Linear elastic material

A rock is linearly elastic if it undergoes strain linearly proportional to the magnitude of applied stress. Or to put it another way, plots as a straight line on a stress strain curve. Furthermore, at the elastic limit, if the load is removed the specimen will still return back to original shape and form.

The uniaxial relation between stress $$\sigma$$ and strain $$\epsilon$$ for a perfectly elastic solid is


 * $$\sigma= E \epsilon$$

Where E is the Young's modulus and is an intrinsic property of the material. The mechanical model for a perfectly elastic material is a simple spring. This equation is known as Hooke's Law and is often written in terms of force F and displacement x (as in simple harmonic motion):


 * $$\ F = - k x $$

where k, called the spring constant, is the elastic proportionality constant between applied stress and strain.