool modeled as a pipe of highly viscoelastic material. For frequency‐dependent quality factors we present a modified numerical scheme to compute a nearly optimal rational approximation of the viscoelastic modulus.

scholarly journals Viscoelastic Contact Simulation under Harmonic Cyclic Load

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Sergiu Spinu
Keyword(s):  
Energy Dissipation ◽  
Internal Energy ◽  
Viscoelastic Material ◽  
Cyclic Load ◽  
Complex Modulus ◽  
Contact Process ◽  
Contact Radius ◽  
Viscoelastic Materials ◽  
Rheological Models ◽  
Viscoelastic Contact

Characterization of viscoelastic materials from a mechanical point of view is often performed via dynamic mechanical analysis (DMA), consisting in the arousal of a steady-state undulated response in a uniaxial bar specimen, allowing for the experimental measurement of the so-called complex modulus, assessing both the elastic energy storage and the internal energy dissipation in the viscoelastic material. The existing theoretical investigations of the complex modulus’ influence on the contact behavior feature severe limitations due to the employed contact solution inferring a nondecreasing contact radius during the loading program. In case of a harmonic cyclic load, this assumption is verified only if the oscillation indentation depth is negligible compared to that due to the step load. This limitation is released in the present numerical model, which is capable of contact simulation under arbitrary loading profiles, irregular contact geometry, and complicated rheological models of linear viscoelastic materials, featuring more than one relaxation time. The classical method of deriving viscoelastic solutions for the problems of stress analysis, based on the elastic-viscoelastic correspondence principle, is applied here to derive the displacement response of the viscoelastic material under an arbitrary distribution of surface tractions. The latter solution is further used to construct a sequence of contact problems with boundary conditions that match the ones of the original viscoelastic contact problem at specific time intervals, assuring accurate reproduction of the contact process history. The developed computer code is validated against classical contact solutions for universal rheological models and then employed in the simulation of a harmonic cyclic indentation of a polymethyl methacrylate half-space by a rigid sphere. The contact process stabilization after the first cycles is demonstrated and the energy loss per cycle is calculated under an extended spectrum of harmonic load frequencies, highlighting the frequency for which the internal energy dissipation reaches its maximum.

Determination of the complex modulus of elasticity of soft viscoelastic materials

1977 ◽  
Vol 12 (1) ◽  
pp. 158-160 ◽  
Author(s):  
N. N. Morozova ◽  
S. A. Rybak
Keyword(s):  
Modulus Of Elasticity ◽  
Complex Modulus ◽  
Viscoelastic Materials

Bayesian approaches for identification of the complex modulus of viscoelastic materials

Automatica ◽  
2007 ◽  
Vol 43 (8) ◽  
pp. 1369-1376 ◽  
Author(s):  
Kaushik Mahata ◽  
Torsten Söderström
Keyword(s):  
Complex Modulus ◽  
Viscoelastic Materials ◽  
Bayesian Approaches
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