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Prof N D Mathur

This course builds on the IB "Mechanics of Materials and Structures", which provided an introduction to tensor manipulation, mainly in the context of stresses and strains (both of which are second rank tensors). The present course is a short one (3 lectures), so the coverage of tensors is not extended very far beyond that of the IB course. However, tensors are quite widely used in Materials Science, particularly for anisotropic materials, and there are certain Part II courses (notably C12 and C16) for which tensor usage is required that goes slightly beyond that of the IB coverage.

The first lecture provides a general extension of tensor usage, particularly relating to matrix notation, while the second and third cover some experimental techniques for measurement of strain and the mechanics of thin films. A Revision Examples Class (relating to the coverage of the IB course) is held immediately before start of the current course.

This lecture course will cover:

  • Use of Tensors. Einstein summation convention. Types of tensor and representation of elastic interactions between them. Stress, strain, stiffness & compliance tensors. Matrix notation for matter tensors. Effect of material symmetry on the number of independent elastic constants.
  • Strain Gauges and Photoelasticity. Theory of strain gauges. Analysis of strain gauge data. Photoelastic analysis using polarised light. Photoelastic fringe patterns. The "frozen stress" technique.
  • Other Strain Measurement Techniques and Mechanics of Thin Films. Digital Image Correlation (DIC). Moiré interferometry. X-ray diffraction. Diffraction of neutrons and synchrotron X-rays. The stress state in thin surface films. The stress state in multi-layers.