Space-time variational material modeling: a new paradigm demonstrated for thermo-mechanically coupled wave propagation, visco-elasticity, elasto-plasticity with hardening, and gradient-enhanced damage

We formulate variational material modeling in a space-time context. The starting point is the description of the space-time cylinder and the definition of a thermodynamically consistent Hamilton functional which accounts for all boundary conditions on the cylinder surface. From the mechanical perspective, the Hamilton principle then yields thermo-mechanically coupled models by evaluation of the stationarity conditions for all thermodynamic state variables which are displacements, internal variables, and temperature. Exemplary, we investigate in this contribution elastic wave propagation, visco-elasticity, elasto-plasticity with hardening, and gradient-enhanced damage. Therein, one key novel aspect are initial and end time velocity conditions for the wave equation, replacing classical initial conditions for the displacements and the velocities. The motivation is intensively discussed and illustrated with the help of a prototype numerical simulation. From the mathematical perspective, the space-time formulations are formulated within suitable function spaces and convex sets. The unified presentation merges engineering and applied mathematics due to their mutual interactions. Specifically, the chosen models are of high interest in many state-of-the art developments in modeling and we show the impact of this holistic physical description on space-time Galerkin finite element discretization schemes. Finally, we study a specific discrete realization and show that the resulting system using initial and end time conditions is well-posed

A novel approach for the consideration of plastic material behavior in thermodynamic topology optimization

In order to find optimal structures for realistic applications, it is essential to include the real material behavior in the optimization process. For this purpose, this research focuses on thermodynamic topology optimization accounting for plasticity for which a surrogate material model is developed. Characteristically, the stress/strain diagram resulting from physical loading and unloading shows a hysteresis for classical plasticity models. Our material model takes only the physical loading during the optimization process into account. To this end, during a virtual unloading in the optimization process, the dissipation of energy is suppressed which yields the same elasto/plastic deformation state as for physical loading. By using this novel material model, optimized structures can be computed without resourceful classical path-dependent plasticity computation

An extended Hamilton principle as unifying theory for coupled problems and dissipative microstructure evolution

An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account non-local effects to capture microstructure evolution. In this case, the evolution of microstructure is described by a partial differential equation. In this contribution, we present how Hamilton’s principle provides a physically sound strategy for the derivation of transient field equations for all state variables. Therefore, we begin with a demonstration how Hamilton’s principle generalizes the principle of stationary action for rigid bodies. Furthermore, we show that the basic idea behind Hamilton’s principle is not restricted to isothermal mechanical processes. In contrast, we propose an extended Hamilton principle which is applicable to coupled problems and dissipative microstructure evolution. As example, we demonstrate how the field equations for all state variables for thermo-mechanically coupled problems, i.e., displacements, temperature, and internal variables, result from the stationarity of the extended Hamilton functional. The relation to other principles, as the principle of virtual work and Onsager’s principle, is given. Finally, exemplary material models demonstrate how to use the extended Hamilton principle for thermo-mechanically coupled elastic, gradient-enhanced, rate-dependent, and rate-independent materials. © 2021, The Author(s)

An extended Hamilton functional for the thermodynamic topology optimization of hyperelastic structures

We present our work on a new variational approach for thermodynamic topology optimization of hyperelastic structures: building upon our previous works, we follow a thermodynamic approach for deriving a field equation that describes the evolution of the density. The problem of topology optimization is consequently solved without the need of expensive optimization routines. Furthermore, our new formulation can also be applied to hyperelastic structures which show a remarkable difference to structures optimized for small deformations. Important aspects like tension/compression asymmetry and buckling are inherently included in the topology optimization approach due to the large deformation formulation

Continuum multiscale modeling of absorption processes in micro- and nanocatalysts

In this paper, we propose a novel, semi-analytic approach for the two-scale, computational modeling of concentration transport in packed bed reactors. Within the reactor, catalytic pellets are stacked, which alter the concentration evolution. Firstly, the considered experimental setup is discussed and a naive one-scale approach is presented. This one-scale model motivates, due to unphysical fitted values, to enrich the computational procedure by another scale. The computations on the second scale, here referred to as microscale, are based on a proper investigation of the diffusion process in the catalytic pellets from which, after continuum-consistent considerations, a sink term for the macroscopic advection–diffusion–reaction process can be identified. For the special case of a spherical catalyst pellet, the parabolic partial differential equation at the microscale can be reduced to a single ordinary differential equation in time through a semi-analytic approach. After the presentation of our model, we show results for its calibration against the macroscopic response of a simple standard mass transport experiment. Based thereon, the effective diffusion parameters of the catalyst pellets can be identified. © 2022, The Author(s)

Efficient and robust numerical treatment of a gradient-enhanced damage model at large deformations

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed by Junker et al. in 2019, to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples including snapback and springback phenomena. © 2021 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd

Numerical and experimental investigation of multi-species bacterial co-aggregation

This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation refers to the physical binding between cells of different microbial species, a system composed of two species is considered in the modeling framework. The extension of the model to an arbitrary number of species is straightforward. In addition to two-species (multi-species growth) dynamics, the transport of a nutritional substance and the extent of co-aggregation are introduced into the model as the third and fourth primary variables. A phase-field modeling approach is employed to describe the co-aggregation between the two species. The mathematical model is three-dimensional and fully based on the continuum description of the problem without any need for discrete agents which are the key elements of the individual-based modeling approach. It is shown that the use of a phase-field-based model is equivalent to a particular form of classical diffusion-reaction systems. Unlike the so-called mixture models, the evolution of each component of the multi-species system is captured thanks to the inherent capability of phase-field modeling in treating systems consisting of distinct multi-phases. The details of numerical implementation in a FEM framework are also presented. Indeed, a new multi-field user element is developed and implemented in ANSYS for this multiphysics problem. Predictions of the model are compared with the experimental observations. By that, the versatility and applicability of the model and the numerical tool are well established

Herbstgrundlinien 2013

Die deutsche Wirtschaft folgt einem moderaten Aufwärtstrend. Zwar war die wirtschaftliche Dynamik im zweiten Quartal hoch, diese Entwicklung dürfte aber durch Sondereffekte überzeichnet sein. Im weiteren Verlauf wird die Produktion dann stetig zunehmen; 2014 liegt das Wachstum bei 1,7 Prozent, nach 0,4 Prozent in diesem Jahr. Nach einem schwachen Jahresauftakt hat die Weltwirtschaft im zweiten Quartal etwas Fahrt aufgenommen. Vor allem die Industrieländer lassen trotz anhaltend restriktiv wirkender Finanzpolitik eine erhöhte wirtschaftliche Dynamik erkennen; geringe Inflationsraten und eine sich verbessernde oder zumindest stabilisierende Arbeitsmarktsituation stützen den Konsum. Im Zuge zurückgehender Unsicherheit und anhaltend expansiver Geldpolitik dürfte im weiteren Verlauf auch die bisher zögerliche Investitionstätigkeit an die kräftigere Entwicklung des Konsums anknüpfen. Hingegen ist in vielen Schwellenländern aufgrund der verhaltenen binnen- und außenwirtschaftlichen Entwicklung das Expansionstempo gedämpfter. Alles in allem dürfte sich das Wachstum der Weltwirtschaft beschleunigen und im kommenden Jahr bei knapp vier Prozent liegen, nach etwa drei Prozent im laufenden Jahr. In Deutschland war die konjunkturelle Dynamik im zweiten Quartal kräftig; diese Entwicklung war aber durch Nachholeffekte in der Bauwirtschaft infolge des strengen Winters überzeichnet. Im dritten Quartal dürfte das Wachstum etwas schwächer ausfallen, denn die Produktion in der Industrie wird nur zögerlich ausgeweitet, zuletzt war sie sogar rückläufig. Die Auftragseingänge lassen weitere, wenngleich nur moderate Zuwächse erwarten. Die gute und sich weiter aufhellende Stimmung in den Unternehmen des verarbeitenden Gewerbes spricht dafür, dass die Produktion im weiteren Verlauf anziehen wird. Die Lage auf dem Arbeitsmarkt ist nach wie vor gut und der Beschäftigungsaufbau setzt sich - wenn auch in etwas abgeschwächtem Tempo fort. Die zunehmende Zahl an Arbeitnehmern spiegelt sich allerdings nicht in einem entsprechenden Rückgang bei der Zahl der Arbeitslosen wider; stattdessen profitiert der Arbeitsmarkt in Deutschland auch im kommenden Jahr von Wanderungsgewinnen. Auch die Arbeitslosenquote verharrt in diesem und im nächsten Jahr bei knapp sieben Prozent. Die Lohnentwicklung wird etwas schwächer als in den vergangenen zwei Jahren, aber weiterhin kräftig sein. In einem Umfeld moderater Teuerung - die Inflationsrate dürfte in diesem Jahr bei 1,6 Prozent und im kommenden bei 1,9 Prozent liegen - wird der private Konsum die wirtschaftliche Entwicklung merklich antreiben. Dies lässt auch die Investitionen nach und nach zunehmen, die zudem durch die sich im Zuge der weltwirtschaftlichen Erholung belebenden deutschen Exporte gestützt werden. Aufgrund der binnenwirtschaftlichen Entwicklung legen die Importe allerdings etwas stärker zu, so dass der Außenhandel per Saldo das Wachstum leicht dämpft. Wie bereits im Jahr 2012 werden die öffentlichen Haushalte auch im Prognosezeitraum mit einem Überschuss abschließen; in Relation zum nominalen Bruttoinlandsprodukt liegt er in diesem Jahr bei 0,2 und im kommenden Jahr bei 0,3 Prozent. Die günstige Entwicklung der öffentlichen Finanzen eröffnet Spielräume, die nun entschieden genutzt werden sollten, um das potentielle Wachstum der deutschen Wirtschaft zu erhöhen. So besteht in Deutschland mittlerweile erheblicher Nachholbedarf bei den öffentlichen Investitionen, allein um die Substanz zu erhalten. Gerade weil die Finanzlage der Kommunen sich zusehends verbessert, ist jetzt ein guter Zeitpunkt für eine Stärkung der wirtschaftspolitischen Aktivitäten in diesem Bereich.The German economy is following a moderate upward trend. At 0.7 per cent, growth in the second quarter was strong compared to the first quarter, but this development was overstated by special effects. In the course of the next quarters production accelerates. In the coming year, growth will reach 1.7 per cent. After a weak start into the year, the global economy picked up somewhat in the second quarter. Overall, the momentum has shifted towards industrialized countries where, despite limited scope for fiscal policy to stimulate the economy, low inflation rates and the improving or at least stabilizing labor market situation are fostering consumption. As a result of declining uncertainty and still expansionary global monetary policy, previously subdued investment activity builds on the upward movement of consumption and the thus stimulated revival of world trade. On the opposite, the pace of expansion in many emerging countries remains subdued due to both weak domestic and foreign demand. Altogether, the world economy continues to recover due to the impetus from industrial countries and is expected to grow at about four per cent in the coming year, after three per cent in 2013. Growth in Germany was strong in the second quarter, but this development was boosted by a catch-up effect in the construction industry due to the severe winter. In the current quarter, growth is expected to be slightly weaker since industrial production is growing only at a moderate pace and has even fallen recently. However, new orders indicate a mild upward movement of the economy thereafter. In addition, the continued positive sentiment in the manufacturing sector signals an increase in production. The labor market conditions are still favorable and employment growth is expected to continue - albeit at a slightly lower rate. Nevertheless, the increase in employment is not reflected in a corresponding decrease in persons unemployed; instead, the German labor market is profiting from positive net migration. Hence, this year and next year, the unemployment rate remains at seven per cent. Wages will rise less than in the previous two years, but still at a tangible rate. Price increases will remain moderate. An inflation rate of 1.6 per cent is expected for this year and of 1.9 per cent for the coming year. Against this backdrop, private consumption continues to be a main pillar of the expansion. The recovering global economy will lead to rising exports and will subsequently encourage companies to invest more dynamically. However, imports - driven by robust domestic demand - will increase by more than exports such that a negative current account slightly curbs growth. The public sector is expected to have a surplus in the forecast period; it amounts to 0.2 per cent in relation to nominal GDP this year and to 0.3 per cent next year. Economic policy should use the existing scope decisively to enhance the growth potential of the economy. By now, there exists considerably backlog in investment, even to maintain the current level of the capital stock. Given the improving fiscal balances of the municipals in particular, it is time for them to boost public investment

Sommergrundlinien 2013

Die deutsche Wirtschaft wird wegen des schwachen Winterhalbjahres in diesem Jahr nur um 0,4 Prozent wachsen. Allerdings dürfte die Schwächephase wohl bereits überwunden sein; im kommenden Jahr wird das Wachstum mit 1,8 Prozent kräftig sein. Die Weltkonjunktur ist wieder auf einen Aufwärtstrend eingeschwenkt; die wirtschaftliche Entwicklung in vielen Schwellenländern, aber auch in den USA und Japan hat zuletzt etwas Fahrt aufgenommen, vielerorts unterstützt durch eine expansive Wirtschaftspolitik. Darüber hinaus haben die zur Stabilisierung der Finanzmärkte im Euroraum geschaffenen Instrumente einen spürbaren Rückgang der Unsicherheit mit sich gebracht. Die Arbeitslosigkeit ist aber nach wie vor hoch und die Verschuldung - öffentlich wie auch privat - muss weiter deutlich zurückgeführt werden. Im Euroraum wird die Wirtschaft zunächst weiter schrumpfen, allerdings bei Weitem nicht mehr so stark. Vielerorts zeichnet sich eine Ausweitung der Exporte ab, die zum Teil auch auf eine Verbesserung der preislichen Wettbewerbsfähigkeit zurückzuführen ist. In vielen Krisenländern ist der Abbau von Überkapazitäten merklich vorangeschritten und damit verbundene dämpfende Effekte fallen nach und nach weg. Ab dem Jahreswechsel 2013/14 dürfte die Wirtschaft auch in den Krisenländern wachsen.Due to a weak winter half-year, the German economy will only grow by 0.4 percent in 2013. However, the economic slowdown seems to be coming to an end now; growth in 2014 is expected to be above average at 1.8 percent. The global economy is experiencing an upswing again; growth in many emerging markets as well as in the US and Japan has recently gained momentum, facilitated in many places by an expansive economic policy. Moreover, the mechanisms created to stabilize financial markets in the euro area have noticeably alleviated uncertainty. However, high unemployment and the need to reduce the high level of debt - public as well as private - remain a problem. The euro area economy will continue to shrink for the time being, but the extent of the economic slowdown has already diminished significantly. A rise in exports is on the horizon in many places, which can be partly attributed to improved competitiveness. In many crisis countries, there has been considerable progress in reducing excess capacities, resulting in dampening effects being increasingly eliminated. By the beginning of 2014, positive growth rates can be expected again in the crisis countries, too