The Stress: Strain Relation for Elastic Newtonian Deformable Bodies

  • Michael Tsamparlis
Part of the Undergraduate Lecture Notes in Physics book series (ULNP)


An important type of Newtonian deformable bodies are the ones in which the stress is a homogeneous function of the rate of strain. That is, when the stress and the rate of strain vanish simultaneously. The simplest such bodies are the ones for which the stress is a linear homogeneous function of the strain, that is the following relation holds:
$$\displaystyle \begin{aligned} t_{\mu \nu }=\sum_{\lambda ,\rho }Y_{\mu \nu }^{\lambda \rho }\tilde{e} _{\lambda \rho } {} \end{aligned} $$
where \(Y_{\mu \nu }^{\lambda \rho }\) is a tensor (the coupling tensor).The dimensions of \(Y_{\mu \nu }^{\lambda \rho }\) are [T]. These Newtonian deformable bodies we call elastic Newtonian bodies.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Michael Tsamparlis
    • 1
  1. 1.Faculty of Physics Department of Astronomy – Astrophysics – MechanicsUniversity of AthensAthensGreece

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