Die Lage eines Punkte P im Raum wird durch den Ortsvektor r(t) beschrieben.

Räumliche Bewegung: Die Bewegung eines starren Körpers wird durch das Bewegungsgesetz (auch Impulssatz in differentieller Form, Kräftesatz oder Schwerpunktsatz) sowie durch den Drallsatz (Momentensatz) beschrieben.

Die Bewegung eines starren Körpers lässt sich aus einer Translationund einer Rotation zusammensetzen.

Stoß: Als Stoß bezeichnet man ein plötzliches Aufeinanderprallen zweier Körper.

The International Association of Applied Mathematics and Mechanics (Gesellschaft f & uuml;r Angewandte Mathematik und Mechanik, GAMM) was founded in 1923 with the goal to strengthen the field of scientific engineering by the foundation of an Engineering Association with strong scientific contacts to Applied Mathematics. Already at the Leipzig Naturalists' Day (Leipziger Naturforschertag) in 1922, the idea of combining mathematical and mechanical knowledge arose and led to the decision to found a German engineering association with close organizational ties to the Association of German Engineers (Verein Deutscher Ingenieure, VDI). This was the origin of GAMM, where 26 people spontaneously signed up to join the upcoming society. GAMM has grown over the years and currently (in 2023) has 1338 full members from 40 countries and 9 institutional members. The present article sheds light on the history of GAMM between 1921 and 2023 and also examines the motivations behind the founding and ongoing promotion of GAMM. In addition, it considers the achievements of GAMM members and further scientists over the years.

ZusammenfassungDie Bewegung eines Massenpunktes unter der Wirkung von Kräften wird beschrieben durch $$ \boxed{\frac{{d(mv)}}{{dt}} = \dot{p} = F}, $$ mit F = ∑ F i und dem Impuls $$ p = mv. $$

ZusammenfassungFormt man das Newtonsche Grundgesetz für die Bewegung eines Massenpunktes (oder des Schwerpunktes eines starren Körpers) um $$ ma = \sum {F \to \sum {F - ma = 0} } $$ und führt die Trägheitskraft (Scheinkraft) $$ {{F}_{T}} = - ma $$ ein, so erhält man das „dynamische Gleichgewicht“ $$ \boxed{\sum F + {{F}_{T}} = 0}. $$

Massenpunktsystem: Auf die Masse m i wirken die äußere Kraft F i und die inneren Kräfte F ij = -F ji. Bleiben die Abstände r ij zwischenden Massen konstant, so liegt ein starrer Punkthaufen vor.

The phase-field approach applied to fracturing solids has recently been embedded in the Theory of Porous Media for the description of dynamic hydraulic fracturing scenarios based on fully saturated porous media. This method has further been enhanced by the introduction of a crack-opening indicator to distinguish between open and closed cracks accompanied by a switch between Darcy-type and NavierStokes-type flow situations in the unbroken porous domain and in fully broken areas. In the present article, this procedure is extended towards partially saturated media consisting of a porous solid, the soil, and an immiscible pore content of a pore liquid and a pore gas.

This work introduces a novel application for predicting the macroscopic intrinsic permeability tensor in deformable porous media, using a limited set of micro-CT images of real microgeometries. The primary goal is to develop an efficient, machine-learning (ML)-based method that overcomes the limitations of traditional permeability estimation techniques, which often rely on time-consuming experiments or computationally expensive fluid dynamics simulations. The novelty of this work lies in leveraging Convolutional Neural Networks (CNN) to predict pore-fluid flow behavior under deformation and anisotropic flow conditions. Particularly, the described approach employs binarized CT images of porous micro-structure as inputs to predict the symmetric second-order permeability tensor, a critical parameter in continuum porous media flow modeling. The methodology comprises four key steps: (1) constructing a dataset of CT images from Bentheim sandstone at different volumetric strain levels; (2) performing pore-scale simulations of single-phase flow using the lattice Boltzmann method (LBM) to generate permeability data; (3) training the CNN model with the processed CT images as inputs and permeability tensors as outputs; and (4) exploring techniques to improve model generalization, including data augmentation and alternative CNN architectures. Examples are provided to demonstrate the CNN's capability to accurately predict the permeability tensor, a crucial parameter in various disciplines such as geotechnical engineering, hydrology, and material science. An exemplary source code is made available for interested readers.

This work introduces a novel application for predicting the macroscopic intrinsic permeability tensor in deformable porous media, using a limited set of μ-CT images of real microgeometries. The primary goal is to develop an efficient, machine learning (ML)-based method that overcomes the limitations of traditional permeability estimation techniques, which often rely on time-consuming experiments or computationally expensive fluid dynamics simulations. The novelty of this work lies in leveraging convolutional neural networks (CNNs) to predict pore-fluid flow behavior under deformation and anisotropic flow conditions. The approach utilizes binarized CT images of porous microstructures to predict the permeability tensor, a crucial parameter in continuum porous media flow modeling. The methodology involves four steps: (1) constructing a dataset of CT images from Bentheim sandstone at varying volumetric strain levels; (2) conducting pore-scale flow simulations using the lattice Boltzmann method (LBM) to obtain permeability data; (3) training the CNN model with processed CT images as inputs and permeability tensors as outputs; and (4) employing techniques like data augmentation to enhance model generalization. Examples demonstrate the CNN’s ability to accurately predict the permeability tensor in connection with the deformation state through the porosity parameter. A source code has been made available as open access.

The Theory of Porous Media (TPM) with an embedded phase-field approach to fracture provides an elegant opportunity to study complex flow phenomena in fractured porous materials in a unified single-domain approach. On this basis, the interactive flow behaviour between free flow and porous-media flow is studied using the example of flow through a thin porous plate containing a rectangular channel. By considering different boundary conditions and investigating the flow behaviour for a range of hydraulic conductivities, our study is designed to reveal insights into phenomena which are relevant for various sub-surface geo-engineered applications. Furthermore, we show that the applied macroscopic single-domain approach is able to reveal local flow effects near the porous interface (channel walls), namely the so-called velocity profile inversion phenomenon. Moreover, we introduce a geometrically motivated estimation of the length-scale parameter ϵ used in phase-field approaches, which is directly related to the roughness of the fracture surface. Thus, values for ϵ are proposed for microfluidic devices and different rock types. Furthermore, we apply fully three-dimensional simulations to evaluate the influence of the thickness of thin porous plates on the overall flow resistance, which is typically relevant in microfluidic devices. In a combined numerical–experimental study, we compare results from representative microfluidic experiments and simulations and confirmed the choice of ϵ to correctly predict the flow transition across the porous interface.

Under 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.

At the end of the 18th century, serious problems in dyke constructions in Northern Germany and the need to understand coupled solid-water problems initiated first attempts to describe porous media. Many attempts followed until a sound Theory of Porous Media (TPM) was born on the basis of continuum mechanics of multi-component materials with multi-physical properties. The present article roughly describes the development of the TPM from its origins to contemporary applications, thus presenting a short historical review of porous-media research.

Hydraulically induced fracturing is widely used in practice for several exploitation techniques. The chosen macroscopic model combines a phase‐field approach to fractures with the Theory of Porous Media (TPM) to describe dynamic hydraulic fracturing processes in fully‐saturated porous materials. In this regard, the solid's state of damage shows a diffuse transition zone between the broken and unbroken domain. Rocks or soils in grown nature are generally inhomogeneous with material imperfections on the microscale, such that modelling homogeneous porous material may oversimplify the behaviour of the solid and fluid phases in the fracturing process. Therefore, material imperfections and inhomogeneities in the porous structure are considered through the definition of location‐dependent material parameters. In this contribution, a deterministic approach to account for predefined imperfection areas as well as statistical fields of geomechanical properties is proposed. Representative numerical simulations show the impact of solid skeleton heterogeneities in porous media on the fracturing characteristics, e. g. the crack path.