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TY - THES AU - Eggersmann, Robert TI - Constitutive-model-free data-driven computational mechanics PB - Rheinisch-Westfälische Technische Hochschule Aachen VL - Dissertation CY - Aachen M1 - RWTH-2022-00043 SP - 1 Online-Ressource : Illustrationen PY - 2021 N1 - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2022 N1 - Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2021 AB - One of the most powerful tools for the design and engineering of technical innovations is numerical simulation. Based on simulations, engineers have to make decisions that influence everyone’s daily life. This can affect how we deal with resources in any sense, personal safety, or simply our well-being. Among all engineering disciplines, the field of solid mechanics is essential and also well-established. For many years, researchers have been developing great improvements of the finite element method to design structures and compute, e.g., critical loads. Here, a central challenge is to formulate material models. Over the years, these models became more and more accurate, but also more complex and complicated. To circumvent this complexity, a paradigm shift has taken place in recent years. Next to classical material modeling, the idea of data-driven computing has gained importance. The present cumulative dissertation targets to make a helpful contribution in this regard. It 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. The overall goal is to develop methods for finite element simulations, which come along without the formulation of a constitutive model. 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 formulate complicated constitutive equations or to fit model parameters. On the one hand, uncertainties that come along with the material modeling step are bypassed. On the other hand, this method standardizes material modeling in order to save time and resources. The current thesis begins with an introduction, including a literature overview and a detailed description of research-relevant questions. The first article follows the introduction and 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. To derive the underlying theory, we investigate three material representations: (1) materials with memory, (2) differential materials, and (3) materials de- scribed by history variables. We use the equivalence between these three formulations to derive possible representations of data sets, describing, among others viscoelastic, and elastoplastic material behavior. The second article deals with an extension to the data-driven computing paradigm for sparse data sets. These data sets appear, e.g. for history-dependent materials. The article states the possible incorporation of locally-linear tangent spaces into the solver. Here, the key idea is that the data’s underlying structures can be used and approximated by linear representations. Those linear representations are computed by the tensor voting method introduced by Mordohai and Medioni. The tensor voting method can be seen as an unsupervised machine learning technique based on manifold learning. In contrast to global approximations, the method is instance-based and, therefore, analyzes the data structure pointwise. Numerical examples are investigated to illustrate the higher-order convergence behavior of the extension w.r.t. the data set size.The final article addresses the efficiency of the data-driven solver. This iterative solver mainly consists of two steps or projections in each iteration. Starting from a state in the material data set, the constraint set’s closest state is computed, where equilibrium and kinematics are fulfilled. Afterwards, we find the closest state in the data set. The article focuses on treating the latter step, which is the most time consuming for large data sets since a nearest neighbor problem is solved at each integration point. Therefore, we analyzed and adopted different data structures. We discovered that approximate nearest neighbor algorithms accelerate the search in these problems by many orders of magnitude compared to exact algorithms. The treated numerical examples cover computations with up to a billion data points analyzing a 3D elastic solid. LB - PUB:(DE-HGF)11 DO - DOI:10.18154/RWTH-2022-00043 UR - https://publications.rwth-aachen.de/record/837746 ER -