Time-Dependent Response of Mass Continuous Solid Phase Media by Integral Form of Constitutive Equations - Mathematical Modeling

2016 ◽  
Vol 837 ◽  
pp. 163-166
Author(s):  
Jozef Sumec ◽  
Lubos Hrustinec

Mathematical modeling of boundary value problems in linear theory of viscoelasticity. Definitions and basic principles in the mathematical modeling theory. Constitutive functional and its transformation into a form of Stieltjes integral. Application of theory of algebraic sets and corresponding subsets. Riesz theorem of representation and its application for derivation of constitutive equations. Integral operator forms of stress-strain relationships for a solid-phase continuous media.

2016 ◽  
Vol 837 ◽  
pp. 121-126
Author(s):  
Ivana Veghova ◽  
Jozef Sumec

Mathematical modeling of boundary value problems in linear theory of viscoelasticity. Definitions and basic principles in the mathematical modeling theory. Constitutive functional and its transformation into a form of Stieltjes integral. Application of theory of algebraic sets and corresponding subsets. Riesz theory of representation and its application for derivation of constitutive equations. Integral and differential operator forms of stress-strain relationships for a solid-phase continuous media.


1995 ◽  
Vol 40 (7-8) ◽  
pp. 474-483 ◽  
Author(s):  
L. A. Berrueta ◽  
B. Gallo ◽  
F. Vicente

2006 ◽  
Vol 11 (6) ◽  
pp. 575-595 ◽  
Author(s):  
L. Fusi ◽  
A. Farina ◽  
D. Ambrosi

The mechanical behavior of a mixture composed by an elastic solid and a fluid that exchange mass is investigated. Both the liquid flow and the solid deformation depend on how the solid phase has increased (diminished) its mass, i.e. on the mass conversion between constituents. The model is developed introducing a decomposition of the solid phase deformation gradient. In particular, exploiting the criterion of maximization of the rate of entropy production, we determine an explicit evolution equation for the so-called growth tensor which involves directly the solid stress tensor. An example of a possible choice of the constitutive functions is also presented.


1984 ◽  
Vol 12 (9) ◽  
pp. 529-533 ◽  
Author(s):  
Ivar K. Rossavik ◽  
Russell L. Deter

2013 ◽  
Vol 2013 ◽  
pp. 1-22 ◽  
Author(s):  
Evan Mitsoulis

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.


2021 ◽  
Vol 1203 (2) ◽  
pp. 022093
Author(s):  
Valery Varentsov ◽  
Valentina Kuzina ◽  
Alexander Koshev ◽  
Valentina Varentsova

Abstract The report provides data on the electrochemical modification of carbon-graphite fibers as the basis for the creation of composite materials. The results of studies of the electrodeposition of metals on pre-electrochemically modified carbon fiber materials (CFM) in order to obtain composite materials based on them are presented. The use of CFM for the creation of composite materials is associated with the possibility of deposition of metals, alloys or their compounds on the surface of their constituent fibers. Electrochemical treatment in aqueous solutions of electrolytes is a promising method for modifying the surface properties of carbon materials, including in order to improve their adhesive properties. Preliminary electrochemical modification of carbon fiber materials in indifferent solutions of electrolytes made it possible to obtain composite and nanocomposite materials with good adhesion of the electrodeposited metal to the surface of the fibers of carbon materials.When metals are deposited on carbon fiber materials, it is necessary to solve the problem of applying a uniform metal deposit or with a certain profile in the thickness of the material. In this case, it is effective to use methods of mathematical modeling of metal deposition processes in a flowing three-dimensional electrode. Depending on the selected modes of deposition of metal sediment on the CFM, some electrochemical parameters of the process and system may be dependent on both the time of the process and the thickness coordinate of the electrode. This is especially true for the value of the resistivity of the solid phase of the system, that is, carbon-graphite fibrous material. Other electrochemical parameters, such as the specific electrode surface, the exchange current and the transfer coefficient of the electrochemical reaction, the porosity of the material, etc., can also change during the electrodeposition of the metal on the CFM. It is proposed to take into account the change in the characteristic properties of modified carbon fiber materials in the mathematical modeling of the processes of electrodeposition of metals on carbon fiber materials in order to determine the technological parameters to improve the efficiency of the properties of composite materials. In order to implement mathematical models used in the calculation of electrochemical processes in the volume and on the surface of carbon fiber materials, a set of programs based on modern computational methods and programming languages has been developed.


2011 ◽  
Vol 219-220 ◽  
pp. 1652-1655 ◽  
Author(s):  
Ji Xue Dong ◽  
Hong Zhang

The article analyzes undergraduate Mathematical Modeling Competition’s characteristics and the theory foundation thoroughly,and points out the significance of this competition both in improving colledge students’innovation ability and in higher mathematical education reform. It concentrately summarizes and expatiates the prominent problems in present undergraduate Mathematical Modeling education from four aspects:students’ ability,teachers’quality,teaching facilities and the management and organization of the school,on basis of this,the article puts forward teaching strategies for undergraduate Mathematical Modeling,and also dwells on how to improve the thinking principles and capabilities about undergraduate Mathematical Modeling by examples. Establishes the teaching mode of colledge mathematical modeling and thoroughly analyses the hierarchy of mathematical modeling’s teaching and basic principles for selecting titles.At last,the article proposes several questions which we should pay attention to about colledge mathematical modeling teaching.


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