What causes elastic hysteresis?

Hint: In simple terms, it is the phenomenon in which any physical quantity lags behind the changes in the physical effect driving that quantity.
For example: If you stretch and release an elastic material, the length at the end would be slightly greater than at the start.
Due to the hysteresis, more energy is required to stretch the material as opposed to releasing it.

Complete answer:
Hysteresis is nonlinear and can be mathematically challenging to model. In some of the hysteretic models, Hysteresis is important because it always describes a natural method of storing information in a circuit. Examples are ferroelectric materials known as rubber bands.
 You can sometimes have a magnetic material that is not initially magnetic. But when you apply an electric field, it acquires a (near-permanent) magnetism.
 Similarly, we can have something like elastic material (like your socks) which will spring back to its original form if you apply some force. But if we stretch out our socks too much, they will be permanently stretched out.
Finally, due to the difference between strain energy required to generate given stress in the material to the material’s elastic energy at the given stress, the elastic hysteresis is generated

Note: Hysteresis describes a change in the transfer characteristics of a circuit, usually amplifier circuits.
It is especially useful when we have a comparator amplifier that compares the voltage between its two inputs and then finalizes an output based on the result.
In real life, electrical signals are noisy and when the compared voltages are similar then the output is going to flicker between two possibilities: