Analysis to Stress Relaxation Phenomena of Viscoelastic Materials by Means of Irreversible Thermodynamics (Ⅰ)

2005 ◽  
Vol 297-300 ◽  
pp. 365-370
Author(s):  
Guang Ze Dai ◽  
Lanying Yu ◽  
Jian Ke ◽  
Qing Qing Ni
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Medium ◽  
Stable Equilibrium ◽  
Uniaxial Stress ◽  
Thermodynamic System ◽  
Irreversible Thermodynamics ◽  
Stable Equilibrium State ◽  
Viscoelastic Solid ◽  
Solid Materials ◽  
Generalized Coordinates

Through defining a piece of viscoelastic medium as a thermodynamic system described by the generalized coordinates in the stress relaxation process, the evolution equation is derived by making use of the 1st law of thermodynamics, the 2nd law of thermodynamics and the Onsager’s principle. Based on the general solutions of the evolution, the constitutive expressions of uniaxial stress relaxation are obtained for both ideal viscoelastic solid materials and ideal viscoelastic fluid one respectively, in terms of the situation whether the coordinates participating in the entropy production are in stable or neutrally stable equilibrium state. As the result, whether the stress relaxes to a constant or zero depends on whether the free energy in viscoelastic medium is left or not.

Equilibrium dynamics in a model of growth and spatial agglomeration

2021 ◽  
pp. 1-26
Author(s):  
Shota Fujishima ◽  
Daisuke Oyama
Keyword(s):  
Economic Activity ◽  
Capital Accumulation ◽  
Time Preference ◽  
Stable Equilibrium ◽  
Spillover Effects ◽  
Spatial Equilibrium ◽  
Stable Equilibrium State ◽  
Macroeconomic Variables ◽  
Equilibrium Dynamics ◽  
Endogenous Growth Model

Abstract We present a multiregional endogenous growth model in which forward-looking agents choose their regions to live in, in addition to consumption and capital accumulation paths. The spatial distribution of economic activity is determined by the interplay between production spillover effects and urban congestion effects. We characterize the global stability of the spatial equilibrium states in terms of economic primitives such as agents’ time preference and intra- and interregional spillovers. We also study how macroeconomic variables at the stable equilibrium state behave according to the structure of the spillover network.

scholarly journals Disturbance Due to a Time Harmonic Source in Orthotropic Micropolar Viscoelastic Medium

2005 ◽  
Vol 12 (2) ◽  
pp. 261-272
Author(s):  
Rajneesh Kumar ◽  
Suman Choudhary
Keyword(s):  
Couple Stress ◽  
Viscoelastic Medium ◽  
Numerical Technique ◽  
Integral Transforms ◽  
Physical Domain ◽  
Viscoelastic Solid ◽  
Eigenvalue Approach ◽  
Time Harmonic ◽  
Concentrated Source ◽  
Displacement Force

Abstract The present study is concerned with the plane strain problem in homogeneous orthotropic micropolar viscoelastic solid. The disturbance due to the time harmonic concentrated source is investigated by employing the eigenvalue approach. Integral transforms have been inverted by a numerical technique to obtain the components of displacement, force stress and couple stress in the physical domain. The results obtained are given and illustrated graphically.

A Simple Estimating Method for Reduction of Welding Residual Stresses in Thick Welded Joint From Stress-Relief Annealing—Part IV: Applicability of the Simple Estimating Method for Stress-Relief Annealing of Thick Welded Joint

2002 ◽  
Vol 124 (2) ◽  
pp. 207-214 ◽  
Author(s):  
Keiji Nakacho
Keyword(s):  
Stress State ◽  
Stress Relaxation ◽  
Residual Stresses ◽  
Welded Joint ◽  
Uniaxial Stress ◽  
Stress Relief ◽  
Pressure Vessels ◽  
Relaxation Phenomenon ◽  
Multiaxial Stress ◽  
Creep Theory

Stress-relief annealing (SR treatment) is often applied to relieve welding residual stresses in the fabrication process of pressure vessels, etc. This study aims at development of an efficient method as simple as hand calculation to estimate reduction of residual stresses of a very thick welded joint by SR treatment. In the first report, an estimating method was developed for relaxation tests, in uniaxial stress state, at changing and constant temperatures because the stress relaxation phenomenon may be considerably similar to that observed in the SR treatment of a joint. In the second report, the stresses relaxed by SR treatment in a very thick welded joint were analyzed accurately by the finite element method based on thermal elastic-plastic creep theory. The characteristics of the changes of the welding residual stresses in multiaxial stress state were studied in detail for further development of the estimating method to SR treatment of a very thick welded joint, of which the stress state and boundary condition are very complex. In the third report, the estimating equations in multiaxial stress states were developed for the stress relaxation phenomenon in the thick welded joints, based on the foregoing characteristics. In this report, the applicability of the simple estimating method is investigated for SR treatment of the thick welded joint, by comparing the estimated results with the accurate ones obtained by FEM.

Uniaxial stress relaxation behavior of marble after cyclic disturbance loads

2020 ◽  
Author(s):  
Yaoliang Zhu ◽  
Jin Yu ◽  
Xianqi Zhou ◽  
Zhehao Yang ◽  
Xin Tang ◽  
...  
Keyword(s):  
Stress Relaxation ◽  
Uniaxial Stress ◽  
Relaxation Behavior ◽  
Stress Relaxation Behavior

An Improved Analytical Method for Life Prediction of Bolting

2000 ◽  
Vol 123 (1) ◽  
pp. 70-74 ◽  
Author(s):  
F. V. Ellis ◽  
D. R. Sielski ◽  
R. Viswanathan
Keyword(s):  
Stress Relaxation ◽  
Creep Strain ◽  
Life Prediction ◽  
Prediction Method ◽  
Uniaxial Stress ◽  
Life Assessment ◽  
Flow Rule ◽  
Creep Equation ◽  
Strain Limit ◽  
History Of

A research project was conducted to develop and validate an improved, analytical life prediction method for high-temperature turbine and valve studs/bolts. The life prediction method used the two-parameter creep equation, an incremental calculation procedure and a strain hardening flow rule. The failure criterion was an accumulated inelastic or creep strain limit of 1 percent. The life prediction procedure recommends the use of the service history of operating temperature, number/stress level of tightenings, cycle time, etc., to calculate the stress relaxation behavior. Life assessment uses the measured bolt length to calculate the accumulated creep strain. The link between the current condition, i.e., accumulated creep strain, and the remaining creep life, i.e., time to accumulate 1 percent strain, is obtained by a prediction of the future creep strain accumulation under the intended loading cycle(s) imposed during future operation. In order to validate the approach, the calculated results were compared to the results of uniaxial stress relaxation testing, bolt model testing, and service experience. The analytical procedure coupled with other industry wide NDE and measurement procedures is expected to provide broad guidelines to utilities for bolting life assessment.

scholarly journals Entropy Generation Rate in a Chemically Reacting System

1993 ◽  
Vol 115 (3) ◽  
pp. 208-212 ◽  
Author(s):  
E. P. Gyftopoulos ◽  
G. P. Beretta
Keyword(s):  
Equilibrium State ◽  
Entropy Generation ◽  
Chemical Potential ◽  
Stable Equilibrium ◽  
Entropy Generation Rate ◽  
Stable Equilibrium State ◽  
Microscopic Reversibility ◽  
Chemical Reaction Mechanisms ◽  
Chemically Reacting ◽  
Surrogate System

For a nonchemical-equilibrium state of an isolated system A that has r constituents with initial amounts na = {n1a, n2a, …, nra}, and that is subject to τ chemical reaction mechanisms, temperature, pressure, and chemical potentials cannot be defined. As time evolves, the values of the amounts of constitutents vary according to the stoichiometric relations ni(t) = nia + Σj=1τ νi(j) εj(t), where νi(j) is the stoichiometric coefficient of the ith constituent in the j-reaction mechanism and εj(t) the reaction coordinate of the jth reaction at time t. For such a state, we approximate the values of all the properties at time t with the corresponding properties of the stable equilibrium state of a surrogate system B consisting of the same constituents as A with amounts equal to ni(t) for i = 1, 2, …, r, but experiencing no chemical reactions. Under this approximation, the rate of entropy generation is given by the expression S˙irr = ε˙ · Y, where ε˙ is the row vector of the τ rates of change of the reaction coordinates, ε˙ = { ε˙1, …, ε˙τ }, Y the column vector of the τ ratios aj/Toff for j = 1, 2, …, τ, aj = −Σi=1r νi(j) μi,off, that is, the jth affinity of the stable equilibrium state of the surrogate system B, and μi,off, and Toff are the chemical potential of the ith constituent and the temperature of the stable equilibrium state of the surrogate system. Under the same approximation, by further assuming that ε˙ can be represented as a function of Y only that is, ε˙(Y), with ε˙(0) = 0 for chemical equilibrium, we show that ε˙ = L·Y + (higher order terms in Y), where L is a τ × τ matrix that must be non-negative definite and symmetric, that is, such that the matrix elements Lij satisfy the Onsager reciprocal relations, Lij = Lji. It is noteworthy that, for the first time, the Onsager relations are proven without reference to microscopic reversibility. In our view, if a process is irreversible, microscopic reversibility does not exist.

scholarly journals Finite-dimensional maps describing the dynamics of a logistic equation with delay

2019 ◽  
Vol 487 (6) ◽  
pp. 611-616
Author(s):  
S. D. Glyzin ◽  
S. A. Kashchenko
Keyword(s):  
Numerical Simulation ◽  
Equilibrium State ◽  
Stable Equilibrium ◽  
Dynamic Properties ◽  
Logistic Equation ◽  
Mathematical Ecology ◽  
Stable Equilibrium State ◽  
Finite Dimensional ◽  
Equation With Delay ◽  
Dynamics Of Populations

This article discusses a family of maps that are used in the numerical simulation of a logistic equation with delay. This equation and presented maps are widely used in problems of mathematical ecology as models of the dynamics of populations. The paper compares the dynamic properties of the trajectories of these mappings and the original equation with delay. It is shown that the behavior of the solutions of maps can be quite complicated, while the logistic equation with delay has only a stable equilibrium state or cycle.

scholarly journals Numerical Studies on the Design of Self-Resetting Active Bistable Cross-Shaped Structure for Morphing Applications

Proceedings ◽  
2020 ◽  
Vol 64 (1) ◽  
pp. 16
Author(s):  
P. M. Anilkumar ◽  
A. Haldar ◽  
S. Scheffler ◽  
B. N. Rao ◽  
R. Rolfes
Keyword(s):  
Stable Equilibrium ◽  
Fibre Composite ◽  
Equilibrium Shape ◽  
Middle Portion ◽  
Stable Equilibrium State ◽  
Control Effort ◽  
Unsymmetric Laminates ◽  
Numerical Studies ◽  
Finite Element Package ◽  
Equilibrium Shapes

Multistable structures that possess more than one elastically stable equilibrium state are highly attractive for advanced shape-changing (morphing) applications due to the nominal control effort required to maintain the structure in any of its specific stable shapes. The aim of the paper is to develop a bistable cross-shaped structure consisting of symmetric and unsymmetric laminate actuated using Macro Fibre Composite (MFC) actuators. The critical snap-through voltages required to change the shapes are investigated in a commercially available finite element package. The use of MFC actuators to snap the bistable laminate from one equilibrium shape to another and back again (self-resetting) is demonstrated. A new cross-shaped design of active bistable laminate with MFC actuators is proposed where the cross-shape consist of four rectangles on the four legs and a square on the middle portion. All the rectangles are made up of unsymmetric laminates, and the central portion is designed with a symmetric laminate. MFC actuators are bonded on both sides of the four legs to trigger snap-through and snap-back actions. An attempt is made to address the possible design difficulties arising from the additional stiffness contribution by MFC layers on the naturally cured equilibrium shapes of cross-shaped bistable laminates.

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