Hooke's Law is a way to understand how materials stretch or compress. It usually works best with materials that behave in a simple, predictable way. When we apply Hooke's Law, we can say that stress, which is the force applied to a material, is equal to the elasticity of that material multiplied by how much it stretches. This is written as $\sigma = E\epsilon$, where $\sigma$ is stress, $\epsilon$ is strain, and $E$ is the modulus of elasticity.

But, Hooke's Law can also be used for materials that don't follow these simple rules, but we have to adjust how we use it.

First, some non-linear materials can still act like linear ones if we only look at small amounts of stretching. In these cases, we can use Hooke's Law in a limited way. We do this by using something called an effective modulus. This helps engineers predict how the material will behave until it can’t be described by Hooke's Law anymore.

Second, for non-linear materials, the way stress and strain relate to each other can be understood using special equations. For example, in the power-law model, stress is not just a simple number. Instead, we can write it as $\sigma = K \epsilon^n$, where $K$ is a constant for that material, and $n$ shows how the material doesn’t behave in a straight line.

Also, when things get more complicated—like when a material is under different types of forces or has been used in various ways—engineers can use advanced methods like Finite Element Analysis, or FEA. This approach helps solve problems by breaking things down into smaller parts. Here, we can switch between using Hooke's Law for linear behavior and other methods for the non-linear parts.

In summary, even though Hooke's Law is mainly used for linear materials, we can still apply its ideas to understand how non-linear materials behave. We do this by using effective moduli and advanced formulas to analyze different material responses in real-life situations.