Dear colleagues, do any one investigate such case?

Thank you

Dear Mr. Ali

I hope this article will be helpful

https://www.researchgate.net/publication/222164646_Stress-strain_curves_for_steel-fiber_reinforced_concrete_under_compression

Article Stress–strain curves for steel-fiber reinforced concrete und...

As I see, the secant modulus of elasticity of concrete did not increased by adding crimped steel fibers to the mixture in the ascending branch of the stress strain relation. While it increased in the descending branch.

Thank you dear Dr.Mohannad.

Welcome Mr. Ali...

In general, the secant modulus of elasticity of concrete decrease as the strain increased regardless to the branch of the stress-strain curve, i.e ascending or descending.

Dear Mr Ali

you can see the following article regarding your question.

Thank you dear Dr.Abbas

Dear Ali..I hope the attached paper can be useful for you

www.civil.ist.utl.pt/~cristina/GDBAPE/Artigos/fib_RuiNeves_JAlmeida.pdf

Thank you dear Dr.Amjad