Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Tensors in Materials Science Summary
Tensors in Materials Science AimsBefore you start - The basicsIntroductionScalars, Vectors and MatricesWhat is a Tensor?Tensor UsageTensor NotationTransformation of axesPrincipal axesThe representation surfaceMagnitude of a property in a given directionThe effects of crystal symmetrySummaryQuestionsGoing further
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Summary

  • Tensors can be used in a wide variety of Material Science fields, including but not limited to stress and strain, temperature and entropy, electricity and magnetism.
  • A tensor is a set of coefficients which transform from one basis to another according to the transformation law: Tijk...'   = rimrjnrko...Tmno...
  • The representation surface of a second rank symmetric tensor is an ellipsoid constructed from the equation: Tijxixj = 1.
  • The principal values, λ, of a tensor can be found by solving the equation |T − λI| =  0 and the principal axes by finding the vector such that (T − λI) x= 0.
  • We can impose conditions on the components of matter tensors as they must adhere to the symmetry of the crystal class.
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