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Name: Lana
Status: student
Grade: 9-12
Location: Outside U.S.
Country: Senegal
Date: Winter 2009-2010

What is the "plastic deformation" according to Hooke's Law?

When you press on a material, it can deform (change shape). Since you are asking about Hooke's law, I will use a spring as an example. When you pull on a spring, it extends (and according to Hooke's law, the extension is proportional to the force you use in pulling on it). If then spring returns to its normal shape, this is known as an elastic deformation.

However, if you pull too hard, the spring might get bent out of shape, and not return to its previous shape. This change is known as plastic deformation.

Hooke's Law does not apply to plastic deformation, which means that the equation (F=kx) cannot be used to predict/describe the permanently bent spring. Hooke's law only applies to elastic deformation.

Hope this helps,
Burr Zimmerman

Hi Lana,

In fact, Hooke's law is not applicable to plastic deformation at all, and cannot predict it. Hooke's Law only applies to non-plastic deformation.

As an example, take a simple coil spring. When you compress it or stretch it less than the amount that will cause permanent distortion when it is released, Hooke's law states that the force required to stretch or extend it, is in direct proportion to the spring's change in length. For example, if you pull on a spring with a force equal to 1 kg, and it stretches 10 cm, then it will stretch 20 cm with a force of 2 kg.

This linear relationship between force and distance was described by Hooke, but it is only true if the force is not so high that the material (the spring's steel, in this case) is not stressed beyond its Yield Point. In simple terms, this means that if you stretch the spring (or anything else) so much that it no longer returns to its original length or position when the force is removed, the spring has undergone "plastic deformation" and Hooke's Law no longer applies.

Similarly, let us say you have a 3mm diameter steel rod that is a meter long. You clamp one end in a vice, and allow the rest of its 1 meter length to stick up vertically. Let us say you push sideways on the free end with a small force of "X" grams. The rod bends a small amount and the end deflects "Y" cm.

Now try pushing with 2X kg, and you will find the end deflects exactly 2Y cm. Because you are not pushing so hard that the rod gets permanently bent, it can be seen that Hooke's Law is being obeyed. But if you push hard enough that Plastic (or permanent) Deformation takes place, the relationship between force and distance (described by Hooke) no longer holds true, and Hooke's Law is inapplicable and cannot predict what happens.

Bob Wilson

Hooke's law does not really address plastic deformation. The simple Hooke's law force F = -kx does not depend on velocity or time: all it depends on is displacement. This is an approximation to the behavior of real materials, which is valid for short times when internal friction, damping, and re-orientation of the material's internal structure are not significant.

Plastic deformation is when an object does NOT return to its original shape/displacement after the stress is removed. Hooke's law does not explain this; Hooke's law instead predicts that the object will continue oscillating forever. Plastic deformation is a consequence of the object's micro-structures--its chemical bonds, polymer chains, or whatever--rearrange while the object is deformed, so that it is not quite the same object that it was before the stress was applied.

Richard Barrans, Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming

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