Eshelby tensor of concave superspherical inclusions

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Table of contents

PART 1 INTRODUCTION
I General framework
1.1 Background Context
1.2 Fundamental Eshelby problems
1.3 Homogenization schemes
1.4 Goals of the thesis
1.5 Organization of the work
PART 2 PROPERTY CONTRIBUTION TENSORS OF MATERIAL CONTAINING 3-D NONELLIPSOIDAL INHOMOGENEITIES
II Eshelby tensor of concave superspherical inclusions
1 INTRODUCTION & BACKGROUND
1.1 The first Eshelby problem for ellipsoidal inclusions
1.2 Isotropic material containing non-ellipsoidal inclusion
2 NUMERICAL EVALUATION OF THE ESHELBY TENSOR FOR A CONCAVE INCLUSION (IJES, 2015A)
2.1 Introduction
2.2 Average S-tensor for superspherical inclusion
2.3 Numerical approach
2.4 Discussion
2.5 Conclusions
3 DISCUSSIONS: EFFECT OF THE SHAPE FACTOR ON THE ELASTIC ENERGY
III Property contribution tensor of superspherical pores
1 INHOMOGENEITY PROBLEM: BACKGROUND
1.1 The second Eshelby problem for ellipsoidal inhomogeneities
1.2 Homogenization schemes of effective properties
1.3 Isotropic materials containing superspherical inhomogeneities
2 EVALUATION OF THE EFFECTIVE ELASTIC AND CONDUCTIVE PROPERTIES OF A MATERIAL CONTAINING CONCAVE PORE (IJES, 2015B)
2.1 Introduction
2.2 Property contribution tensors for a superspherical inhomogeneity
2.3 Effective properties of a material containing superspherical pores
2.4 Cross-property connections for a material containing superspherical pores
2.5 Concluding remarks
IV PROPERTY CONTRIBUTION TENSOR OF SUPERSPHEROIDAL PORES
1 OVERVIEW OF NUMERICAL PROCEDURES
2 COMPLIANCE AND RESISTIVITY CONTRIBUTION TENSORS OF AXISYMMETRIC CONCAVE PORES OF SUPERSPHEROIDAL SHAPE (IJES, 2016)
2.1 Introduction
2.2 Property contribution tensors for a superspheroidal inhomogeneity.
2.2.1 Compliance and resistivity contribution tensors
2.3 Analytical approximations for property contribution tensors of a superspheroidal pore
2.4 Concluding remarks
PART 3 APPLICATIONS TO THE HETEROGENEOUS ROCK LIKE MATERIALS
V Effective thermal conductivity of oolitic rocks using the Maxwell homogenization method (IJRMMS, 2015)
1.1 Introduction
1.2 Background results
1.3 Microstructure of a reference porous oolitic limestone
1.4 A two-scale porosity model for effective thermal conductivity of isotropic porous oolitic rocks
1.5 Numerical results
1.6 Conclusion
VI Accuracy of the replacement relations for materials with non-ellipsoidal inhomogeneities (IJSS, 2016)
2.1 Introduction.
2.2 Compliance and stiffness contribution tensors and replacement relations for ellipsoidal inhomogeneities.
2.3 Calculation of compliance and stiffness contribution tensors and Hill tensor P for a superspherical inhomogeneity
2.4 Using replacement relations for calculation effective properties of materials.
2.5 Concluding remarks.
PART 4 CONCLUDING REMARKS AND PERSPECTIVES
1.1 Concluding remarks for the mains results
1.2 Perspectives
REFERENCES