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Formally, ideal-elastic deformation behavior is described by the elasticity law:

Equation 4.10

τ = G · γ

Robert Hooke (1635 to 1703) wrote in 1676, in his textbook “de potentia restitutiva” [4.13]: Deformation of solids is proportional to the applied force (“ut tensio sic vis”; meaning: as the extension so is the force). Based on later works on solid-state physics and mechanics by Jakob Bernoulli (in 1689) and Leonhard Euler (in 1736/1765, “mechanica” [4.14]), finally Augustin L. Cauchy (in 1827 [4.15]) stated the modern form of what was called later Hooke’s elasticity law.

If the τ/γ-function is presented in a diagram, ideal-elastic behavior is displayed in the form of a straight line coming from the origin point, showing a constant slope. This slope value corresponds to the value of G. When presented as a function of G(γ) or G(τ), both curves indicate a constant plateau value for G if the limiting value of the linear-elastic range is not exceeded.

The values of the shear modulus of ideal-elastic or Hookean solids are independent of the degree and duration of the shear load applied, when remaining within the linear-elastic range.

For “Mr. and Ms. Cleverly“

For tensile tests, similarly to shear tests, the elasticity law applies in the following form (see also Chapter 4.2.2):

Equation 4.11

σ = E · ε