Concise syllabus

Inclusions and inhomogeneities in isotropic elastic solid; Volterra and Somigliana dislocations; disclinations; point defects; Force on a singularity; interaction between defects; the concept of eigenstrain; cracks; homogenisation and macroscopic properties; composite materials.

Detailed syllabus

I. Lecture 1:

• Introduction to the subject; the nature of defects in solids; applications

II. Lectures 2-4:

• Revision of elasticity theory; strain compatibility; stress

III. Lectures 5-8:

• Eshelby solution to inclusion in an elastic solid; solution for ellipsoidal shapes

IV. Lectures 9-11:

• Ellipsoidal inhomogeneities

V. Lecture 12:

• Energetics of inclusions and inhomogeneities

VI. Lectures 13-16:

• Elastic field of dislocations; Volterra and Somigliana dislocations; dislocation loop, continuous distribution of dislocations and its relation to strain compatibility

VII. Lectures 17-18:

• Disclinations and their elastic fields

VIII. Lectures 19-22:

• Cracks

IX. Lectures 23-28:

• Interaction of various defects; force acting on a defect; Solution to several problems, for e.g. inclusion interacting with a dislocation etc.

X. Lectures 29-33:

• Elementary homogenisation theory; Mori-Tanaka theory; macroscopic properties of matter

XI. Lectures 34-38:

• Average elastic moduli of composite materials

XII. Lectures 39-40:

• Plasticity of polycrystalline metals

References:

1. Micromechanics of defects in solids, by T. Mura (Nijhoff)
2. Collected works of J. D. Eshelby (Springer)
3. Introduction to the elasticity theory of crystal defects, by R. W. Balluffi (Cambridge Univ. Press)