How to start a dendrometry dimension build (Dimensions of Trees) for research?
The measuring principle, that is describe in that link, is quite cool and simple.

The string is wrapped around the tree. One end is connected to a fixed point (here the casing of the sensor). The other end is connected to a spring, which in turn is again connected to a fixed point. As the tree get's bigger, it will pull at the string. At the first side of the string nothing happens (because it is a fixed point). But the end with the spring will move according to the force of the tree. Force and displacement have a linear relationship for a spring (as long as you don't overload it): F = k*x with the force F, the spring constant k and the displacement x.

The displacement of the springs end can be measured with a linear potentiometer. That is just a simple strip of resistive material with a glider, which can be set to any position at the strip. It will create a voltage divider, giving you an analog voltage depending on the position (most potentiometers are linear, but there are also others). Connect both ends of the potentiometer to Vcc (supply voltage) and ground respectively and the glider to an analog pin of the Arduino. Then you can measure the voltage with analogRead().

As jsotola mentioned in his comment: Be sure to use a string, that will not stretch too much, as this will make your measurement less precise.