What is the name for the ratio of stress to strain for a material in the elastic region of deformation?

The name for the ratio of stress to strain for a material in the elastic region of deformation is called Young's Modulus.

Here are the steps to understand this concept:

1. Stress: Stress is a measure of the internal forces in a material that change shape when a force is applied. It is defined as the force acting per unit area within materials that causes deformation. When a material is loaded with a force, it produces stress, which then causes material deformation.

2. Strain: Strain is a measure of deformation representing the displacement between particles in the material body. It's a dimensionless measure of deformation representing the relative displacement between particles in the material body.

3. Elastic Region of Deformation: This is the region on a stress-strain curve where the material will return to its original shape