On general decay for a nonlinear viscoelastic equation

2021 ◽  
pp. 1-19
Author(s):  
Abdelkarim Kelleche ◽  
Baowei Feng
Keyword(s):  
General Decay ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation

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.

scholarly journals General decay rate of a weakly dissipative viscoelastic equation with a general damping

2020 ◽  
Vol 40 (6) ◽  
pp. 647-666
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Wide Class ◽  
Nonlinear Damping ◽  
Numerical Results ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Viscoelastic Equation

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

scholarly journals Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

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