Dynamic contact problems play an important role in dictating the integity, performance and safety of many engineering systems/components involved in vehicle design, annament and ballistics, metal forming/cutting, and surface treatments, just to name a few. Despite their importance to the mechanical integrity of the systems examined, dynamic contact effects are frequently treated using oversimplifying assumptions, which neglect the main feature of the problem. This is because of the complexity of the governing system of equations.

In this work, dynamic frictionai contact problems are fonnulated using the more diable and consistent variational inequalities (VI) approach. Three aspects of the problem are accordingly examined The fit is concemed with the development of the appropriate variationai inequality formulations and solution strategies for dynamic frictional contact problems involving material and geometrical nonlinearity. Two models of surfaces are taken into account:​ (i) perfectiy smooth surfaces, and (ii) more reaüstic surfaces, which take into account the change in cornpliance due to surface roughness. A new technique for representing the kinernatic contact conditions is developed Two newly devised numerical procedures are devised to solve the general dynamic fictionai contact problem for elastic and elasto-plastic media. The first solution strategy, which regdarises Won, is based upon the iterative use of mathematical programming and Lagrange mdtipliers. The second approach is accomplished using a nondifferentiable optimisation algorith, through a sequence of mathernatîcd programming sub-problems.

The second aspect of the work is concemed with the selection of a suitable the integration scheme for contact probiems. The values of the the integration parameters are so chosen to ensure that the solution is second order accurate, unconditionally stable, preserves energy and momentum during rigid impact, thus minimising numerical oscillations and ensuring optimal numerical dissipation.

Enaily, the developed aigorithms are validated and applied to the analysis of several interesting engineering problems. The numericd predictions are compared to existing experiments as well as a commercial finite element code. The results reved that the new dynamic fiction contact formulations are more accurate than the traditional variationai methods. These newly developed aigonthms should provide designers with a powerful tool for treating dynamic elasto-plastic problems involving fictional contact.