The Fracture of Solids with Microcracks: Experiments, Statistical Thermodynamics and Constitutive Equations

1989 ◽  
pp. 3845-3852 ◽  
Author(s):  
V.I. BETECHTIN ◽  
O.B. NAIMARK ◽  
V.V. SILBERSCHMIDT
Keyword(s):  
Constitutive Equations ◽  
Statistical Thermodynamics

MEMORY-DEPENDENT CONSTITUTIVE EQUATIONS IN INFORMATIONAL STATISTICAL THERMODYNAMICS

1995 ◽  
Vol 09 (16) ◽  
pp. 1933-1944 ◽  
Author(s):  
ÁUREA ROSAS VASCONCELLOS ◽  
ROBERTO LUZZI ◽  
LEOPOLDO S. GARCIA-COLIN
Keyword(s):  
Infinite Series ◽  
Constitutive Equations ◽  
Hamiltonian Dynamics ◽  
Relaxation Times ◽  
Operator Method ◽  
Statistical Thermodynamics ◽  
Irreversible Thermodynamics ◽  
Relaxation Processes ◽  
Kinetic Coefficients ◽  
Statistical Operator

The nonequilibrium Statistical Operator Method, seemingly contained within the scope of Jaynes’ Predictive Statistical Mechanics, provides a foundation for irreversible thermodynamics in what is called Informational Statistical Thermodynamics, and within it a way of deriving generalized constitutive equations which contain non-localities on space. Here we present a derivation of these equations of evolution describing how memory effects are incorporated into the theory. We show that the memory kernels in the kinetic coefficients and relaxation times can be expressed in terms of an infinite series of instantaneous collisions integrals, of ever increasing order in the interaction strengths that are related to the slow relaxation processes that develop in the system. The kinetic coefficients are derived on the basis of the Hamiltonian dynamics of the system accompanied by appropriate averages over the nonequilibrium informational statistical ensemble.

Equilibrium and Non-Equilibrium Statistical Thermodynamics

2004 ◽  
Author(s):  
Michel Le Bellac ◽  
Fabrice Mortessagne ◽  
G. George Batrouni
Keyword(s):  
Statistical Thermodynamics ◽  
Non Equilibrium

Prediction of Tread Pattern Wear by an Explicit Finite Element Model3

2007 ◽  
Vol 35 (4) ◽  
pp. 276-299 ◽  
Author(s):  
J. C. Cho ◽  
B. C. Jung
Keyword(s):  
Finite Element ◽  
Wear Rate ◽  
Tangential Stress ◽  
Rate Equation ◽  
Constitutive Equations ◽  
Slip Velocity ◽  
Test Results ◽  
Explicit Finite Element ◽  
Driving Condition ◽  
Driving Conditions

Abstract Tread pattern wear is predicted by using an explicit finite element model (FEM) and compared with the indoor drum test results under a set of actual driving conditions. One pattern is used to determine the wear rate equation, which is composed of slip velocity and tangential stress under a single driving condition. Two other patterns with the same size (225/45ZR17) and profile are used to be simulated and compared with the indoor wear test results under the actual driving conditions. As a study on the rubber wear rate equation, trial wear rates are assumed by several constitutive equations and each trial wear rate is integrated along time to yield the total accumulated wear under a selected single cornering condition. The trial constitutive equations are defined by independently varying each exponent of slip velocity and tangential stress. The integrated results are compared with the indoor test results, and the best matching constitutive equation for wear is selected for the following wear simulation of two other patterns under actual driving conditions. Tens of thousands of driving conditions of a tire are categorized into a small number of simplified conditions by a suggested simplification procedure which considers the driving condition frequency and weighting function. Both of these simplified conditions and the original actual conditions are tested on the indoor drum test machines. The two results can be regarded to be in good agreement if the deviation that exists in the data is mainly due to the difference in the test velocity. Therefore, the simplification procedure is justified. By applying the selected wear rate equation and the simplified driving conditions to the explicit FEM simulation, the simulated wear results for the two patterns show good match with the actual indoor wear results.

Constitutive Equations of Soils: 4. Macro-Rheology

1978 ◽  
Vol 18 (3) ◽  
pp. 85-95
Author(s):  
Hideo Sekiguchi
Keyword(s):  
Constitutive Equations

scholarly journals Shaping Microstructure and Mechanical Properties of High-Carbon Bainitic Steel in Hot-Rolling and Long-Term Low-Temperature Annealing

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 384
Author(s):  
Tomasz Dembiczak ◽  
Marcin Knapiński
Keyword(s):  
Mathematical Models ◽  
Hot Rolling ◽  
Constitutive Equations ◽  
Rolling Process ◽  
Bainitic Steel ◽  
Compression Tests ◽  
High Carbon ◽  
Bainite Steel ◽  
Dilatometric Studies

Based on the research results, coefficients in constitutive equations, describing the kinetics of dynamic, meta-dynamic, and static recrystallization in high-carbon bainitic steel during hot deformation were determined. The developed mathematical model takes into account the dependence of the changing kinetics in the structural size of the preliminary austenite grains, the value of strain, strain rate, temperature, and time. Physical simulations were carried out on rectangular specimens. Compression tests with a flat state of deformation were carried out using a Gleeble 3800. Based on dilatometric studies, coefficients were determined in constitutive equations, describing the grain growth of the austenite of high-carbon bainite steel under isothermal annealing conditions. The aim of the research was to verify the developed mathematical models in semi-industrial conditions during the hot-rolling process of high-carbon bainite steel. Analysis of the semi-industrial studies of the hot-rolling and long-term annealing process confirmed the correctness of the predicted mathematical models describing the microstructure evolution.

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