Stress Analysis in Viscoelastic Materials

Abstract

The problems of stress analysis for linearly viscoelastic materials are considered. This is the simplest group of materials which exhibit the general stress-strain characteristics found in polymers and plastics. Three basic aspects are considered: measurement of material properties, determination from these of the operator equations between stress and strain or equivalently of the viscoelastic model, and use of this in the theoretical analysis of stress distributions. Quasi-static analysis, in which inertia forces are negligible, is treated quite generally. The wave problems which arise when inertia effects are included are restricted to one-dimensional space variations. A series of typical solutions of these types is discussed.

Rheological Properties of Paddy Soil Under Various Pressure, Water Content and Tool Shapes

“…Theoretical described of (Liping and Chongyin, 1985;Gupta and Pandya, 1966;Lee 1956;Dey and Basudhar, 2010;Abubakar et al, 2010): Visco-elastic body of stress and strain analysis and the general media as a row, according to the same basic equation. The difference only lies in the different stress-strain relationship.…”

“…Science Publications China's GM rice paddy soil rheological model, the rheological equation (Gupta and Pandya, 1966;Lee, 1956):…”

“…Though, these methods and instruments were not considered the time factor, therefore, the stress-strain relationship of time has a strong dependence of paddy field (Liping and Chongyin, 1985). Many scholars soil rheological properties, especially water the field soil rheological properties of the (Liping and Chongyin, 1985;Gupta and Pandya, 1966;Lee 1956;Dey and Basudhar, 2010;Abubakar et al, 2010). But so far, consider the rheological properties of the soil have not yet proposed a practical method to predict the paddy vehicle subsidence amount, nor instruments designed for this purpose.…”

Response of shallow viscoelastic spherical shells to time-dependent axisymmetric loads

“…The method of solution employed in such problems rests on the use of the Laplace transform (to eliminate the dependence on time), and the correspondence principle-between the field equations and boundary conditions in the linear theories of homogeneous and isotropic elasticity and viscoelasticity-which, in the absence of thermal effects, has been established for incompressible media by Alfrey [1], and in general form by Lee [2], The extension of Lee's analogy to problems involving time-dependent temperature fields has been very recently given by Sternberg [3]. Also, considerable attention has been given to oscillation and wave propagation problems of viscoelasticity in which the inertia terms have been included, e.g., [4,5,6], and additional references on the subject may be found in a recent survey by Lee [7], Closely related to the scope of the present investigation is the recent work on vibrations of thin shallow elastic shells by E. Reissner [8], who, by utilizing the linear differential equations due to Marguerre [9], has shown that for transverse vibrations of shallow shells the longitudinal inertia terms (with negligible error) may be omitted; and hence, the formulation of the elastokinetic problems of shallow shells, as in the case of elastostatics, may be reduced to the determination of axial (or transverse) displacement and an Airy stress function. Subsequently, E. Reissner [10] dealt with transverse vibrations of axisymmetric shallow elastic spherical shells, and in particular, obtained the solution for an unlimited shell due to an oscillating point load (varying harmonically in time) at the apex.…”

“…For such steady state solutions, it is more convenient to return to the viscoelastic solution (4.5) in the Laplace-Hankel transform-plane. Following Lee [6], we replace s by iu in all quantities except in p*(i, s) which is replaced by7 P*(£), and then take the inverse Hankel transform leading to the (real) steady state amplitude W(r) for the axial displacement. When p(r, t) is specified by (5.6a), through the process just described and with the aid of (4.14a), we obtain…”