Model reduction and substructuring for computing responses of structures containing frequency-dependent viscoelastic materials

2002 ◽  
Author(s):  
Sylvain Germes ◽  
Francois van Herpe
Keyword(s):  
Model Reduction ◽  
Viscoelastic Materials ◽  
Frequency Dependent

Frequency Dependence of Viscoelastic Materials for Small Joint Replacements

2007 ◽  
Author(s):  
Aziza Mahomed ◽  
David W. Hukins ◽  
Duncan E. T. Shepherd ◽  
Stephen N. Kukureka
Keyword(s):  
Frequency Dependence ◽  
Loading Frequency ◽  
Viscoelastic Materials ◽  
Frequency Dependent ◽  
Joint Replacements ◽  
Storage And Loss Moduli ◽  
Small Joint ◽  
Wrist Joints ◽  
Medical Grade

Elastomers, such as silicone, are currently used for many designs of artificial finger and wrist joints because they are inert, durable, flexible and allow the necessary range of movements [1–6]. The disadvantage of these silicone joints is that they fracture in vivo [3,5,7]. In addition, these elastomers are viscoelastic so that their properties may depend on loading frequency. It is then possible that the performance of the joints may be frequency dependent. As a first stage in investigating such effects, we have determined the storage and loss moduli of a medical grade silicone in compression.

scholarly journals Frequency-dependent scaling from mesoscale to macroscale in viscoelastic random composites

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150801 ◽  
Author(s):  
Jun Zhang ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Scaling Function ◽  
Initial Boundary ◽  
Volume Element ◽  
Viscoelastic Materials ◽  
Static Properties ◽  
Frequency Dependent ◽  
Random Composites ◽  
Set Up ◽  
Initial Boundary Value ◽  
The Hill

This paper investigates the scaling from a statistical volume element (SVE; i.e. mesoscale level) to representative volume element (RVE; i.e. macroscale level) of spatially random linear viscoelastic materials, focusing on the quasi-static properties in the frequency domain. Requiring the material statistics to be spatially homogeneous and ergodic, the mesoscale bounds on the RVE response are developed from the Hill–Mandel homogenization condition adapted to viscoelastic materials. The bounds are obtained from two stochastic initial-boundary value problems set up, respectively, under uniform kinematic and traction boundary conditions. The frequency and scale dependencies of mesoscale bounds are obtained through computational mechanics for composites with planar random chessboard microstructures. In general, the frequency-dependent scaling to RVE can be described through a complex-valued scaling function, which generalizes the concept originally developed for linear elastic random composites. This scaling function is shown to apply for all different phase combinations on random chessboards and, essentially, is only a function of the microstructure and mesoscale.

scholarly journals Adaptive model reduction technique for large-scale dynamical systems with frequency-dependent damping

2018 ◽  
Vol 332 ◽  
pp. 363-381 ◽  
Author(s):  
Xiang Xie ◽  
Hui Zheng ◽  
Stijn Jonckheere ◽  
Axel van de Walle ◽  
Bert Pluymers ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Large Scale ◽  
Reduction Technique ◽  
Adaptive Model ◽  
Frequency Dependent ◽  
Model Reduction Technique

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.

Sign in / Sign up

Export Citation Format

Share Document