Infinitesimal strain theory

Imagine you are playing with a rubber band, and you stretch it a little bit. The change in the length of the rubber band is called strain. Infinitesimal strain theory is a way to understand how materials change shape and size when they are under stress or pressure, but only for very small changes, like stretching the rubber band just a tiny bit.

Infinitesimal strain theory uses a math concept called calculus, which is like a special way of doing math that helps us understand how things change. We use this math to calculate how much a material has changed in size and shape when it is under stress.

To make it easier to understand, let's imagine you are playing with a piece of play-doh. If you squeeze it, it will become shorter and wider, and if you stretch it, it will become longer and thinner. Infinitesimal strain theory helps us calculate exactly how much the play-doh has changed in length and width when we squeeze or stretch it.

But how does it work? Well, when we squeeze or stretch something, it moves in all directions, not just in one direction. Infinitesimal strain theory uses something called a strain tensor to measure how much the material has changed in all directions.

So, in summary, infinitesimal strain theory helps us understand how materials change shape and size when they are under stress or pressure, but only for very small changes. It uses a special kind of math called calculus and a strain tensor to measure the changes in all directions.