The results of the impact and friction work go substantively beyond the state of the art. The problem of energy creation of frictional models during sliding reversal has been open for 40 years in the contact mechanics community. In this project, we proved that an already existing model, the Frémond model of impact and friction, always avoided energy creation in continuous time (when treated analytically), while the existing and widely used model, the Moreau model, could only avoid energy creation in continuous time in certain special cases. We then demonstrated how to treat the Frémond model numerically to guarantee that the energy creation was avoided in discrete time (as occurs when models are integrated numerically on computers), and provided an example of where the special case of the Moreau model that avoids energy creation in continuous time, still creates energy in discrete time. An example of practical application (a rockfall impacting a protection wall made of concrete blocks) was treated, showing how even in the least favourable case beyond where our mathematical proofs are valid, the new numerical treatment of the Frémond model performed much better than the old Moreau model. The paper was accompanied by a collection of codes and data allowing other researchers to immediately reproduce our results, and extend them if they so choose. The potential impacts of this work are that scientists can now have greater confidence in the quality of the model used when studying rapid impacts combined with friction, and engineers who study practical problems such as rockfall impacts have access to a model that is more accurate. Wider uptake can occur with further research, particularly in the large rotations case, and development of faster software implementations of the numerical solution technique.
The results of the fracture, impact and friction work also go substantively beyond the state of the art. Previous work by the awardees considered a purely mode I fracture problem (the crack is created by the surfaces being pulled apart) with impact. This work manged to avoid certain pathologies that previously existed in the broader model family (extrinsic cohesive zone models), prove that the numerical method always has a solution (and that solution is unique), so the computer will always return a sensible answer when we give it sensible information, and never creates energy. However, it is very rare that a crack occurs in pure mode I (in fact, this essentially only ever occurs in experiments designed to force this to occur). As such, a model that had the benefits of the previous work in pure mode I, but that could also handle mode II (cracking due to the surfaces being slid alongside each other) was required. Mode II fracture also implies the presence of friction along the crack surfaces, so this aspect also needed to be included in the model. Once again, the model that was developed avoided the pathologies that previously existed in the extrinsic cohesive zone model family, the numerical method always has a solution, and it is dissipative. In addition, this work comes with a very substantial code base that allows the crack to be inserted "on-the-fly", meaning that arbitrary crack paths can be treated. This means that essentially any geometry can be treated and any crack path can be followed, with the model implementation in code always able to handle the solution accurately while maintaining the appropriate guarantees. Further uptake and success can be assured by further research to include the desired thermal and hydrological effects in the model, and by fully integrating the model in the Akantu software suite that it currently relies on to follow the arbitrary crack paths. These are both the subject of ongoing work.
