A method for digital treatment planning may include defining a set of contact points on a tooth of a patient's dentition and a plurality of connections between pairs of the plurality of contact points. The plurality of connections may include Hookian stiffness parameters of a dental appliance between the plurality of contact points. The method may also include generating a relaxed model of a dental appliance using the plurality of contact points and the plurality of connections. The method may also include generating a deformed model of the dental appliance using the plurality of contact points and plurality of connections. The method may also include transforming the relaxed model to the deformed model to direct the patient dentition towards a target tooth arrangement.