Martin Abendroth

Computational homogenization has become an attractive path to determine the macroscopic inelastic behavior of a structure from the knowledge of the behavior of its (usually simpler) constituents, using a Representative Volume Element (RVE) at the microscale. Since the numerical solution of both scales by means of the FE² method is prohibitively expensive, much research effort has been spent on the development of surrogate models, particularly by making use of data‐driven machine learning methods. Due to the vast spectrum of proposed surrogate modeling approaches, the decision on the method of choice for potential applicants is difficult. While computational efficiency is usually used as the central performance measure, a careful distinction between on‐ and offline efforts is important. Moreover, the simulation context should also influence the selection. If, for instance, a thousand simulations are to be carried out for a single microstructure, the choice of approach may be different than if single, or a few, simulations are to be carried out for a thousand different microstructures. In the latter case, the flexibility and adaption effort of the method to new microstructures plays a key role. The present study aims to derive guidelines in this direction, by comparing different such approaches and carefully analyzing their performance in simulating inelastic macroscale behaviors, influenced by the morphology of 3D foam‐like microstructures. Four formulations are considered: the Deshpande–Fleck phenomenological macroscale model, a general analytical surrogate model, a hybrid neural network surrogate model, and a hyper‐reduced FE² approach. The methods are compared with respect to computational costs and predictive capabilities for two 3D benchmark scenarios.

The properties of two‐phase materials, with the special case of foams, strongly depend on their microstructure. These structures are generally modeled with Hill homogenization methods to reduce the computational effort compared to full‐resolution simulations. For applications where the macroscopic dimensions of the structure under consideration are only a few multiples of its internal length, size effects occur, that is, the effective mechanical properties depend on the structure size. To achieve adequate homogenization, higher‐order continuum theories must then be used to account for strong gradients in mechanical quantities. The present contribution extends the classical approach with the corresponding micromorphic degrees of freedom. In contrast to previous studies in the literature, all components of the micromorphic curvature tensor are incorporated. It has shown how the individual components of the third‐order curvature tensor have to be implemented. Their effects on the structural behavior are investigated in depth.

To capture and predict the chemo-thermo-mechanical behavior of ceramic foam filters, material models and simulation tools are required. The description of the thermo-mechanical inelastic behavior as well as the in-situ layer formation on reactive filters have been the aims of this subproject. Challenging aspects in the whole progress are the exact geometrical replication of the underlying foam structure of the filter and the lack of experimental data for many relevant loading cases. The software FoamGUI is developed to generate parametrized, periodic three-dimensional representative volume elements (RVE) of foam structures, which are used in continuum and fluid mechanical simulations as well as for 3D-printing. Calculation concepts are formulated to predict the inelastic deformation and failure behavior of ceramic open-cell foams under thermo-mechanical loading. First-order homogenization approaches are used to conclude from the mesoscopic behavior of the foam RVE to the macroscopic response of filter structures. A hybrid approach is developed in the established framework of rate-independent plasticity in combination with neural networks, which replace the plastic flow potential and the evolution equations of internal state variables. Another modeling aspect is motivated by the experimentally observed growth of an in situ layer during the so-called reactive phase of the filtration process. This phenomenon motivates the development of a model to describe diffusion, chemical reactions and phase transition processes of multi-phase/multi-component systems using the phase-field method. This allows the simulation of spatially and temporally resolved microstructure evolution leading to the layer formation.

Iron-based shape memory alloys (Fe-SMAs) are currently of high interest for potential smart material applications in civil engineering construction but also other fields that do not require biocompatibility but demand low cost of the SMA. The envisioned civil engineering application examples, for some of which prototypes have already been realized, include connectors in concrete, metal, and timber structures, concrete reinforcement, and isolators/dampers for earthquake-resistant technologies. In this contribution, we first present results regarding the experimental characterization of Fe-SMAs using a versatile miniaturized testing method, specifically the small punch test (SPT). Its main advantages are that it is relatively simple, requires only small amounts of material, and allows testing under well-defined biaxial stress states (triaxiality of approximately 0.6). The difficulty of identifying material parameters with this test and its variants is that it always requires the numerical solution of an inverse problem because the experiment records a structural response rather than a pure constitutive response. To address this, an in-house parameter identification tool has been developed, which combines finite element analysis, user-defined material models, and nonlinear optimization algorithms. Building on this expertise, our current contribution investigates the employment of the SPT as an efficient methodology to characterize Fe-SMAs under biaxial loading. Such data is of great interest to constitutive model developers for both calibration and validation purposes. Generally, sufficiently rich experimental data on SMA behavior that goes beyond results obtained in one-dimensional tests (e.g., tension-compression-torsion or planar-biaxial loading) is scarce in the literature.

In this article, a proof‐of‐concept study is presented, in which in‐situ full‐field deformation measurements via digital image correlation, finite element analysis, and nonlinear optimization techniques are combined to characterize the heterogeneous structural behavior of a bio‐based material 3D‐printed via binder jetting. The special features of this composite material are its biodegradability and its easy manufacturability using conventional 3D printers. The binder‐jetting process enables innovative applications such as additively manufactured, highly customized, recyclable, or compostable packaging solutions. Compared to other 3D printing techniques, it is relatively fast and inexpensive and can make use of raw material powders that are by‐products of the food or other industries. As an initial step towards gaining a simulation‐supported understanding of the complex process‐structure‐property relations, a first quantitative assessment of the effective behavior of a bio‐based binder‐jetted material is conducted under the following operating assumptions: (i) Its mechanical response can be described by means of a nonlinear elasto‐plastic constitutive law, enriched by a cohesive damage model capturing failure on the structural level, (ii) established mechanical tests on a 3D‐printed component, involving standardized sample geometries, and optical measurements, should yield sufficient information to allow the identification of the corresponding material parameters. First, experimental results of optically monitored four‐point bending tests, with varying alignments of loading axes and printing directions, are presented in detail. Then the proposed parameter identification strategy is explained and its capabilities and limitations, as made evident from quantitative case studies based on the measured structural response data, are thoroughly discussed.