Incorporating sufficient physical information into artificial neural networks: a guaranteed improvement via physics-based Rao-Blackwellization

The concept of Rao-Blackwellization is employed to improve predictions of artificial neural networks by physical information. The error norm and the proof of improvement are transferred from the original statistical concept to a deterministic one, using sufficient information on physics-based conditions. The proposed strategy is applied to material modeling and illustrated by examples of the identification of a yield function, elasto-plastic steel simulations, the identification of driving forces for quasi-brittle damage and rubber experiments. Sufficient physical information is employed, e.g., in the form of invariants, parameters of a minimization problem, dimensional analysis, isotropy and differentiability. It is proven how intuitive accretion of information can yield improvement if it is physically sufficient, but also how insufficient or superfluous information can cause impairment. Opportunities for the improvement of artificial neural networks are explored in terms of the training data set, the networks' structure and output filters. Even crude initial predictions are remarkably improved by reducing noise, overfitting and data requirements

Numerical analysis of wave propagation in fluid-filled deformable tubes

The theory of Biot describing wave propagation in fluid saturated porous media is a good effective approximation of a wave induced in a fluid-filled deformable tube -- Nonetheless, it has been found that Biot’s theory has shortcomings in predicting the fast P-wave velocities and the amount of intrinsic attenuation -- These problems arises when complex mechanical interactions of the solid phase and the fluid phase in the micro-scale are not taken into account -- In contrast, the approach proposed by Bernabe does take into account micro-scopic interaction between phases and therefore poses an interesting alternative to Biot’s theory -- A Wave propagating in a deformable tube saturated with a viscous fluid is a simplified model of a porous material, and therefore the study of this geometry is of great interest -- By using this geometry, the results of analytical and numerical results have an easier interpretation and therefore can be compared straightforward -- Using a Finite Difference viscoelastic wave propagation code, the transient response was simulated -- The wave source was modified with different characteristic frequencies in order to gain information of the dispersion relation -- It was found that the P-wave velocities of the simulations at sub-critical frequencies closely match those of Bernabe’s solution, but at over-critical frequencies they come closer to Biot’s solutio

Dilute suspensions in annular shear flow under gravity: simulation and experiment

A dilute suspension in annular shear flow under gravity was simulated using multi-particle collision dynamics (MPC) and compared to experimental data. The focus of the analysis is the local particle velocity and density distribution under the influence of the rotational and gravitational forces. The results are further supported by a deterministic approximation of a single-particle trajectory and OpenFOAM CFD estimations of the overcritical frequency range. Good qualitative agreement is observed for single-particle trajectories between the statistical mean of MPC simulations and the deterministic approximation. Wall contact and detachment however occur earlier in the MPC simulation, which can be explained by the inherent thermal noise of the method. The multi-particle system is investigated at the point of highest particle accumulation that is found at 2/3 of the particle revolution, starting from the top of the annular gap. The combination of shear flow and a slowly rotating volumetric force leads to strong local accumulation in this section that increases the particle volume fraction from overall 0.7% to 4.7% at the outer boundary. MPC simulations and experimental observations agree well in terms of particle distribution and a close to linear velocity profile in radial direction

Waves in partially saturated porous media

Mechanische Wellenausbreitung in teilgesättigten, porösen Medien ist von großem Interesse für die wissenschaftliche Forschung und Anwendung, z. B. für geophysikalische Erkundungen, schallabsorbierende Materialien sowie die Mobilisierung von Fluidansammlungen. Mit dem Ziel der Vorhersage und Charakterisierung von Welleneigenschaften wird zuerst ein Modell für die Wellenausbreitung in teilgesättigten, porösen Medien hergeleitet, z. B. für luft- und wassergefüllte Gesteine oder Schäume. Ein Fokus auf die kleinskaligen, oszillierenden Flüsse führt anschließend zu einer verallgemeinerten Definition der charakteristischen Frequenz. Ein zusätzliches Modell für residuale Sättigung vervollständigt den theoretischen Ansatz für Situationen mit diskontinuierlichen Fluidansammlungen wie einzelnen, getrennten Wassereinschlüssen. Daran schließt sich eine Klassifizierung der Resonanzeffekte von individuellen Fluidansammlungen durch eine theoretische, numerische und experimentelle Studie an.Mechanical wave propagation in partially saturated porous media is of great interest in science and applications, e.g., for geophysical exploration, sound-absorbing materials, and support of ganglia mobilization. This work models linear, mechanical wave propagation in partially saturated porous media (such as air- and water-filled rocks or foams) with the objectives of accurate prediction and characterization. Additionally, the investigation of smaller-scale, oscillatory flows yields a generalized, characteristic frequency. A secondary model for residual saturation completes the theoretical approach, e.g., for systems including disconnected water conglomerations. An appropriate classification of oscillating fluid clusters follows, with a theoretical, numerical, and experimental investigation

Dilute suspensions in annular shear flow under gravity: simulation and experiment

A dilute suspension in annular shear flow under gravity was simulated using multi-particle collision dynamics (MPC) and compared to experimental data. The focus of the analysis is the local particle velocity and density distribution under the influence of the rotational and gravitational forces. The results are further supported by a deterministic approximation of a single-particle trajectory and OpenFOAM CFD estimations of the overcritical frequency range. Good qualitative agreement is observed for single-particle trajectories between the statistical mean of MPC simulations and the deterministic approximation. Wall contact and detachment however occur earlier in the MPC simulation, which can be explained by the inherent thermal noise of the method. The multi-particle system is investigated at the point of highest particle accumulation that is found at 2/3 of the particle revolution, starting from the top of the annular gap. The combination of shear flow and a slowly rotating volumetric force leads to strong local accumulation in this section that increases the particle volume fraction from overall 0.7% to 4.7% at the outer boundary. MPC simulations and experimental observations agree well in terms of particle distribution and a close to linear velocity profile in radial direction

Dilute suspensions in annular shear flow under gravity: simulation and experiment

A dilute suspension in annular shear flow under gravity was simulated using multi-particle collision dynamics (MPC) and compared to experimental data. The focus of the analysis is the local particle velocity and density distribution under the influence of the rotational and gravitational forces. The results are further supported by a deterministic approximation of a single-particle trajectory and OpenFOAM CFD estimations of the overcritical frequency range. Good qualitative agreement is observed for single-particle trajectories between the statistical mean of MPC simulations and the deterministic approximation. Wall contact and detachment however occur earlier in the MPC simulation, which can be explained by the inherent thermal noise of the method. The multi-particle system is investigated at the point of highest particle accumulation that is found at 2/3 of the particle revolution, starting from the top of the annular gap. The combination of shear flow and a slowly rotating volumetric force leads to strong local accumulation in this section that increases the particle volume fraction from overall 0.7% to 4.7% at the outer boundary. MPC simulations and experimental observations agree well in terms of particle distribution and a close to linear velocity profile in radial direction