Viscoelastic Behavior of Heterogeneous Media

1965 ◽  
Vol 32 (3) ◽  
pp. 630-636 ◽  
Author(s):  
Zvi Hashin
Keyword(s):  
Linear Viscoelasticity ◽  
Elastic Moduli ◽  
Heterogeneous Media ◽  
Correspondence Principle ◽  
Viscoelastic Behavior ◽  
Effective Elastic Moduli ◽  
Macroscopic Behavior ◽  
Linear Viscoelastic

The macroscopic viscoelastic behavior of linear viscoelastic heterogeneous media is defined in terms of effective relaxation moduli and creep compliances. It is shown that these effective relaxation and creep functions are related to effective elastic moduli of elastic heterogeneous media by the correspondence principle of the theory of linear viscoelasticity. This analogy is applied to the determination of macroscopic behavior of some special kinds of viscoelastic heterogeneous media, in dilatation and shear.

Viscoelastic Effects in Birefringent Coatings

1961 ◽  
Vol 28 (4) ◽  
pp. 601-607 ◽  
Author(s):  
P. S. Theocaris ◽  
C. Mylonas
Keyword(s):  
Epoxy Resins ◽  
Viscoelastic Behavior ◽  
Viscoelastic Layer ◽  
Pure Epoxy ◽  
Plastic Surface ◽  
Viscoelastic Effects ◽  
Linear Viscoelastic ◽  
Relaxation Curves ◽  
Viscoelastic Coatings

The method of birefringent coatings for the determination of elastic and plastic surface strains of opaque bodies like metals assumes perfect elasticity of the coating material. In reality the coating, assumed much softer than the metal, presents the problem of a general viscoelastic layer under prescribed boundary displacements (at the metal-plastic interface). As already shown, this problem is greatly simplified for isotropic linear viscoelastic coatings, for small strains, for a linear law of strain birefringence, and for interface displacements expressed as a product of a function of space co-ordinates by a time function. The obviously advantageous stress-strain-optical linearity was experimentally verified in pure and in plasticized epoxy resins which make the best coatings. Tests were carried out in uniaxial loading and in shear, in creep, as well as in relaxation. The main conclusion is that the pure epoxy resins show negligible inelasticity, and the plasticized have a linear photo-viscoelastic behavior. Explicit laws were fitted to the creep and relaxation curves. Tests were also carried out with deeply notched coated steel bars deformed in the plastic range. The variation of fringe pattern with time was found to be negligible for the pure epoxy resins and to diminish slightly and proportionally with time throughout the model for the plasticized resins.

Mechanical analysis of viscoelastic models for Earth media

2019 ◽  
Vol 220 (3) ◽  
pp. 1762-1773 ◽  
Author(s):  
Igor B Morozov ◽  
Wubing Deng ◽  
Danping Cao
Keyword(s):  
Physical Properties ◽  
Elastic Moduli ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Mechanical Analysis ◽  
Inertial Body ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
The Difference ◽  
Quality Factor Q

SUMMARY Linear and non-linear viscoelastic (VE) models such as the standard linear solid (SLS) and the generalized SLS (GSLS) are broadly used to represent the anelasticity of materials and Earth's media. However, although the VE approach is often satisfactory for any given observation, the inferred physical causes of anelasticity may be significantly misrepresented by this paradigm, and its predictions may be wrong or inaccurate in other cases. This problem is particularly important in heterogeneous media, including most cases of interest for seismology. For example, in homogenous media, VE and mechanics-based models predict identical quality-factor Q(f) and phase velocity c(f) spectra, but in heterogenous media, these models yield different time-stepping equations and interactions with material–property boundaries. The commonly used VE algorithms for modelling seismic waves rely on postulated convolutional integrals in time, whereas physically, models of rock rheologies should still be based on spatial interactions. To understand how VE models relate to mechanics, it is instructive to consider which physical properties of the medium are constrained reliably and which of them remain unconstrained by a pair of Q(f) and c(f) spectra, that is by VE properties. Despite its popular association with ‘attenuation,’ the peak value of Q−1(f) is actually a purely elastic property representing the existence of two (for SLS) or multiple (for GSLS) elastic moduli. These moduli are analogous to the drained and undrained moduli in poroelasticity or isothermal and adiabatic moduli in thermodynamics. By virtue of the Kramers–Krönig relations, the peak Q−1 is related to the total velocity dispersion, which is also caused by the difference between elastic moduli. By contrast, true anelasticity-related physical properties like viscosity are represented not by Q−1 values but by the frequencies of Q−1(f) peaks in the data. However, these frequencies also depend on multiple material properties that are not recognized or arbitrarily selected in the SLS and GSLS models. Inertial, body-force friction and the corresponding boundary effects are also ignored in VE models, which may again be improper for layered media. Thus, for physically accurate interpretation of laboratory experiments and numerical modelling of seismic waves, first-principle equations of mechanics should be used instead of VE models.

scholarly journals A three-dimensional model for rain-wind induced vibration of stay cables in cable-stayed bridges

2020 ◽  
Vol 14 (1) ◽  
pp. 15-27
Author(s):  
Nguyen Thi Hai Nhu ◽  
Tran Anh Binh ◽  
Ha Manh Hung
Keyword(s):  
Elastic Moduli ◽  
Heterogeneous Media ◽  
Effective Properties ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Main Idea ◽  
Data Driven ◽  
Effective Elastic Moduli ◽  
Three Dimensional Model ◽  
Data Driven Approach

The most rigorous effective medium approximations for elastic moduli are elaborated for matrix composites made from an isotropic continuous matrix and isotropic inclusions associated with simple shapes such as circles or spheres. In this paper, we focus specially on the effective elastic moduli of the heterogeneous composites with arbitrary inclusion shapes. The main idea of this paper is to replace those inhomogeneities by simple equivalent circular (spherical) isotropic inclusions with modified elastic moduli. Available simple approximations for the equivalent circular (spherical) inclusion media then can be used to estimate the effective properties of the original medium. The data driven technique is employed to estimate the properties of equivalent inclusions and the Extended Finite Element Method is introduced to modeling complex inclusion shapes. Robustness of the proposed approach is demonstrated through numerical examples with arbitrary inclusion shapes. Keywords: data driven approach; equivalent inclusion, effective elastic moduli; heterogeneous media; artificial neural network.

Sign in / Sign up

Export Citation Format

Share Document