Abstract We present a workflow for the inverse design of architected materials with targeted effective mechanical properties. The approach leverages a low‐dimensional descriptor space to represent the topology and morphology of complex mesostructures, enabling efficient navigation within the design space. Data for training is generated through numerical homogenization using a Fast Fourier Transform (FFT)‐based solver, providing high‐fidelity mappings from structural descriptors on the mesoscale to effective properties. A neural network (NN)‐based surrogate model is trained to approximate this mapping. The inverse design task is then formulated as an optimization problem over the descriptor space, where gradient‐based optimizers are applied to identify the descriptors, the inputs of the surrogate. We focus on the case of anisotropic linear elasticity and demonstrate the method using spinodoid architected materials, which offer tunable anisotropy and a low‐dimensional descriptor space. The framework is validated for the inverse design targeting the anisotropic stiffness of a femoral bone sample. In addition, we propose a method to determine the anisotropy class of a given stiffness tensor. This enables a quantitative evaluation of how closely the bone's anisotropy class can be approximated by spinodoids. We analyze the influence of the optimization loss function on the inverse design outcome by comparing results across different losses. Ultimately, a logarithmic loss function is chosen, as it enables simultaneous optimization of the stiffness and compliance.

Abstract This review provides an introduction to—and overview of—the current state of the art in neural‐network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for regularizing inverse problems in imaging. Distinguishing features of this review are, among others, an easily accessible introduction to learned generators and learned priors, in particular diffusion models, for inverse problems, and a section focusing explicitly on existing results in function space analysis of neural‐network‐based approaches in this context.

Abstract Brake squeal describes noise with different frequencies that can be emitted during the braking process. Typically, the frequencies are in the range of 1 to 16 kHz. Although the noise has virtually no effect on braking performance, strong attempts are made to identify and eliminate the noise as it can be very unpleasant and annoying. In the field of numerical simulation, the brake is typically modeled using the Finite Element method, and this results in a high‐dimensional equation of motion. For the analysis of brake squeal, gyroscopic and circulatory effects, as well as damping and friction, must be considered correctly. For the subsequent analysis, the high‐dimensional damped nonlinear equation system is linearized. This results in terms that are non‐symmetric and dependent on the rotational frequency of the brake rotor. Many parameter points to be evaluated implies many evaluations to determine the relevant parameters of the unstable system. In order to increase the efficiency of the process, the system is typically reduced with a truncated modal transformation. However, with this method the damping and the velocity‐dependent terms, which have a significant influence on the system, are neglected for the calculation of the eigenmodes, and this can lead to inaccurate reduced models. In this paper, we present results of other methods of model order reduction applied on an industrial high‐dimensional brake model. Using moment matching methods combined with parametric model order reduction, both the damping and the various parameter‐dependent terms of the brake model can be taken into account in the reduction step. Thus, better results in the frequency domain can be obtained. On the one hand, as usual in brake analysis, the complex eigenvalues are evaluated, but on the other hand also the transfer behavior in terms of the frequency response. In each case, the classical and the new reduction method are compared with each other.

Abstract Pores are inherent to additively manufactured components and critical especially in technical components. Since they reduce the component's fatigue life, a reliable identification and description of pores is vital to ensure the component's performance. X‐ray computed tomography (CT) is an established and non‐destructive testing method to investigate internal defects. The CT scan process can induce noise and artefacts in the resulting images which afterwards have to be reduced through image processing. To reconstruct the internal defects of a component, the images need to be segmented in defect region and bulk material by applying a threshold. The application of the threshold as well as the previous image processing alter the geometry and size of the identified defects. This contribution aims to quantify the influence of selected commercial image processing and segmentation methods on identified pores in several additively manufactured components made of AlSi10Mg and Ti6Al4V as well as in an artificial CT scan. To that aim, gray value histograms and characteristic parameters thereof are compared for different image processing tools. After the segmentation of the processed images, particle characteristics are compared. The influence of image processing and segmentation on the predicted fatigue life of the material is evaluated through the change of the largest pore in each set of data applying Murakami's empirical ‐parameter model.

Abstract Investigations of biphasic monodisperse soft (rubber) and stiff (glass) particle mixtures under hydrostatic conditions show an interesting behavior with regard to the effective stiffness. P‐wave modulus measured by acoustic wave propagation at ultrasonic frequencies showed a significant decline while more soft particles are added, that is, higher rubber volume fractions, due to a change in the microstructure of the granular medium. However, for small volume fractions of soft particles, it could be observed that the P‐wave modulus is increasing. This result cannot be explained by classical mixture rules or effective medium theories. For the understanding of those effects, a detailed insight into the microstructure of the granular medium is necessary. To gain this information and link it later back to the measured effective mechanical properties, high‐resolution micro X‐ray computed tomography (XRCT) imaging is a well‐established tool. With XRCT imaging, the granular microstructure can be visualized in 3D and characterized subsequently. Combining classical effective characterization methods with XRCT imaging can help to solve a variety of multi‐scale problems. Performing the characterization step in situ, meaning inside the laboratory‐based XRCT scanner, has the advantage that exactly the same samples are mechanically characterized and visualized. To address the mentioned observation above, we designed a low X‐ray absorbing oedometer cell with integrated broadband piezoelectric P‐wave transducers which enables this kind of investigation inside a laboratory‐based XRCT scanner. The focus of this contribution is on the general experimental methodology which can be transferred to other multi‐scale problems. It starts with a description of the image acquisition and ends with the post‐processing of the in situ acquired image data. To demonstrate this, cylindrical samples consisting of the same monodisperse rubber and glass particle mixtures that were studied before under hydrostatic stress conditions are considered. Selected results are presented to explain the single steps.

Abstract This work presents direct numerical simulations (DNS) of a circular turbulent jet impinging on rough plates. The roughness is once resolved through an immersed boundary method (IBM) and once modeled through a parametric forcing approach (PFA) which accounts for surface roughness effects by applying a forcing term into the Navier–Stokes equations within a thin layer in the near‐wall region. The DNS with the IBM setup is validated using optical flow field measurements over a smooth and a rough plate with similar statistical surface properties. In the study, IBM‐resolved cases are used to show that the PFA is capable of reproducing mean flow features well at large wall‐normal distances, while less accurate predictions are observed in the near‐wall region. The demarcation between these two regions is approximately identified with the mean wall height of the surface roughness distribution. Based on the observed differences in the results between IBM‐ and PFA‐resolved cases, plausible future improvements of the PFA are suggested.

Abstract 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.

Abstract This work presents multilayer phase‐field simulation of selective sintering process and the calculation of effective mechanical properties and residual stress of the microstructure using the finite element method. The dependence of the effective properties and residual stress on the process parameters, such as beam power and scan speed, are analyzed. Significant partial melting of powders is observed for large beam power and low scan speed, which results in low porosity of the microstructure. Nonlinear relationship between the effective mechanical properties and process parameters is observed. The increasing rate of effective mechanical properties decreases with increasing beam power, while increases with decreasing scan speed. The dependence of effective Young's modulus and Poisson's ratio on porosity are well established using power law models. Stress concentrations are found at the necking region of powders and the intensity increases with the level of partial melting, which results in increasing residual stress in the microstructure. The numerical results reveal quantitatively the process‐microstructure‐property relation, which implies the feasibility of the subsequent data‐driven approach.

Abstract This work presents a review of the current state of research in data‐driven turbulence closure modeling. It offers a perspective on the challenges and open issues but also on the advantages and promises of machine learning (ML) methods applied to parameter estimation, model identification, closure term reconstruction, and beyond, mostly from the perspective of large Eddy simulation and related techniques. We stress that consistency of the training data, the model, the underlying physics, and the discretization is a key issue that needs to be considered for a successful ML‐augmented modeling strategy. In order to make the discussion useful for non‐experts in either field, we introduce both the modeling problem in turbulence as well as the prominent ML paradigms and methods in a concise and self‐consistent manner. In this study, we present a survey of the current data‐driven model concepts and methods, highlight important developments, and put them into the context of the discussed challenges.