Longtime dynamics for a nonlinear viscoelastic equation with time-dependent memory kernel

2022 ◽  
Vol 64 ◽  
pp. 103432
Author(s):  
Yue Sun ◽  
Zhijian Yang
Keyword(s):  
Time Dependent ◽  
Memory Kernel ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation

scholarly journals Phenomenological memory-kernel master equations and time-dependent Markovian processes

2010 ◽  
Vol 81 (6) ◽  
Author(s):  
L. Mazzola ◽  
E.-M. Laine ◽  
H.-P. Breuer ◽  
S. Maniscalco ◽  
J. Piilo
Keyword(s):  
Master Equations ◽  
Time Dependent ◽  
Memory Kernel ◽  
Markovian Processes

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 Delayed electromechanical instability of a viscoelastic dielectric elastomer balloon

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190316 ◽  
Author(s):  
Xiongfei Lv ◽  
Liwu Liu ◽  
Jinsong Leng ◽  
Yanju Liu ◽  
Shengqiang Cai
Keyword(s):  
Hoop Stress ◽  
Mechanical Load ◽  
Viscoelastic Model ◽  
Dielectric Elastomer ◽  
Time Dependent ◽  
Convex Shape ◽  
Nonlinear Viscoelastic ◽  
Electromechanical Instability ◽  
Electromechanical Loading ◽  
Nonlinear Viscoelastic Model

When a dielectric elastomer (DE) balloon is subjected to electromechanical loading, instability may happen. In recent experiments, it has been shown that the instability configuration of a DE balloon under electromechanical loading can be very different from that only subjected to mechanical load. It has also been observed in the experiments that the electromechanical instability phenomena of a DE balloon can be highly time-dependent. In this article, we adopt a nonlinear viscoelastic model for the DE membrane to investigate the time-dependent electromechanical instability of a DE balloon. Using the model, we show that under a constant electromechanical loading, a DE balloon may gradually evolve from a convex shape to a non-convex shape with bulging out in the centre, and compressive hoop stress can also gradually develop the balloon, resulting in wrinkles as observed in the experiments. We have further shown that the snap-through instability phenomenon of the DE balloon also greatly depends on the ramping rate of the applied voltage.

scholarly journals Global Nonexistence for a Nonlinear Viscoelastic Equation with Nonlinear Damping and Velocity-Dependent Material Density

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Jian Dang ◽  
Qingying Hu ◽  
Hongwei Zhang
Keyword(s):  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Material Density ◽  
Nonexistence Result ◽  
Nonlinear Viscoelastic ◽  
Global Nonexistence ◽  
Viscoelastic Equation

We consider the initial boundary value problem of a nonlinear viscoelastic equation of Kirchhoff-type with nonlinear damping and velocity-dependent material density. We establish a nonexistence result of global solutions with positive initial energy and negative initial energy, respectively.

Cohesive Layer Modeling of Time-Dependent Debond Growth in Aggressive Environments

2005 ◽  
Vol 128 (1) ◽  
pp. 11-17 ◽  
Author(s):  
Samit Roy ◽  
Yong Wang ◽  
Soojae Park ◽  
Kenneth M. Liechti
Keyword(s):  
Time Dependent ◽  
Mixed Mode Fracture ◽  
Test Bed ◽  
Moisture Concentration ◽  
Simplified Approach ◽  
Rate Dependent ◽  
Nonlinear Viscoelastic ◽  
Convolution Integrals ◽  
Dependent Behavior ◽  
Moving Wedge

The objective of this paper is to model the synergistic bond-degradation mechanisms that may occur at the interface between a fiber-reinforced polymer (FRP) that is adhesively bonded to a substrate and subjected to elevated temperature and humidity. For this purpose, a two-dimensional cohesive-layer constitutive model with a prescribed traction-separation law is constructed from fundamental principles of continuum mechanics and thermodynamics, taking into account strain-dependent, non-Fickian hygrothermal effects as well as diffusion-induced degradation in the cohesive layer. In the interest of solution tractability, a simplified approach is employed where the rate-dependent behavior in the cohesive layer is implemented through the characterization of rate dependence of the maximum stresses and maximum strains in the cohesive layer, rather than through the use of convolution integrals in the free-energy definition. The remainder of the polymeric adhesive outside the cohesive layer is modeled as a nonlinear viscoelastic continuum with time-dependent constitutive behavior. The influence of temperature and moisture concentration on the work-of-separation and on crack growth is derived from first principles. The model is implemented in a test-bed finite element code. Results predicted by the computational model are benchmarked through comparison to experimental data from mixed-mode fracture experiments performed using a moving wedge test.

Time Dependent Nonlinear Viscoelastic Behavior of Polymer Fluids—A Review of Current Understanding

1981 ◽  
Vol 54 (3) ◽  
pp. 641-661 ◽  
Author(s):  
David S. Soong
Keyword(s):  
Viscoelastic Behavior ◽  
Time Dependent ◽  
Polymer Dynamics ◽  
Industrial Processes ◽  
Future Research ◽  
Transient Flows ◽  
Nonlinear Viscoelastic ◽  
Transient Data ◽  
Nonlinear Viscoelastic Behavior ◽  
Active Investigation

Abstract The behavior of concentrated polymer solutions and melts in transient flows has been under active investigation in recent years. This research interest stems from the realization that a better understanding of these time dependent phenomena has the potential to greatly improve existing industrial processes and to provide new insights to polymer dynamics. In this article, various aspects of the transient viscoelastic properties are discussed. Special emphases are placed on some important considerations in acquiring reliable transient data. Several promising network theories capable of interpreting these experimental results are reviewed. Future research challenges, such as the design of more complicated and stringent rheological tests for the established models, have also been identified.

Behavior of Circular Footings and Plate Anchors Embedded in Permafrost

1974 ◽  
Vol 11 (4) ◽  
pp. 531-553 ◽  
Author(s):  
B. Ladanyi ◽  
G. H. Johnston
Keyword(s):  
Mathematical Model ◽  
Bearing Capacity ◽  
Soil Mechanics ◽  
Normal Pressure ◽  
Strength Properties ◽  
Frozen Soil ◽  
Time Dependent ◽  
Nonlinear Viscoelastic ◽  
Permafrost Soils ◽  
Failure Loads

The purpose of this paper is to develop a method for predicting the creep settlement and the bearing capacity of frozen soils under deep circular loads. The theory uses experimentally determined creep parameters of frozen soil and is intended to be applicable to the design of deep circular footings and screw anchors embedded in permafrost soils. On the basis of available experimental evidence, it was concluded that a mathematical model different from that usual in soil mechanics should be used in solving the time-dependent bearing capacity problem of such footings. The solution proposed in the paper was obtained by using the mathematical model of an expanding spherical cavity in a nonlinear viscoelastic-plastic medium with time, temperature, and normal pressure dependent strength properties. For a given footing or anchor, the theory furnishes either isochronous load-displacement curves, or load-creep rate curves, or a time-dependent bearing capacity for which formulas and graphs of nonlinear elastic-plastic bearing capacity factors are supplied.The theoretical predictability of creep rates and ultimate failure loads was checked against the results of screw anchor tests carried out by the Division of Building Research, N.R.C.C., at a permafrost site in Thompson, Manitoba. It was found that the use in the theory of the creep parameters determined by creep-pressuremeter tests performed at the site, resulted in a satisfactory agreement between the predicted and the observed behavior.

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