Book Description:
This book is the first volume of the trilogy “Analytical Models of Thermal Stresses in Composite Materials”, presenting, in each of the volumes, genuine results created solely by the author. The fact that the author proceeds from fundamental equations of Mechanics of Solid Continuum confirms the genuineness of the results and accordingly establishment of new scientific school with an interdisciplinary character belonging to the scientific branch Applied Mechanics. As an imagination considered for the analytical models, an elastic solid continuum is represented by a multi-particle-(envelope)-matrix system consisting of components represented by spherical particles periodically distributed in an infinite matrix, without or with a spherical envelope on the surface of each of the spherical particles. The multi-particle-(envelope)-matrix system with different distribution of the spherical particles is considered as a model system for a determination of the thermal stresses in real composite materials with finite dimensions included in the categories.

Table of Contents:
Table of Contents:
Preface
About the author

1 Outline of principles
1.1 Cell model
1.2 Mathematical techniques
1.3 Reasonof thermal stresses
1.4 Radial stresses p1, p2
1.5 Temperaturerange
1.6 Finite matrix
1.7 Subscriptsand notation
1.8 Recommendations of author

2 Cell model
2.1 Geometricboundary condition for cell matrix
2.2 Particlevolume fraction
2.3 Determination of distance rc = rc
2.4 Realcomposite material

3 Thermal stresses in elastic solid continuum 33
3.1 Selected topics of Mechanics of Solid Continuum
3.2 Reason for thermal stresses
3.3 Determination of radii R1, R2
3.3.1 Multi-particle-matrix system

4 Boundary conditions
4.1 Multi-particle-(envelope)-matrix system
4.2 One-particle-(envelope)-matrix system
4.3 Supplement

5 Isotropic multi-and one-particle-(envelope)-matrix systems. Solutions
5.1 Mathematicaltechniques 1
5.2 Mathematicaltechniques 2
5.3 Mathematicaltechniques 3
5.4 Analysis of solutions
5.5 Multi-particle-matrix system
5.6 Multi-particle-envelope-matrix system

6 Isotropic multi-and one-particle-(envelope)-matrix systems. Solution
6.1 Mathematical techniques
6.2 Analysisof solution
6.3 Multi-particle-matrix system
6.4 Multi-particle-envelope-matrix system

7 Isotropic multi-and one-particle-(envelope)-matrix systems. Solutions
7.1 Mathematicaltechniques 5
7.2 Mathematicaltechniques 6
7.3 Analysisof solution
7.4 Multi-particle-matrix system
7.5 Multi-particle-envelope-matrix system 5

8 Isotropic multi-and one-particle-(envelope)-matrix systems. Solutions
8.1 Mathematical techniques

9 Isotropic multi-and one-particle-(envelope)-matrix systems. Solution

10 Radial stresses p1, p2 and temperature range
10.1 Radial stresses p1, p2 03
10.2 Dependencies p1 = p1 (v, R1,R2), p2 = p2 (v, R1,R2) 10.3 Temperature range
11 Related phenomenon
12 Appendix
12.1 Phase-transformation induced radial displacement and radial strain

Bibliography

Index