scholarly journals 50 Years of the K-BKZ Constitutive Relation for Polymers

2013 ◽  
Vol 2013 ◽  
pp. 1-22 ◽  
Author(s):  
Evan Mitsoulis
Keyword(s):  
Mathematical Modeling ◽  
Constitutive Model ◽  
Particle Tracking ◽  
Constitutive Equations ◽  
Historical Perspective ◽  
Governing Equations ◽  
Dimensionless Numbers ◽  
Flow Problems ◽  
Polymer Flows ◽  
Method Of Solution

The K-BKZ constitutive model is now 50 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experiment, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction a historical perspective is given on developments in the last 50 years of the K-BKZ model. Then a section follows on mathematical modeling of polymer flows, including governing equations of flow, rheological constitutive equations (with emphasis on viscoelastic integral constitutive equations of the K-BKZ type), dimensionless numbers, and boundary conditions. The Method of Solution section reviews the major developments of techniques necessary for particle tracking and calculation of the integrals for the viscoelastic stresses in flow problems. Finally, selected examples are given of successful application of the K-BKZ model in polymer flows relevant to rheology.

DIMENSIONLESS PHYSICAL-MATHEMATICAL MODELING OF TURBULENT NATURAL CONVECTION

2021 ◽  
Vol 20 (3) ◽  
pp. 37
Author(s):  
S. A. Verdério Júnior ◽  
V. L. Scalon ◽  
S. R. Oliveira ◽  
P. C. Mioralli ◽  
E. Avellone
Keyword(s):  
Mathematical Modeling ◽  
Natural Convection ◽  
Turbulent Flows ◽  
Convection Heat Transfer ◽  
Thermal Engineering ◽  
Physical Parameters ◽  
Problem Situation ◽  
Dimensionless Numbers ◽  
Turbulent Natural Convection ◽  
Cooling Coils

Natural convection heat transfer is present in the most diverse applications of Thermal Engineering, such as in electronic equipment, transmission lines, cooling coils, biological systems, etc. The correct physical-mathematical modeling of this phenomenon is crucial in the applied understanding of its fundamentals and the design of thermal systems and related technologies. Dimensionless analyses can be applied in the study of flows to reduce geometric and experimental dependence and facilitate the modeling process and understanding of the main influence physical parameters; besides being used in creating models and prototypes. This work presents a methodology for dimensionless physical-mathematical modeling of natural convection turbulent flows over isothermal plates, located in an “infinite” open environment. A consolidated dimensionless physical-mathematical model was defined for the studied problem situation. The physical influence of the dimensionless numbers of Grashof, Prandtl, and Turbulent Prandtl was demonstrated. The use of the Theory of Dimensional Analysis and Similarity and its application as a tool and numerical device in the process of building and simplifying CFD simulations were discussed.

Entropy Production as a Predictive Performance Measure: I — Turbomachinery

1999 ◽  
Author(s):  
David M. Paulus ◽  
Richard A. Gaggioli ◽  
William R. Dunbar
Keyword(s):  
Mathematical Modeling ◽  
Energy Conversion ◽  
Entropy Production ◽  
Predictive Performance ◽  
Performance Measure ◽  
Governing Equations ◽  
Compressor Performance

Abstract It is proposed that consideration be given to an alternative, streamlined manner for mathematical modeling of the performance of energy conversion and transfer equipment. We make the case, here, by application to compressors. It is advocated that, instead of using an expression for efficiency as one of the governing equations, performance can be accounted for directly, with entropy production. It is shown that (1) the modeling is more straightforward, using fewer relations, and (2) that compressor performance (e.g. maps) can be represented equally well.

A Dislocation Density Based Constitutive Model for Cyclic Deformation

1996 ◽  
Vol 118 (4) ◽  
pp. 441-447 ◽  
Author(s):  
Y. Estrin ◽  
H. Braasch ◽  
Y. Brechet
Keyword(s):  
Cyclic Loading ◽  
Dislocation Density ◽  
Constitutive Model ◽  
Constitutive Equations ◽  
Cyclic Deformation ◽  
Internal Variables ◽  
Density Evolution ◽  
Alloy 800H ◽  
Material Response ◽  
Dislocation Densities

A new constitutive model describing material response to cyclic loading is presented. The model includes dislocation densities as internal variables characterizing the microstructural state of the material. In the formulation of the constitutive equations, the dislocation density evolution resulting from interactions between dislocations in channel-like dislocation patterns is considered. The capabilities of the model are demonstrated for INCONEL 738 LC and Alloy 800H.

Fundamental Concepts of Strength of Materials

2015 ◽  
pp. 10-30
Keyword(s):  
Constitutive Model ◽  
Constitutive Equations ◽  
Virtual Work ◽  
Elementary Theory ◽  
Elastic Beam ◽  
Theory Of Elasticity ◽  
Principle Of Virtual Work ◽  
Basic Tool ◽  
Strength Of Materials

This chapter presents the concepts of strength of materials that are relevant to the analysis of frames. These are the modified Timoshenko theory of elastic beams (Sections 2.1-2.3) and the Euler-Bernoulli one (Section 2.4). These concepts are not presented as in the conventional textbooks of strength of materials. Instead, the formulations are described using the scheme that is customary in the theory of elasticity and that was described in Chapter 1 (Section 1.1.1) (i.e. in terms of kinematics, statics, and constitutive equations). Kinematics is the branch of mechanics that studies the movement of solids and structures without considering its causes. Statics studies the equilibrium of forces; the basic tool for this analysis is the principle of virtual work. The constitutive model that describes a one-to-one relationship between stresses and deformations completes the formulation of the elastic beam problem. Finally, in Section 2.5, some concepts of the elementary theory of torsion needed for the formulation of tridimensional frames are recalled.

On the constitutive equations of fresh mortar

2016 ◽  
Vol 25 (5-6) ◽  
pp. 183-187
Author(s):  
P.A. Kakavas ◽  
A. Konstantinidis ◽  
N.K. Hatzitrifon ◽  
P. Papadopoulos ◽  
E.C. Aifantis
Keyword(s):  
Constitutive Model ◽  
Cultural Heritage ◽  
Rheological Properties ◽  
Constitutive Equations ◽  
Base Matrix ◽  
Concrete Matrix

AbstractA preliminary constitutive model is suggested for fresh mortar by taking into account the rheological properties of the base matrix (concrete matrix), as well as the interaction of the aggregates (concrete suspensions). The model may be applicable for interventions in monuments and restoration/protection of objects of cultural heritage.

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