An object-oriented programming approach to the Lagrangian FEM analysis of large inelastic deformations and metal-forming processes

The general deformation problem with material and geometric non-linearities is typically divided into a number of subproblems including the kinematic, the constitutive, and the contact=friction subproblems. These problems are introduced for algorithmic purposes; however, each of them represents distinct physical aspects of the deformation process. For each of these subproblems, several well-established mathematical and numerical models based on the nite element method have been proposed for their solution. Recent developments in software engineering and in the eld of object-oriented C++ programming have made it possible to model physical processes and mechanisms more expressively than ever before. In par- ticular, the various subproblems and computational models in a large inelastic deformation analysis can be implemented using appropriate hierarchies of classes that accurately represent their underlying physical, math- ematical and=or geometric structures. This paper addresses such issues and demonstrates that an approach to deformation processing using classes, inheritance and virtual functions allows a very fast and robust implementation and testing of various physical processes and computational algorithms. Here, speci c ideas are provided for the development of an object- oriented C++ programming approach to the FEM analysis of large inelastic deformations. It is shown that the maintainability, generality, expandability, and code re-usability of such FEM codes are highly improved. Finally, the e ciency and accuracy of an object-oriented programming approach to the analysis of large inelastic deformations are investigated using a number of benchmark metal-forming examples.