Fourth Order Tensors in Physics and Mechanics

  • Liqun Qi
  • Haibin Chen
  • Yannan Chen
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 39)


Fourth order tensors have also wide applications in physics and mechanics. Examples include the piezo-optical tensor, the elasto-optical tensor and the flexoelectric tensor. The most well-known fourth order tensor is the elasticity tensor (Huang et al., Tensor Analysis (in Chinese). Tsinghua University Press, Beijing, 2003, [134], Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices. Clarendon Press, Oxford, 1985, [212], Zou et al., J. Mech. Phys. Solids. 58:346–372, 2010, [318]). It is closely related to the strong ellipticity condition in nonlinear mechanics.

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsThe Hong Kong Polytechnic University Hong KongHong Kong
  2. 2.School of Management Sciences Qufu Normal UniversityRizhaoChina
  3. 3.The Hong Kong Polytechnic University Hong KongHong Kong

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