Beschreibung
For many years, researchers have been developing great improvements to the finite element method. Here, a central challenge is to formulate material models. To circumvent the complexity of material modeling, a paradigm shift to data-driven computing has taken place. This dissertation represents a merger of three published works of the author and his coauthors concentrating on the data-driven computing paradigm in mechanics initially introduced by Kirchdoerfer and Oritz in 2016. Here, the ansatz is to treat the fundamental laws in mechanics, i.e., the equilibrium of forces and compatibility, as boundary conditions of a minimization problem. The material data is used directly in the computation without replacing it by any model simplification. This procedure makes it unnecessary to fit model parameters and bypasses uncertainties that come along with the material modeling step. The current thesis begins with an introduction, including a literature overview and a detailed description of research-relevant questions. The first article extends the data-driven formulation to inelasticity. This fundamental extension enables computations with history-dependent or path-dependent materials and, therefore, represents a generalization to the data-driven paradigm. The second article deals with an extension to the data-driven computing paradigm for sparse data set. The article states the possible incorporation of locally-linear tangent spaces into the solver using the tensor voting method. The final article addresses the efficiency of the data-driven solver. Therefore, various data structures are compared and adopted to the nearest neighbor problem in data-driven computing. It is shown that approximate nearest neighbor algorithms can accelerate the method considerably.
