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When confining pressure is low or absent, extensional fractures are typical, with fractures occurring on unloaded planes in rock. These “paradox” fractures can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. But this criterion makes unrealistic strength predictions in biaxial compression and tension. A new extension strain criterion overcomes this limitation by adding a weighted principal shear component. The weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting failure modes, which are unexpected in the understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak P. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
FEM shakedown analysis of structures under random strength with chance constrained programming
(2022)
Direct methods, comprising limit and shakedown analysis, are a branch of computational mechanics. They play a significant role in mechanical and civil engineering design. The concept of direct methods aims to determine the ultimate load carrying capacity of structures beyond the elastic range. In practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and constraints. If strength and loading are random quantities, the shakedown analysis can be formulated as stochastic programming problem. In this paper, a method called chance constrained programming is presented, which is an effective method of stochastic programming to solve shakedown analysis problems under random conditions of strength. In this study, the loading is deterministic, and the strength is a normally or lognormally distributed variable.
Retinal vessels are similar to cerebral vessels in their structure and function. Moderately low oscillation frequencies of around 0.1 Hz have been reported as the driving force for paravascular drainage in gray matter in mice and are known as the frequencies of lymphatic vessels in humans. We aimed to elucidate whether retinal vessel oscillations are altered in Alzheimer's disease (AD) at the stage of dementia or mild cognitive impairment (MCI). Seventeen patients with mild-to-moderate dementia due to AD (ADD); 23 patients with MCI due to AD, and 18 cognitively healthy controls (HC) were examined using Dynamic Retinal Vessel Analyzer. Oscillatory temporal changes of retinal vessel diameters were evaluated using mathematical signal analysis. Especially at moderately low frequencies around 0.1 Hz, arterial oscillations in ADD and MCI significantly prevailed over HC oscillations and correlated with disease severity. The pronounced retinal arterial vasomotion at moderately low frequencies in the ADD and MCI groups would be compatible with the view of a compensatory upregulation of paravascular drainage in AD and strengthen the amyloid clearance hypothesis.
Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element-based formulation of ES-FEM and FS-FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element-based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS-FEM applications found in the literature. Shape functions for non-simplex 3D elements are proposed in order to apply FS-FEM to any standard finite element.
The mechanical behavior of the large intestine beyond the ultimate stress has never been investigated. Stretching beyond the ultimate stress may drastically impair the tissue microstructure, which consequently weakens its healthy state functions of absorption, temporary storage, and transportation for defecation. Due to closely similar microstructure and function with humans, biaxial tensile experiments on the porcine large intestine have been performed in this study. In this paper, we report hyperelastic characterization of the large intestine based on experiments in 102 specimens. We also report the theoretical analysis of the experimental results, including an exponential damage evolution function. The fracture energies and the threshold stresses are set as damage material parameters for the longitudinal muscular, the circumferential muscular and the submucosal collagenous layers. A biaxial tensile simulation of a linear brick element has been performed to validate the applicability of the estimated material parameters. The model successfully simulates the biomechanical response of the large intestine under physiological and non-physiological loads.
Biocompatibility, flexibility and durability make polydimethylsiloxane (PDMS) membranes top candidates in biomedical applications. CellDrum technology uses large area, <10 µm thin membranes as mechanical stress sensors of thin cell layers. For this to be successful, the properties (thickness, temperature, dust, wrinkles, etc.) must be precisely controlled. The following parameters of membrane fabrication by means of the Floating-on-Water (FoW) method were investigated: (1) PDMS volume, (2) ambient temperature, (3) membrane deflection and (4) membrane mechanical compliance. Significant differences were found between all PDMS volumes and thicknesses tested (p < 0.01). They also differed from the calculated values. At room temperatures between 22 and 26 °C, significant differences in average thickness values were found, as well as a continuous decrease in thicknesses within a 4 °C temperature elevation. No correlation was found between the membrane thickness groups (between 3–4 µm) in terms of deflection and compliance. We successfully present a fabrication method for thin bio-functionalized membranes in conjunction with a four-step quality management system. The results highlight the importance of tight regulation of production parameters through quality control. The use of membranes described here could also become the basis for material testing on thin, viscous layers such as polymers, dyes and adhesives, which goes far beyond biological applications.
Following the recent successful landings and occasional re-awakenings of PHILAE, the lander carried aboard ROSETTA to comet 67P/Churyumov-Gerasimenko, and the launch of the Mobile Asteroid Surface Scout, MASCOT, aboard the HAYABUSA2 space probe to asteroid (162173) Ryugu we present an overview of the characteristics and peculiarities of small spacecraft missions to small solar system bodies (SSSB). Their main purpose is planetary science which is transitioning from a ‘pure’ science of observation of the distant to one also supporting in-situ applications relevant for life on Earth. Here we focus on missions at the interface of SSSB science and planetary defence applications. We provide a brief overview of small spacecraft SSSB missions and on this background present recent missions, projects and related studies at the German Aerospace Center, DLR, that contribute to the worldwide planetary defence community. These range from Earth orbit technology demonstrators to active science missions in interplanetary space. We provide a summary of experience from recently flown missions with DLR participation as well as a number of studies. These include PHILAE, the lander of ESA’s ROSETTA comet rendezvous mission now on the surface of comet 67P/Churyumov-Gerasimenko, and the Mobile Asteroid Surface Scout, MASCOT, now in cruise to the ~1 km diameter C-type near-Earth asteroid (162173) Ryugu aboard the Japanese sample-return probe HAYABUSA2. We introduce the differences between the conventional methods employed in the design, integration and testing of large spacecraft and the new approaches developed by small spacecraft projects. We expect that the practical experience that can be gained from projects on extremely compressed timelines or with high-intensity operation phases on a newly explored small solar system body can contribute significantly to the study, preparation and realization of future planetary defence related missions. One is AIDA (Asteroid Impact & Deflection Assessment), a joint effort of ESA, JHU/APL, NASA, OCA and DLR, combining JHU/APL’s DART (Double Asteroid Redirection Test) and ESA’s AIM (Asteroid Impact Monitor) spacecraft in a mission towards near-Earth binary asteroid system (65803) Didymos. DLR is currently applying MASCOT heritage and lessons learned to the design of MASCOT2, a lander for the AIM mission to support a bistatic low frequency radar experiment with PHILAE/ROSETTA CONSERT heritage to explore the inner structure of Didymoon which is the designated impact target for DART.
We present the novel concept of a combined drilling and melting probe for subsurface ice research. This probe, named “IceMole”, is currently developed, built, and tested at the FH Aachen University of Applied Sciences’ Astronautical Laboratory. Here, we describe its first prototype design and report the results of its field tests on the Swiss Morteratsch glacier. Although the IceMole design is currently adapted to terrestrial glaciers and ice shields, it may later be modified for the subsurface in-situ investigation of extraterrestrial ice, e.g., on Mars, Europa, and Enceladus. If life exists on those bodies, it may be present in the ice (as life can also be found in the deep ice of Earth).
Interplanetary trajectories for low-thrust spacecraft are often characterized by multiple revolutions around the sun. Unfortunately, the convergence of traditional trajectory optimizers that are based on numerical optimal control methods depends strongly on an adequate initial guess for the control function (if a direct method is used) or for the starting values of the adjoint vector (if an indirect method is used). Especially when many revolutions around the sun are re-
quired, trajectory optimization becomes a very difficult and time-consuming task that involves a lot of experience and expert knowledge in astrodynamics and optimal control theory, because an adequate initial guess is extremely hard to find. Evolutionary neurocontrol (ENC) was proposed as a smart method for low-thrust trajectory optimization that fuses artificial neural networks and evolutionary algorithms to so-called evolutionary neurocontrollers (ENCs) [1]. Inspired by natural archetypes, ENC attacks the trajectoryoptimization problem from the perspective of artificial intelligence and machine learning, a perspective that is quite different from that of optimal control theory. Within the context of ENC, a trajectory is regarded as the result of a spacecraft steering strategy that maps permanently the actual spacecraft state and the actual target state onto the actual spacecraft control vector. This way, the problem of searching the optimal spacecraft trajectory is equivalent to the problem of searching (or "learning") the optimal spacecraft steering strategy. An artificial neural network is used to implement such a spacecraft steering strategy. It can be regarded as a parameterized function (the network function) that is defined by the internal network parameters. Therefore, each distinct set of network parameters defines a different network function and thus a different steering strategy. The problem of searching the optimal steering strategy is now equivalent to the problem of searching the optimal set of network parameters. Evolutionary algorithms that work on a population of (artificial) chromosomes are used to find the optimal network parameters, because the parameters can be easily mapped onto a chromosome. The trajectory optimization problem is solved when the optimal chromosome is found. A comparison of solar sail trajectories that have been published by others [2, 3, 4, 5] with ENC-trajectories has shown that ENCs can be successfully applied for near-globally optimal spacecraft control [1, 6] and that they are able to find trajectories that are closer to the (unknown) global optimum, because they explore the trajectory search space more exhaustively than a human expert can do. The obtained trajectories are fairly accurate with respect to the terminal constraint. If a more accurate trajectory is required, the ENC-solution can be used as an initial guess for a local trajectory optimization method. Using ENC, low-thrust trajectories can be optimized without an initial guess and without expert attendance.
Here, new results for nuclear electric spacecraft and for solar sail spacecraft are presented and it will be shown that ENCs find very good trajectories even for very difficult problems. Trajectory optimization results are presented for 1. NASA's Solar Polar Imager Mission, a mission to attain a highly inclined close solar orbit with a solar sail [7] 2. a mission to de ect asteroid Apophis with a solar sail from a retrograde orbit with a very-high velocity impact [8, 9] 3. JPL's \2nd Global Trajectory Optimization Competition", a grand tour to visit four asteroids from different classes with a NEP spacecraft
A laser-enhanced solar sail is a solar sail that is not solely propelled by solar radiation but additionally by a laser beam that illuminates the sail. This way, the propulsive acceleration of the sail results from the combined action of the solar and the laser radiation pressure onto the sail. The potential source of the laser beam is a laser satellite that coverts solar power (in the inner solar system) or nuclear power (in the outer solar system) into laser power. Such a laser satellite (or many of them) can orbit anywhere in the solar system and its optimal orbit (or their optimal orbits) for a given mission is a subject for future research. This contribution provides the model for an ideal laser-enhanced solar sail and investigates how a laser can enhance the thrusting capability of such a sail. The term ”ideal” means that the solar sail is assumed to be perfectly reflecting and that the laser beam is assumed to have a constant areal power density over the whole sail area. Since a laser beam has a limited divergence, it can provide radiation pressure at much larger solar distances and increase the radiation pressure force into the desired direction. Therefore, laser-enhanced solar sails may make missions feasible, that would otherwise have prohibitively long flight times, e.g. rendezvous missions in the outer solar system. This contribution will also analyze exemplary mission scenarios and present optimial trajectories without laying too much emphasis on the design and operations of the laser satellites. If the mission studies conclude that laser-enhanced solar sails would have advantages with respect to ”traditional” solar sails, a detailed study of the laser satellites and the whole system architecture would be the second next step
Physical interaction with small solar system bodies (SSSB) is key for in-situ resource utilization (ISRU). The design of mining missions requires good understanding of SSSB properties, including composition, surface and interior structure, and thermal environment. But as the saying goes "If you've seen one asteroid, you've seen one Asteroid": Although some patterns may begin to appear, a stable and reliable scheme of SSSB classification still has to be evolved. Identified commonalities would enable generic ISRU technology and spacecraft design approaches with a high degree of re-use. Strategic approaches require much broader in-depth characterization of the SSSB populations of interest to the ISRU community. The DLR-ESTEC GOSSAMER Roadmap Science Working Groups identified target-flexible Multiple Near-Earth asteroid (NEA) Rendezvous (MNR) as one of the missions only feasible with solar sail propulsion, showed the ability to access any inclination and a wide range of heliocentric distances as well as continuous operation close to Earth's orbit where low delta-v objects reside.
The search for life on Mars and in the Solar System - strategies, logistics and infrastructures
(2018)
The question "Are we alone in the Universe?" is perhaps the most fundamental one that affects mankind. How can we address the search for life in our Solar System? Mars, Enceladus and Europa are the focus of the search for life outside the terrestrial biosphere. While it is more likely to find remnants of life (fossils of extinct life) on Mars because of its past short time window of the surface habitability, it is probably more likely to find traces of extant life on the icy moons and ocean worlds of Jupiter and Saturn. Nevertheless, even on Mars there could still be a chance to find extant life in niches near to the surface or in just discovered subglacial lakes beneath the South Pole ice cap. Here, the different approaches for the detection of traces of life in the form of biosignatures including pre-biotic molecules will be presented. We will outline the required infrastructure for this enterprise and give examples of future mission concepts to investigate the presence of life on other planets and moons. Finally, we will provide suggestions on methods, techniques, operations and strategies for preparation and realization of future life detection missions.
For now, the Planetary Defense Conference Exercise 2021's incoming fictitious(!), asteroid, 2021 PDC, seems headed for impact on October 20th, 2021, exactly 6 months after its discovery. Today (April 26th, 2021), the impact probability is 5%, in a steep rise from 1 in 2500 upon discovery six days ago. We all know how these things end. Or do we? Unless somebody kicked off another headline-grabbing media scare or wants to keep civil defense very idle very soon, chances are that it will hit (note: this is an exercise!). Taking stock, it is barely 6 months to impact, a steadily rising likelihood that it will actually happen, and a huge uncertainty of possible impact energies: First estimates range from 1.2 MtTNT to 13 GtTNT, and this is not even the worst-worst case: a 700 m diameter massive NiFe asteroid (covered by a thin veneer of Ryugu-black rubble to match size and brightness), would come in at 70 GtTNT. In down to Earth terms, this could be all between smashing fireworks over some remote area of the globe and a 7.5 km crater downtown somewhere. Considering the deliberate and sedate ways of development of interplanetary missions it seems we can only stand and stare until we know well enough where to tell people to pack up all that can be moved at all and save themselves. But then, it could just as well be a smaller bright rock. The best estimate is 120 m diameter from optical observation alone, by 13% standard albedo. NASA's upcoming DART mission to binary asteroid (65803) Didymos is designed to hit such a small target, its moonlet Dimorphos. The Deep Impact mission's impactor in 2005 successfully guided itself to the brightest spot on comet 9P/Tempel 1, a relatively small feature on the 6 km nucleus. And 'space' has changed: By the end of this decade, one satellite communication network plans to have launched over 11000 satellites at a pace of 60 per launch every other week. This level of series production is comparable in numbers to the most prolific commercial airliners. Launch vehicle production has not simply increased correspondingly – they can be reused, although in a trade for performance. Optical and radio astronomy as well as planetary radar have made great strides in the past decade, and so has the design and production capability for everyday 'high-tech' products. 60 years ago, spaceflight was invented from scratch within two years, and there are recent examples of fast-paced space projects as well as a drive towards 'responsive space'. It seems it is not quite yet time to abandon all hope. We present what could be done and what is too close to call once thinking is shoved out of the box by a clear and present danger, to show where a little more preparedness or routine would come in handy – or become decisive. And if we fail, let's stand and stare safely and well instrumented anywhere on Earth together in the greatest adventure of science.
Low-thrust space propulsion systems enable flexible high-energy deep space missions, but the design and optimization of the interplanetary transfer trajectory is usually difficult. It involves much experience and expert knowledge because the convergence behavior of traditional local trajectory optimization methods depends strongly on an adequate initial guess. Within this extended abstract, evolutionary neurocontrol, a method that fuses artificial neural networks and evolutionary algorithms, is proposed as a smart global method for low-thrust trajectory optimization. It does not require an initial guess. The implementation of evolutionary neurocontrol is detailed and its performance is shown for an exemplary mission.
Innovative interplanetary deep space missions, like a main belt asteroid sample
return mission, require ever larger velocity increments (∆V s) and thus ever
more demanding propulsion capabilities. Providing much larger exhaust velocities than chemical high-thrust systems, electric low-thrust space-propulsion
systems can significantly enhance or even enable such high-energy missions. In
1995, a European-Russian Joint Study Group (JSG) presented a study report
on “Advanced Interplanetary Missions Using Nuclear-Electric Propulsion”
(NEP). One of the investigated reference missions was a sample return (SR)
from the main belt asteroid (19) Fortuna. The envisaged nuclear power plant,
Topaz-25, however, could not be realized and also the worldwide developments
in space reactor hardware stalled. In this paper, we investigate, whether such
a mission is also feasible using a solar electric propulsion (SEP) system and
compare our SEP results to corresponding NEP results.
This paper describes the results and methods used during the 8th Global Trajectory Optimization Competition (GTOC) of the DLR team. Trajectory optimization is crucial for most of the space missions and usually can be formulated as a global optimization problem. A lot of research has been done to different type of mission problems. The most demanding ones are low thrust transfers with e.g. gravity assist sequences. In that case the optimal control problem is combined with an integer problem. In most of the GTOCs we apply a filtering of the problem based on domain knowledge.
Recently, in his vision for space exploration, US president Bush announced to extend human presence across the solar system, starting with a human return to the Moon as early as 2015 in preparation for human exploration of Mars and other destinations. In Europe, an exploration program, termed AURORA, was established by ESA in 2001 – funded on a voluntary basis by ESA member states – with a clear focus on Mars and the ultimate goal of landing humans on Mars around 2030 in international cooperation. In 2003, a Human Spaceflight Vision Group was appointed by ESA with the task to develop a vision for the role of human spaceflight during the next quarter of the century. The resulting vision focused on a European-led lunar exploration initiative as part of a multi-decade, international effort to strengthen European identity and economy. After a review of the situation in Europe concerning space exploration, the paper outlines an approach for a consistent positioning of exploration within the existing European space programs, identifies destinations, and develops corresponding scenarios for an integrated strategy, starting with robotic missions to the Moon, Mars, and near-Earth asteroids. The interests of the European planetary in-situ science community, which recently met at DLR Cologne, are considered. Potential robotic lunar missions comprise polar landings to search for frozen volatiles and a sample return. For Mars, the implementation of a modest robotic landing mission in 2009 to demonstrate the capability for landing and prepare more ambitious and complex missions is discussed. For near-Earth asteroid exploration, a low-cost in-situ technology demonstration mission could yield important results. All proposed scenarios offer excellent science and could therefore create synergies between ESA’s mandatory and optional programs in the area of planetary science and exploration. The paper intents to stimulate the European discussion on space exploration and reflects the personal view of the authors.
Under DLR-contract, Giessen University and DLR Cologne are studying solar-electric propulsion missions (SEP) to the outer regions of the solar system. The most challenging reference mission concerns the transport of a 1.35-tons chemical lander spacecraft into an 80-RJ circular orbit around Jupiter, which would enable to place a 375 kg lander with 50 kg of scientific instruments on the surface of the icy moon "Europa". Thorough analyses show that the best solution in terms of SEP launch mass times thrusting time would be a two-stage EP module and a triple-junction solar array with concentrators which would be deployed step by step. Mission performance optimizations suggest to propel the spacecraft in the first EP stage by 6 gridded ion thrusters, running at 4.0 kV of beam voltage, which would save launch mass, and in the second stage by 4 thrusters with 1.25 to 1.5 kV of positive high voltage saving thrusting time. In this way, the launch mass of the spacecraft would be kept within 5.3 tons. Without a launcher's C3 and interplanetary gravity assists, Jupiter might be reached within about 4 yrs. The spiraling-down into the parking orbit would need another 1.8 yrs. This "large mission" can be scaled down to a smaller one, e.g., by halving all masses, the solar array power, and the number of thrusters. Due to their reliability, long lifetime and easy control, RIT-22 engines have been chosen for mission analysis. Based on precise tests, the thruster performance has been modeled.
Physical interaction with small solar system bodies (SSSB) is the next step in planetary science, planetary in-situ resource utilization (ISRU), and planetary defense (PD). It requires a broader understanding of the surface properties of the target objects, with particular interest focused on those near Earth. Knowledge of composition, multi-scale surface structure, thermal response, and interior structure is required to design, validate and operate missions addressing these three fields. The current level of understanding is occasionally simplified into the phrase, ”If you’ve seen one asteroid, you’ve seen one asteroid”, meaning that the in-situ characterization of SSSBs has yet to cross the threshold towards a robust and stable scheme of classification. This would enable generic features in spacecraft design, particularly for ISRU and science missions. Currently, it is necessary to characterize any potential target object sufficiently by a dedicated pre-cursor mission to design the mission which then interacts with the object in a complex fashion. To open up strategic approaches, much broader in-depth characterization of potential target objects would be highly desirable. In SSSB science missions, MASCOT-like nano-landers and instrument carriers which integrate at the instrument level to their mothership have met interest. By its size, MASCOT is compatible with small interplanetary missions. The DLR-ESTEC Gossamer Roadmap Science Working Groups‘ studies identified Multiple Near-Earth asteroid (NEA) Rendezvous (MNR) as one of the space science missions only feasible with solar sail propulsion. The Solar Polar Orbiter (SPO) study showed the ability to access any inclination, theDisplaced-L1 (DL1) mission operates close to Earth, where objects of interest to PD and for ISRU reside. Other studies outline the unique capability of solar sails to provide access to all SSSB, at least within the orbit of Jupiter, and significant progress has been made to explore the performance envelope of near-term solar sails for MNR. However, it is difficult for
sailcraft to interact physically with a SSSB. We expand and extend the philosophy of the recently qualified DLR Gossamer solar sail deployment technology using efficient multiple sub-spacecraft integration to also include landers for one-way in-situ investigations and sample-return missions by synergetic integration and operation of sail and lander. The MASCOT design concept and its characteristic features have created an ideal counterpart for thisand has already been adapted to the needs of the AIM spacecraft, former part of the NASA-ESA AIDA missionDesigning the 69th International Astronautical Congress (IAC), Bremen, Germany, 1-5 October 2018. IAC-18-F1.2.3 Page 2 of 17 combined spacecraft for piggy-back launch accommodation enables low-cost massively parallel access to the NEA population.