Universität Stuttgart
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Item Open Access Mass‐exchange processes in a biphasic TPM‐phase‐field model(2026) Rivas, Yann; Ehlers, Wolfgang; Wagner, ArndtThe modelling of hydraulic fracturing processes in porous media gained significant interest in the past. Therefore, several approaches, such as the Biot theory or the Theory of Porous Media (TPM), were used as their modelling basis. In combination with the phase‐field method for a diffuse fracture description, especially the TPM has turned out to be a powerful tool to simulate hydraulic fracturing processes. In this contribution, a first‐principle‐based and thermodynamically consistent procedure is proposed to additionally describe a local porosity change due to the flushing of detached particles within the fractured region by considering mass‐exchange processes within the well‐established TPM‐phase‐field method. In addition, a numerical example is presented showing the possibilities of the derived model.Item Open Access Effects of enzymatically induced carbonate precipitation on capillary pressure : saturation relations(2022) Hommel, Johannes; Gehring, Luca; Weinhardt, Felix; Ruf, Matthias; Steeb, HolgerLeakage mitigation methods are an important part of reservoir engineering and subsurface fluid storage, in particular. In the context of multi-phase systems of subsurface storage, e.g., subsurface CO2 storage, a reduction in the intrinsic permeability is not the only parameter to influence the potential flow or leakage; multi-phase flow parameters, such as relative permeability and capillary pressure, are key parameters that are likely to be influenced by pore-space reduction due to leakage mitigation methods, such as induced precipitation. In this study, we investigate the effects of enzymatically induced carbonate precipitation on capillary pressure-saturation relations as the first step in accounting for the effects of induced precipitation on multi-phase flow parameters. This is, to our knowledge, the first exploration of the effect of enzymatically induced carbonate precipitation on capillary pressure-saturation relations thus far. First, pore-scale resolved microfluidic experiments in 2D glass cells and 3D sintered glass-bead columns were conducted, and the change in the pore geometry was observed by light microscopy and micro X-ray computed tomography, respectively. Second, the effects of the geometric change on the capillary pressure-saturation curves were evaluated by numerical drainage experiments using pore-network modeling on the pore networks extracted from the observed geometries. Finally, parameters of both the Brooks-Corey and Van Genuchten relations were fitted to the capillary pressure-saturation curves determined by pore-network modeling and compared with the reduction in porosity as an average measure of the pore geometry’s change due to induced precipitation. The capillary pressures increased with increasing precipitation and reduced porosity. For the 2D setups, the change in the parameters of the capillary pressure-saturation relation was parameterized. However, for more realistic initial geometries of the 3D samples, while the general patterns of increasing capillary pressure may be observed, such a parameterization was not possible using only porosity or porosity reduction, likely due to the much higher variability in the pore-scale distribution of the precipitates between the experiments. Likely, additional parameters other than porosity will need to be considered to accurately describe the effects of induced carbonate precipitation on the capillary pressure-saturation relation of porous media.Item Open Access Permeability estimation of regular porous structures : a benchmark for comparison of methods(2021) Wagner, Arndt; Eggenweiler, Elissa; Weinhardt, Felix; Trivedi, Zubin; Krach, David; Lohrmann, Christoph; Jain, Kartik; Karadimitriou, Nikolaos; Bringedal, Carina; Voland, Paul; Holm, Christian; Class, Holger; Steeb, Holger; Rybak, IrynaThe intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny-Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.Item Open Access Integrated mechanical computing for autonomous soft machines(2024) Byun, Junghwan; Pal, Aniket; Ko, Jongkuk; Sitti, MetinMechanical computing offers a new modality to formulate computational autonomy in intelligent matter or machines without any external powering or active elements. Transition (or solitary) waves, induced by nonreciprocity in mechanical metamaterials comprising a chain of bistable elements, have proven to be a key ingredient for dissipation-free transmission and computation of mechanical information. However, advanced processing of mechanical information in existing designs is hindered by its dissipation when interacting with networked logic gates. Here, we present a metamaterial design strategy that allows non-dispersive mechanical solitary waves to compute multi-level cascaded logic functions, termed ‘integrated mechanical computing’, by propagating through a network of structurally heterogeneous computing units. From a perspective of characteristic potential energy, we establish an analytical framework that helps in understanding the solitary wave-based mechanical computation, and governs the mechanical design of key determinants for realizing cascaded logic computation, such as soliton profile and logic elements. The developed integrated mechanical computing systems are shown to receive, transmit and compute mechanical information to actuate intelligent soft machine prototypes in a seamless and integrated manner. These findings would pave the way for future intelligent robots and machines that perform computational operations between various non-electrical environmental inputs.Item Open Access Robust inverse material design with physical guarantees using the Voigt‐Reuss net(2026) Keshav, Sanath; Fritzen, FelixWe apply the Voigt‐Reuss net, a spectrally normalized neural surrogate introduced in [38], for forward and inverse mechanical homogenization with a key guarantee that all predicted effective stiffness tensors satisfy Voigt‐Reuss bounds in the Löwner sense during training, inference, and gradient‐driven optimization. The approach operates in a bounded spectral space by reparametrizing each effective tensor relative to its Voigt and Reuss bounds, ensuring that all outputs reside within a unit‐cube domain and are mapped back via a deterministic inverse transform to physically admissible tensors. For 3D elasticity, a fully connected Voigt‐Reuss net is trained on ∼1.18 million high‐fidelity homogenization labels of stochastic biphasic microstructures. The model ingests 236 image‐derived morphological descriptors and phase parameters that encode bulk and shear moduli, enabling a single surrogate to represent material combinations spanning 4 orders of magnitude. Due to the rotational invariance of the descriptor set, the surrogate recovers the isotropic projection of the effective stiffness ( R2≥0.998 for isotropy‐related components). However, anisotropy‐revealing entries remain unlearnable from the available features. At the tensor level, the relative Frobenius error exhibits a median of approximately 1.8% (mean approximately 3.6%) and approaches the irreducible isotropic‐projection floor, far outperforming all alternative surrogates considered. In 2D plane‐strain elasticity, spectral normalization is integrated with a differentiable microstructure renderer and a convolutional regressor, yielding a surrogate that maps generator parameters to effective stiffness tensors for highly anisotropic and high‐contrast composites. Voigt‐Reuss net is compared against vanilla and Cholesky regressors trained with identical architectures, data, and training procedures. The unconstrained surrogates frequently violate Voigt/Reuss bounds and even positive definiteness, whereas Voigt‐Reuss net produces no violations by design and also enables robust inverse design. Utilizing the surrogate with batched first‐order optimization, the approach can match prescribed target tensors and optimize tensor functionals, recovering classical optima while avoiding nonphysical and spurious designs observed with unconstrained surrogates.Item Open Access Direct numerical simulation and analysis of solid body motion in dilute suspensions using Smoothed Particle Hydrodynamics(Stuttgart : Institute of Applied Mechanics, 2024) Kijanski, Nadine; Steeb, Holger (Prof. Dr.-Ing.)Suspensions and their applications are found in many engineering, environmental or medical fields. While the effective rheological behavior is well understood in the framework of non-Newtonian fluid mechanics, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. The motion of single particles immersed in the fluid is still on-going research and depends on hydromechanical forces as well as on solid-solid interactions. Using Smoothed Particle Hydrodynamics, a modeling approach for Direct Numerical Simulations of a single-phase fluid containing non-spherically formed solid aggregates is presented. The motion of single particles in dilute suspensions are observed to analyze effects like shear-wall migration or rolling, as seen in experiments. To be able to simulate the behavior of for example fresh concrete or mud flow as realistic as possible, the simulations taking into account a Newtonian as well as a non-Newtonian material model for the carrier fluid.Item Open Access Multiscale modeling and stability analysis of soft active materials : from electro- and magneto-active elastomers to polymeric hydrogels(Stuttgart : Institute of Applied Mechanics, 2023) Polukhov, Elten; Keip, Marc-André (Prof. Dr.-Ing.)This work is dedicated to modeling and stability analysis of stimuli-responsive, soft active materials within a multiscale variational framework. In particular, composite electro- and magneto-active polymers and polymeric hydrogels are under consideration. When electro- and magneto-active polymers (EAP and MAP) are fabricated in the form of composites, they comprise at least two phases: a polymeric matrix and embedded electric or magnetic particles. As a result, the obtained composite is soft, highly stretchable, and fracture resistant like polymer and undergoes stimuli-induced deformation due to the interaction of particles. By designing the microstructure of EAP or MAP composites, a compressive or a tensile deformation can be induced under electric or magnetic fields, and also coupling response of the composite can be enhanced. Hence, these materials have found applications as sensors, actuators, energy harvesters, absorbers, and soft, programmable, smart devices in various areas of engineering. Similarly, polymeric hydrogels are also stimuli-responsive materials. They undergo large volumetric deformations due to the diffusion of a solvent into the polymer network of hydrogels. In this case, the obtained material shows the characteristic behavior of polymer and solvent. Therefore, these materials can also be considered in the form of composites to enhance the response further. Since hydrogels are biocompatible materials, they have found applications as contact lenses, wound dressings, drug encapsulators and carriers in bio-medicine, among other similar applications of electro- and magneto-active polymers. All above mentioned favorable features of these materials, as well as their application possibilities, make it necessary to develop mathematical models and numerical tools to simulate the response of them in order to design pertinent microstructures for particular applications as well as understand the observed complex patterns such as wrinkling, creasing, snapping, localization or pattern transformations, among others. These instabilities are often considered as failure points of materials. However, many recent works take advantage of instabilities for smart applications. Investigation of these instabilities and prediction of their onset and mode are some of the main goals of this work. In this sense, the thesis is organized into three main parts. The first part is devoted to the state of the art in the development, fabrication, and modeling of soft active materials as well as the continuum mechanical description of the magneto-electro-elasticity. The second part is dedicated to multiscale instabilities in electro- and magneto-active polymer composites within a minimization-type variational homogenization setting. This means that the highly heterogeneous problem is not resolved on one scale due to computational inefficiency but is replaced by an equivalent homogeneous problem. The effective response of the macroscopic homogeneous problem is determined by solving a microscopic representative volume element which includes all the geometrical and material non-linearities. To bridge these two scales, the Hill-Mandel macro-homogeneity condition is utilized. Within this framework, we investigate both macroscopic and microscopic instabilities. The former are important not only from a physical point of view but also from a computational point of view since the macroscopic stability (strong ellipticity) is necessary for the existence of minimizers at the macroscopic scale. Similarly, the investigation of the latter instabilities are also important to determine the pattern transformations at the microscale due to external action. Thereby the critical domain of homogenization is also determined for computation of accurate effective results. Both investigations are carried out for various composite microstructures and it is found that they play a crucial role in the response of the materials. Therefore, they must be considered for designing EAP and MAP composites as well as for providing reliable computations. The third part of the thesis is dedicated to polymeric hydrogels. Here, we develop a minimization-based homogenization framework to determine the response of transient periodic hydrogel systems. We demonstrate the prevailing size effect as a result of a transient microscopic problem, which has been investigated for various microstructures. Exploiting the elements of the proposed framework, we explore the material and structural instabilities in single and two-phase hydrogel systems. Here, we have observed complex experimentally observed and novel 2D pattern transformations such as diamond-plate patterns coupled with and without wrinkling of internal surfaces for perforated microstructures and 3D pattern transformations in thin reinforced hydrogel composites. The results indicate that the obtained patterns can be controlled by tuning the material and geometrical parameters of the composite.Item Open Access Digital laboratory: X-ray computed tomography towards direct numerical simulations(Stuttgart : Institute of Applied Mechanics, 2025) Uribe, David; Steeb, Holger (Prof. Dr.-Ing.)A digital porous media laboratory comprises a set of techniques to analyse and characterize samples using computer simulations and digital measurements to predict or determine material properties. This thesis has implemented the complete workflow of this technique from sample preparation until reporting the gained information pertaining said sample. A complete design of an in house built X-ray computed tomographic system is described. All components of the system are listed and the way they are electrically and mechanically coupled is explained. Software architecture to control the system and the advantages it has to maintain the system is described at a cost of system complexity. The in-house tomographic system was used to characterize engineering, geologic and biological samples.Item Open Access Modelling and simulation of natural hydraulic fracturing applied to experiments on natural sandstone cores(2024) Wang, Junxiang; Sonntag, Alixa; Lee, Dongwon; Xotta, Giovanna; Salomoni, Valentina A.; Steeb, Holger; Wagner, Arndt; Ehlers, WolfgangUnder in-situ conditions, natural hydraulic fractures (NHF) can occur in permeable rock structures as a result of a rapid decrease of pore water accompanied by a local pressure regression. Obviously, these phenomena are of great interest for the geo-engineering community, as for instance in the framework of mining technologies. Compared to induced hydraulic fractures, NHF do not evolve under an increasing pore pressure resulting from pressing a fracking fluid in the underground but occur and evolve under local pore-pressure reductions resulting in tensile stresses in the rock material. The present contribution concerns the question under what quantitative circumstances NHF emerge and evolve. By this means, the novelty of this article results from the combination of numerical investigations based on the Theory of Porous Media with a tailored experimental protocol applied to saturated porous sandstone cylinders. The numerical investigations include both pre-existing and evolving fractures described by use of an embedded phase-field fracture model. Based on this procedure, representative mechanical and hydraulic loading scenarios are simulated that are in line with experimental investigations on low-permeable sandstone cylinders accomplished in the Porous Media Lab of the University of Stuttgart. The values of two parameters, the hydraulic conductivity of the sandstone and the critical energy release rate of the fracture model, have turned out essential for the occurrence of tensile fractures in the sandstone cores, where the latter is quantitatively estimated by a comparison of experimental and numerical results. This parameter can be taken as reference for further studies of in-situ NHF phenomena and experimental results.Item Open Access A mesh‐in‐element method for the theory of porous media(2024) Maike, S.; Schröder, Jörg; Bluhm, J.; Ricken, TimWhile direct homogenisation approaches such as the FE method are subject to the assumption of scale separation, the mesh‐in‐element (MIEL) approach is based on an approach with strong scale coupling, which is based on a discretization with finite elements. In this contribution we propose a two‐scale MIEL scheme in the framework of the theory of porous media (TPM). This work is a further development of the MIEL method which is based on the works of the authors A. Ibrahimbegovic, R.L. Taylor, D. Markovic, H.G. Matthies, R. Niekamp (in alphabetical order); where we find the physical and mathematical as well as the software coupling implementation aspects of the multi‐scale modeling of heterogeneous structures with inelastic constitutive behaviour, see for example, [Eng Comput, 2005;22(5‐6):664‐683.] and [Eng Comput , 2009;26(1/2):6‐28.]. Within the scope of this contribution, the necessary theoretical foundations of TPM are provided and the special features of the algorithmic implementation in the context of the MIEL method are worked out. Their fusion is investigated in representative numerical examples to evaluate the characteristics of this approach and to determine its range of application.