scholarly journals Asymptotic analysis for a nonlinear viscoelastic problem with innite history under a wider class of relaxation functions

2020 ◽  
Author(s):  
Adel Al mahdi ◽  
Mohammed Al Gharabli
Keyword(s):  
Asymptotic Analysis ◽  
Viscoelastic Problem ◽  
Relaxation Functions ◽  
Nonlinear Viscoelastic

scholarly journals A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Fushan Li
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Laplace Transformation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Nonlinear Viscoelastic ◽  
Leading Term ◽  
Viscoelastic Shells

By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional nonlinear viscoelastic shells model satisfied by the leading term of asymptotic expansion of the solution to the three-dimensional equations.

Blow Up of Solutions for a System of Nonlinear Viscoelastic Equations with Damping Terms in Rn

2009 ◽  
Vol 64 (3-4) ◽  
pp. 180-184
Author(s):  
Wenjun Liu ◽  
Shengqi Yub
Keyword(s):  
Initial Data ◽  
Differential Inequality ◽  
Blow Up ◽  
Coupled System ◽  
Initial Energy ◽  
Relaxation Functions ◽  
Nonlinear Viscoelastic ◽  
Linear Damping ◽  
Viscoelastic Equations ◽  
Damping And Source Terms

Abstract We consider a coupled system of nonlinear viscoelastic equations with linear damping and source terms. Under suitable conditions of the initial data and the relaxation functions, we prove a finitetime blow-up result with vanishing initial energy by using the modified energy method and a crucial lemma on differential inequality

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.

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