Elastic Modulus

The elastic modulus relates the applied stress to the strain it produces. In a material that obeys Hooke's Law, the initial uniaxial elastic response is linear with stress and strain coupled through Young's modulus, E, such that: Stress = E (Strain). Young's modulus is, therefore, the slope of the stress/strain curve in the initial linear elastic region.

When an isotropic elastic material experiences a uniaxial stress, its volume is not conserved by the longtitudinal strain response. Transverse strains (normal to the uniaxial stress) also occur. These may be characterized by Poisson's Ratio.

(Poisson's Ratio) = - (Transverse Strain) / (Longitudinal Strain)

For non-linear elastic materials the slope of the stress/strain curve at a given strain may be used to define an elastic modulus, the Tangent Modulus.

(Tangent Modulus) = d(stress)/d(strain) = local slope of stress/strain curve