Stroh formalism for various types of materials and deformations

Chyanbin Hwu, Wilfried Becker

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

The Stroh formalism is a complex variable formulation developed originally for solving the problems of two-dimensional linear anisotropic elasticity. By separation of the third variable for the linear variation of displacements along the thickness direction, it was proved to be applicable for the problems with coupled stretching-bending deformation. By the Radon transform which maps a three-dimensional solid to a two-dimensional plane, it can be applied to the three-dimensional deformation. By the elastic-viscoelastic correspondence principle, it is also valid for the viscoelastic materials in the Laplace domain. By expansion of the matrix dimension, it can be generalized to the coupled-field materials such as piezoelectric, piezomagnetic and magneto-electro-elastic materials. By introducing a small perturbation on the material constants, it can also be applied to the degenerate materials such as isotropic materials. Thus, in this paper, the Stroh formalism for several different types of materials (anisotropic elastic, piezoelectric, piezomagnetic, magneto-electro-elastic, viscoelastic) and deformations (two-dimensional, coupled stretching-bending, three-dimensional) are organized together and presented in the same mathematical form.

Original languageEnglish
Pages (from-to)433-444
Number of pages12
JournalJournal of Mechanics
Volume38
DOIs
Publication statusPublished - 2022

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics

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