## Dissertation

In the present contribution, a general framework for the completely consistent integration of nonlinear dissipative dynamics is proposed, that essentially relies on Finite Element methods in space and time. In this context, fully flexible structures as well as hybrid systems which consist of rigid bodies and inelastic flexible parts are considered. Thereby, special emphasis is placed on the resulting algorithmic fulfilment of fundamental balance equations, and the excellent performance of the presented concepts is demonstrated by means of several representative numerical examples, involving in particular finite elasto-plastic deformations.

In the present work the modelling and numerical treatment of discontinuities in thermo-mechanical solids is investigated and applied to diverse physical problems. From this topic a structure for this work results, which considers the formulation of thermo-mechanical processes in continua in the first part and which forms the mechanical and thermodynamical framework for the description of discontinuities and interfaces, that is performed in the second part. The representation of the modelling of solid materials bases on the detailed derivation of geometrically nonlinear kinematics, that yields different strain and stress measures for the material and spatial configuration. Accordingly, this results in different formulations of the mechanical and thermodynamical balance equations. On these foundations we firstly derive by means of the concepts of the plasticity theory an elasto-plastic prototype-model, that is extended subsequently. In the centre of interest is the formulation of damage models in consideration of rate-dependent material behaviour. In the next step follows the extension of the isothermal material models to thermo-mechanically coupled problems, whereby also the special case of adiabatic processes is discussed. Within the representation of the different constitutive laws, the importance is attached to their modular structure. Moreover, a detailed discussion of the isothermal and the thermo-mechanically coupled problem with respect to their numerical treatment is performed. For this purpose the weak forms with respect to the different configurations and the corresponding linearizations are derived and discretized. The derived material models are highlighted by numerical examples and also proved with respect to plausibility. In order to take discontinuities into account appropriate kinematics are introduced and the mechanical and thermodynamical balance equations have to be modified correspondingly. The numerical description is accomplished by so-called interface-elements, which are based on an adequate discretization. In this context two application fields are distinguished. On the one side the interface elements provide a tool for the description of postcritical processes in the framework of localization problems, which include material separation and therefore they are appropriate for the description of cutting processes. Here in turn one has to make the difference between the domain-dependent and the domain-independent formulation, which mainly differ in the definition of the interfacial strain measure. On the other side material properties are attached to the interfaces whereas the spatial extension is neglectable. A typical application of this type of discontinuities can be found in the scope of the modelling of composites, for instance. In both applications the corresponding thermo-mechanical formulations are derived. Finally, the different interface formulations are highlighted by some numerical examples and they are also proved with respect to plausibility.