How do we know how much strain will occur if we apply a certain amount of stress for any given material?

To answer this we refer to Young’s modulus, also known as the modulus of elasticity - one of the most commonly used materials parameters.

When strains are small, the strain is almost proportional to the stress for many materials. This leads to Hooke’s Law for simple tension:

Where E is Young’s modulus.

A similar relationship applies for the situation in shear, where G is the shear modulus:

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