Global existence and uniform decay for a nonlinear viscoelastic equation with damping

2009 ◽  
Vol 70 (9) ◽  
pp. 3090-3098 ◽  
Author(s):  
Xiaosen Han ◽  
Mingxin Wang
Keyword(s):  
Global Existence ◽  
Uniform Decay ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation

GLOBAL SMOOTH SOLUTION AND UNIFORM RATE OF DECAY IN NONLINEAR VISCOELASTICITY

1994 ◽  
Vol 06 (05) ◽  
pp. 855-868 ◽  
Author(s):  
JAIME E. MUÑOZ RIVERA
Keyword(s):  
Global Existence ◽  
Existence Theorem ◽  
Smooth Solution ◽  
Nonlinear Viscoelasticity ◽  
Small Data ◽  
Bounded Domains ◽  
Nonlinear Viscoelastic ◽  
Global Existence Theorem ◽  
Viscoelastic Equation ◽  
Rate Of Decay

We prove a global existence theorem for the nonlinear viscoelastic equation for small data in H2. Moreover we prove that the solution decays exponentially in bounded domains when t goes to infinity.

scholarly journals On the viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources with variable-exponent nonlinearities

2020 ◽  
Vol 65 (4) ◽  
pp. 599-639
Author(s):  
Abita Rahmoune ◽  
Benyattou Benabderrahmane
Keyword(s):  
Decay Rate ◽  
Relaxation Function ◽  
Variable Exponent ◽  
Nonlinear Boundary ◽  
Variable Exponents ◽  
Nonlinear Feedback ◽  
Uniform Decay ◽  
Nonlinear Viscoelastic ◽  
Solution Energy ◽  
Viscoelastic Equation

This work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping and nonlinear boundary interior sources with variable exponents. Under appropriate assumptions, we establish a uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

scholarly journals Peridynamic model for nonlinear viscoelastic creep and creep rupture of Polypropylene

2019 ◽  
Vol 13 (4) ◽  
pp. 5735-5752 ◽  
Author(s):  
M. A. Azizi ◽  
A. K. Ariffin
Keyword(s):  
Internal State ◽  
Creep Behaviour ◽  
Numerical Data ◽  
Creep Rupture ◽  
Experimental Result ◽  
Viscoelastic Creep ◽  
Nonlinear Viscoelastic ◽  
Secondary Stage ◽  
Peridynamic Model ◽  
Viscoelastic Equation

This paper presents the peridynamic numerical method for nonlinear viscoelastic creep behaviour which consists of primary, secondary, tertiary creep stages and creep rupture. A nonlinear viscoelastic creep constitutive equation based on internal state variable (ISV) theory which covers four creep stages is examined. The viscoelastic equation is substituted into material parameter in the peridynamic equation to derive a new peridynamic method with two time parameters i.e. numerical time and real time. The parameters of the viscoelastic equation is analyzed and evaluated. In validating this peridynamic method, a comparison is made between numerical and experimental data. The peridynamic method for nonlinear viscoelastic creep behaviour (VE-PD) is approved by the good similarity between numerical and experimental creep strain curves with overall difference of 10.67%. The nonlinearity of experimental and numerical data is adequately similar as the error between experimental and numerical curves of secondary stage strain rate against load is 8.022%. The shapes of fractured numerical specimen show good resemblance with the experimental result as well.

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