Stability of a Nonlinear Viscoelastic Problem Governed by Lamé Operator

2019 ◽  
pp. 189-194
Author(s):  
Meflah Mabrouk ◽  
Khoukhi Alae Nore
Keyword(s):  
Viscoelastic Problem ◽  
Nonlinear Viscoelastic

Response of power-law-viscoelastic and time-dependent materials to rate jumps

2009 ◽  
Vol 24 (3) ◽  
pp. 853-862 ◽  
Author(s):  
A.H.W. Ngan ◽  
B. Tang
Keyword(s):  
Elastic Constant ◽  
Time Instant ◽  
Elastic Problem ◽  
Constitutive Law ◽  
Displacement Rate ◽  
Viscoelastic Problem ◽  
Experimental Scheme ◽  
Linear Elastic ◽  
Nonlinear Viscoelastic ◽  
Load Rate

Nonlinear viscoelastic problems are in general not analytically solvable. However, it is shown here that, for any viscoelastic materials describable by a constitutive law with linear elastic and (in general) nonlinear viscous elements arranged in any network fashion, such as the Maxwell or standard linear solid arrangements, it is always possible to eliminate the viscous terms by replacing the displacement, strain, and stress fields of the problem by the jumps in rates of these fields. After the viscous terms are eliminated, the problem is reduced to a linear elastic problem defined on the same spatial domain and with the same elastic constant as in the original viscoelastic problem. Such a reduced elastic problem is analytically solvable in many practical cases, and the solution yields a relation between jumps in the load rate and the displacement rate, pertinent to the boundary conditions in the original problem. Such a relation can often be used as the basis for an experimental scheme to measure the elastic constants of materials. The material can be time- or strain-dependent, and the value of the elastic constant measured corresponds to the time instant or the strain value when the jump in load or displacement rate is implemented.

scholarly journals Asymptotic behavior for a nonlinear viscoelastic problem with a velocity-dependent material density

2005 ◽  
Vol 2005 (10) ◽  
pp. 1497-1506 ◽  
Author(s):  
Nasser-Eddine Tatar
Keyword(s):  
Asymptotic Behavior ◽  
Relaxation Function ◽  
Viscoelastic Problem ◽  
Material Density ◽  
Nonlinear Viscoelastic ◽  
Weaker Conditions ◽  
Uniformly Bounded

We consider a nonlinear viscoelastic problem and prove that the solutions are uniformly bounded and decay exponentially to zero as time goes to infinity. This is established under weaker conditions on the relaxation function than the usually used ones. In particular, we remove the assumptions on the derivative of the kernel. In fact, our kernels are not necessarily differentiable.

scholarly journals Asymptotic stability of a viscoelastic problem with time-varying delay in boundary feedback

2021 ◽  
pp. 3-3
Author(s):  
Abita Rahmoune
Keyword(s):  
Feedback Condition ◽  
Time Varying ◽  
Decay Estimates ◽  
Viscoelastic Problem ◽  
Dissipative Term ◽  
Time Varying Delay ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation ◽  
The Given ◽  
Varying Delay

In this paper, we investigate a nonlinear viscoelastic equation. By assuming time-varying delay feedback acting on the boundary, under certain assumptions on the given data, the general decay estimates for the energy are established by introducing suitable Lyapunov functionals. This model improves earlier ones in the literature in which only the dissipative term in the feedback condition is considered.

Rheological characterization of tack and viscoelasticity of compositions of crepe coating used in the Yankee dryer

TAPPI Journal ◽  
2019 ◽  
Vol 18 (11) ◽  
pp. 641-649
Author(s):  
JOSHUA OMAMBALA ◽  
CARL MCINTYRE
Keyword(s):  
Normal Force ◽  
Weight Ratio ◽  
Good Combination ◽  
Rheological Characterization ◽  
Nonlinear Viscoelastic ◽  
Coating Composition ◽  
Linear And Nonlinear ◽  
Work Done ◽  
Tissue Production

The vast majority of tissue production uses creping to achieve the required set of properties on the base sheet. The Yankee coating helps to develop the desired crepe that in turn determines properties such as bulk and softness. The adhesion of the sheet to the Yankee surface is a very important characteristic to consider in achieving the desired crepe. The coating mix usually consists of the adhesive, modifier, and release. A good combination of these components is essential to achieving the desired properties of the tissue or towel, which often are determined by trials on the machine that can be time consuming and lead to costly rejects. In this paper, five compositions of an industrial Yankee coating adhesive, modifier, and release were examined rheologically. The weight ratio of the adhesive was kept constant at 30% in all five compositions and the modifier and release ratios were varied. The normal force and work done by the different compositions have been shown at various temperatures simulating that of the Yankee surface, and the oscillatory test was carried out to explain the linear and nonlinear viscoelastic characteristic of the optimal coating composition.

Nonlinear Viscoelastic Finite Element Analysis of Adhesive Joints

1988 ◽  
Vol 16 (3) ◽  
pp. 146-170 ◽  
Author(s):  
S. Roy ◽  
J. N. Reddy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Viscoelastic Behavior ◽  
Bonded Joints ◽  
Adhesively Bonded ◽  
Element Analysis ◽  
Adhesively Bonded Joints ◽  
Nonlinear Viscoelastic ◽  
Structural Failures ◽  
Updated Lagrangian

Abstract A good understanding of the process of adhesion from the mechanics viewpoint and the predictive capability for structural failures associated with adhesively bonded joints require a realistic modeling (both constitutive and kinematic) of the constituent materials. The present investigation deals with the development of an Updated Lagrangian formulation and the associated finite element analysis of adhesively bonded joints. The formulation accounts for the geometric nonlinearity of the adherends and the nonlinear viscoelastic behavior of the adhesive. Sample numerical problems are presented to show the stress and strain distributions in bonded joints.

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