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To explain my question, I'll use an example. Let's say that I have a soda can and I apply $10$ N force from the right as well as from the left. Here, the net force is zero, yet the can will get deformed.

My question is: How can an object be deformed with no net force?

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“Net” force is zero only for the whole can as an object of both forces — it doesn't change position (or — more accurate — acceleration) of its mass center.

For individual parts (or particles) of the can the situation is different — the sum of forces are (in general) not zero.

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Net force equals zero is a schema that works for rigid bodies, that are by definition unbreakable or non elastic.

Real objects are elastic so a net force equal zero is obtained by means of a distribution of deformation inside the body that, due to elasticity (linear or not linear) creates an internal distribution of forces (stress) that sum up to create the reaction that makes the total net force (in the elastic body) equal zero, i.e. in equilibrium.So in elastic bodies the deformation comes into play. Hope it helps

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