Numerical simulations for predicting damage and failure of materials and structures are of fundamental importance in many engineering disciplines, since they usually reduce the number of costly and time-consuming practical experiments and allow for deeper insights into processes that would otherwise not or only hardly be possible. The significance of such simulations depends to a large extent on the quality of the applied material models which are themselves constantly being further developed to take more and more phenomena and effects into account that occur in real materials. In this context, the coupled modeling of the complex material phenomena 'damage' and 'plasticity' can be mentioned as a challenging and practically relevant subject the scientific literature has been dealing with for quite some time already. There is still a pressing need for further research in this scientific field. The present cumulative dissertation aims at making a valuable contribution in this regard. It essentially represents a compilation of several published works of the author (and his coauthors) related to the topic. The overall goal is the development and investigation of novel gradient-extended damage-plasticity material models, both for the geometrically linear and nonlinear regime, which are based on a so-called 'two-surface' approach. The latter means that damage and plasticity are modeled as truly distinct (but coupled) dissipative mechanisms by taking separate damage loading and plastic yield criteria as well as loading / unloading conditions into consideration, respectively. Nonlinear Armstrong-Frederick kinematic hardening, nonlinear Voce isotropic hardening and nonlinear damage hardening are also accounted for by the models that can quite flexibly be adapted to various situations in which the considered real material shows either a (quasi-)brittle-type, ductile-type or possibly a mixed-type damaging behavior. The gradient-extension of damage (based on a micromorphic approach) is used to avoid pathological mesh sensitivity issues in finite element simulations that otherwise typically occur when using conventional models involving material softening behavior. After an introductory part with a literature overview and a more detailed clarification of the research-relevant questions, the thesis begins with two works that are concerned with a numerical comparison of two different and competing kind of formulations for large deformation plasticity: hypo- and hyperelastic-based plasticity formulations that rely upon an additive decomposition of the rate of deformation tensor or a multiplicative split of the deformation gradient. At this point, no damage is being considered, yet. The main purpose for the thesis is to clarify whether one of the two formulations should generally be preferred when it later comes to an extension of the geometrically linear gradient-enhanced damage-plasticity model to large deformations. Various simulations with single finite elements finally reveal that the results, which are obtained using the respective modeling approaches, can indeed significantly differ from each other under extreme conditions and that an incautious use of hypoelastic-based plasticity formulations can even lead to physically implausible model behavior. However, in more application-oriented structural simulations these problems are nearly insignificant and the results show a good agreement which suggests that, in principal, both formulations are well-suited for the development of new material models involving large plastic deformations. Afterwards, two works are presented that deal with the theory and numerics of two slightly different two-surface gradient-extended damage-plasticity models for the geometrically linear regime. Among other things, the following topics are discussed: the application of the micromorphic approach to achieve the gradient-extension of the models, the derivation of the strong and weak form of the underlying boundary value problem, the thermodynamically consistent derivation of the evolution equations, the models' implementation into finite element codes, the algorithmic handling of the discretized equations at the integration point level and the computation of the consistent tangent operators which are necessary to retain a quadratic rate of convergence of the Newton scheme at the global finite element level. The results of numerous structural simulations demonstrate the good practical performance and mesh regularizing properties of the models in finite element simulations involving material softening. In the last part of the thesis, the model formulation is extended for its application to geometrically nonlinear problems. For this, a hyperelastic-based plasticity framework is used which relies upon an additional multiplicative split of the plastic part of the deformation gradient in order to allow for the modeling of nonlinear Armstrong-Frederick kinematic hardening at large deformations and which utilizes exclusively symmetric internal variables. Besides the theory, also many numerically relevant topics are discussed, such as a suitable time integration scheme for the evolution equations that preserves both the plastic incompressibility and symmetry of the tensorial internal variables, or the implementation of the model formulation into finite element codes. Finally, the functionality of the geometrically nonlinear model is exemplified by a structural finite element simulation
