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 furtherTLP creditsTLP contentsShow all contentViewing and downloading resourcesAbout the TLPsTerms of useFeedbackCredits Print this page

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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: T
_{ijk...}^{'}= r_{im}r_{jn}r_{ko}...T_{mno...} - The representation surface of a second rank symmetric tensor is an ellipsoid constructed from the equation: T
_{ij}x_{i}x_{j}= 1. - The principal values, λ, of a tensor can be found by solving the equation |
**T**− λ**I**| = 0 and the principal axes by finding the vector such that (**T**− λ**I**) x= 0. - We can impose conditions on the components of matter tensors as they must adhere to the symmetry of the crystal class.