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"modulus of elasticity" is correct and usable in written English.
This term is typically used in the sciences and engineering. For example, you could write "The modulus of elasticity of steel is 200 GPa."
Dictionary
modulus of elasticity
noun
Young's modulus
Exact(60)
The slope of the stress strain curve in the elastic region represents Young modulus or modulus of elasticity.
Young's modulus of elasticity.
Shear modulus of elasticity.
E modulus of elasticity.
Modulus of elasticity of concrete.
Table 9 Modulus of elasticity.
Modulus of elasticity of the steel.
Variation of modulus of elasticity of beam.
Table 3 Average modulus of elasticity and tangent modulus of elasticity.
A compressometer was used to measure the modulus of elasticity.
Modulus of elasticity in the plane of isotropy (MPa).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com