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Dieses Lehr- und Übungsbuch vermittelt auf anschauliche Weise die Methoden der Mehrkörpersimulation und verdeutlicht deren Vor- und Nachteile bei der praktischen Anwendung anhand konkreter Beispiele. Die einzelnen Methoden werden durch Matlab-Skripte und -Funktionen verdeutlicht, wobei die Modellbildung, die mathematische Beschreibung und die numerische Simulation von Systemen starrer Körper die Schwerpunkte bilden. Die vorliegende Auflage wurde unter anderem um Matlab-Live-Skripte erweitert, welche kleine Animationen zur Veranschaulichung der Dynamik der Probleme enthalten. Die Lösungen zu den Übungsbeispielen und die integrierten Matlab-Skripte sowie weitere Beispiele und Anwendungen stehen über QR-Codes zum Download zur Verfügung und ermöglichen dadurch auch ein effizientes Selbststudium.
In the context of production and factory planning, the expansion of the factory must already be taken into account during initial planning. This results in an increase in planning complexity, as the involved planners have to know the expansion stages of the factory in the different time periods and have to evaluate concept modifications across all time periods. This paper presents an idea for a planning tool, which takes expansion stages into consideration. The data model contains all relevant information to generate a simulation model of the factory in an almost automated way. The aim is to enable factory planners to quickly investigate concept changes with the help of simulation, for example, to identify bottlenecks.
To evaluate the performance of a ropeway in an urban environment, simulations of the dynamic passenger transport characteristics are required. Therefore, a modular simulation model for urban ropeway networks was developed, which can be flexibly adapted to any city and passenger volume. This simulation model was used to analyze the ropeway network concept of the German city Regensburg and to determine the expected operating conditions. The passenger volume, different types of persons, their occurrence probability and their destination distribution is depending on the location and daytime and can be defined for each individual station. In an initial analysis, the number of passengers currently occurring in bus traffic were projected onto the ropeway network. To enable climate-friendly and efficient operation, different strategies were developed to significantly reduce the number of gondolas. The best fitting strategies resulted in significant cost savings while passenger comfort, as represented by queue time, remained unchanged.
Simulation Based Approach for Reconfiguration and Ramp up Scenario Analysis in Factory Planning
(2022)
Structural changes in production entail a potential economic risk for manufacturing companies. It is necessary to identify a suitable strategy for the reconfiguration process and to continue to meet the demand during the change in the factory structure and ramp-up phase. A simulation offers the possibility to analyze different ramp-up scenarios for the factory structure and to select a suitable concept for the reconfiguration process. A discrete event simulation approach is presented that can be used to evaluate variants of structural changes and serves as a basis for deciding on a reconfiguration strategy. This approach is demonstrated using a specific production step of a plant producing hydrogen electrolyzers, the results and generalized conclusions are discussed.
This paper briefly presents the challenges for order control and release of multi-zone order picking systems. On the one hand, the order control must ensure that all orders are processed on time, and on the other hand, the space requirements (buffer) and the utilisation of the zones must be considered.
Within the framework of a case study, different strategies for order release were developed. The paper shortly describes the ideas of the strategies and presents results of a case-based simulative evaluation of the strategies. The findings of the simulation study are the basis for the development of a digital twin for the operational control of multi-zone picking systems.
Der Digitale Zwilling (DZ) ist ein wichtiger Bestandteil der Industrie 4.0 und ermöglicht Anwendungen wie Predictive Maintenance, virtuelles Prototyping oder die Steuerung von Produktions- und Logistikprozessen. Herausforderungen bei der Entwicklung des Digitalen Zwillings entstehen durch fehlende Struktur und Standards. Mit diesem Beitrag soll ein Vorgehensmodell für die Erstellung eines Digitalen Zwillings im Bereich der Produktion und Logistik aufgezeigt werden. Das Vorgehensmodell hilft bei der Einordnung, für welche Anwendungsfälle ein Digitaler Zwilling entwickelt werden kann, welche Schritte bei einer Umsetzung erfolgen müssen, und gibt einen Überblick über die Voraussetzungen und Komplexität bei der Entwicklung. Das zentrale Element bildet dabei die zielgerichtete Aufbereitung und Analyse der zugrunde liegenden Daten mittels des in der Industrie etablierten Vorgehensmodell CRISP-DM.
Regarding the prevention of injuries and rehabilitation of the human hand, musculoskeletal simulations using an inverse dynamics approach allow for insights of the muscle recruitment and thus acting forces on the hand. Currently, several hand models from various research groups are in use, which are mainly validated by the comparison of numerical and anatomical moment arms. In contrast to this validation and model-building technique by cadaver studies, the aim of this study is to further validate a recently published hand model [1] by analyzing numerically calculated muscle activities in comparison to experimentally measured electromyographical signals of the muscles. Therefore, the electromyographical signals of 10 hand muscles of five test subjects performing seven different hand movements were measured. The kinematics of these tasks were used as input for the hand model, and the numerical muscle activities were computed. To analyze the relationship between simulated and measured activities, the time difference of the muscle on- and off-set points was calculated, which resulted in a mean on- and off-set time difference of 0.58 s between the experimental data and the model. The largest differences were detected for movements that mainly addressed the wrist. One major issue comparing simulated and measured muscle activities of the hand is cross-talk. Nevertheless, the results show that the hand model fits the experiment quite accurately despite some limitations and is a further step toward patient-specific modeling of the upper extremity.
Outputs of musculoskeletal models should be considered probabilistic rather than deterministic as they are affected by inaccuracies and estimations associated with the development of the model. One of these uncertainties being critical for modeling arises from the determination of the muscles' line of action and the physiological cross-sectional area. Therefore, the aim of this study was to evaluate the outcome sensitivity of model predictions from a musculoskeletal hand model in comparison to the uncertainty of these input parameters. For this purpose, the kinematics and muscle activities of different hand movements (abduction of the fingers, abduction of the thumb, and flexion of the thumb) were recorded. One thousand simulations were calculated for each movement using the Latin hypercube sampling method with a corresponding variation of the muscle origin/insertion points and the cross-sectional area. Comparing the standard hand to simulations incorporating uncertainties of input parameters shows no major deviations in on- and off-set time point of muscle activities. About 60% of simulations are located within a ± 30% interval around the standard model concerning joint reaction forces. The comparison with the variation of the input data leads to the conclusion that the standard hand model is able to provide not over-scattered outcomes and, therefore, can be considered relatively stable. These results are of practical importance to the personalization of a musculoskeletal model with subject-specific bone geometries and hence changed muscle line of action.
The Sandia Fracture Challenges provide a forum for the mechanics community to assess its ability to predict ductile fracture through a blind, round-robin format where mechanicians are challenged to predict the deformation and failure of an arbitrary geometry given experimental calibration data. The Third Challenge (SFC3) required participants to predict fracture in an additively manufactured (AM) 316L stainless steel bar containing through holes and internal cavities that could not have been conventionally machined. The volunteer participants were provided extensive data including tension and notched tensions tests of 316L specimens built on the same build-plate as the Challenge geometry, micro-CT scans of the Challenge specimens and geometric measurements of the feature based on the scans, electron backscatter diffraction (EBSD) information on grain texture, and post-test fractography of the calibration specimens. Surprisingly, the global behavior of the SFC3 geometry specimens had modest variability despite being made of AM metal, with all of the SFC3 geometry specimens failing under the same failure mode. This is attributed to the large stress concentrations from the holes overwhelming the stochastic local influence of the AM voids and surface roughness. The teams were asked to predict a number of quantities of interest in the response based on global and local measures that were compared to experimental data, based partly on Digital Image Correlation (DIC) measurements of surface displacements and strains, including predictions of variability in the resulting fracture response, as the basis for assessment of the predictive capabilities of the modeling and simulation strategies. Twenty-one teams submitted predictions obtained from a variety of methods: the finite element method (FEM) or the mesh-free, peridynamic method; solvers with explicit time integration, implicit time integration, or quasi-statics; fracture methods including element deletion, peridynamics with bond damage, XFEM, damage (stiffness degradation), and adaptive remeshing. These predictions utilized many different material models: plasticity models including J2 plasticity or Hill yield with isotropic hardening, mixed Swift-Voce hardening, kinematic hardening, or custom hardening curves; fracture criteria including GTN model, Hosford-Coulomb, triaxiality-dependent strain, critical fracture energy, damage-based model, critical void volume fraction, and Johnson-Cook model; and damage evolution models including damage accumulation and evolution, crack band model, fracture energy, displacement value threshold, incremental stress triaxiality, Cocks-Ashby void growth, and void nucleation, growth, and coalescence. Teams used various combinations of calibration data from tensile specimens, the notched tensile specimens, and literature data. A detailed comparison of results based of these different methods is presented in this paper to suggest a set of best practices for modeling ductile fracture in situations like the SFC3 AM-material problem. All blind predictions identified the nominal crack path and initiation location correctly. The SFC3 participants generally fared better in their global predictions of deformation and failure than the participants in the previous Challenges, suggesting the relative maturity of the models used and adoption of best practices from previous Challenges. This paper provides detailed analyses of the results, including discussion of the utility of the provided data, challenges of the experimental-numerical comparison, defects in the AM material, and human factors.
The fracture propagation and arrest control for pipelines transporting rich natural gases and high vapor pressure liquids is based on the Battelle Two-Curve Model (BTCM). Distinct limitations of this model were demonstrated for past and modern steels and gas mixtures. These can be related to the insufficient description of individual physical processes and interactions between the pipe material and transported mixture during the running ductile fracture. In the past, fluid-structure interaction (FSI) models enabled a more sophisticated, coupled analysis of the failure scenario. To quantify their capability of describing the multi-physical processes, the FSI models need to be verified by experimental data from full-scale burst tests (FSBT). Therefore, this paper deals with the simulation of five FSBTs from the literature on API grade X65 pipes with different pipe geometries, mixtures and initial conditions. The FSI is modeled by the coupled Euler-Lagrange (CEL) method. The modified Mohr-Coulomb (MMC) model is implemented in the CEL framework to describe the deformation and ductile fracture in the X65/L450 pipes. 3D Euler equations are used to calculate the mixture decompression with the GERG-2008 equation of state defining the volumetric behavior of a CO2-rich mixture, CH4 and H2. The extended model considers the effect of soil backfill on the pipe deformation and inertia. The numerical predictions agree well with the experimental findings in terms of the crack propagation speed and arrest length underlining the capability of the developed numerical tool.
Thermo-mechanical simulation offers great opportunities to optimize welding processes of plastics. For realistic simulation, the temperature dependent mechanical properties need to be implemented from ambient temperature to temperatures above the flow temperature. Standard test methods are insufficient for characterization in the entire temperature range because close to the flow temperature the material is too soft for tensile tests and too stiff for rheometry. Therefore, an optimization strategy is developed, that determines unknown material parameters by testing in welding simulations. The unknown parameters are iteratively adjusted to minimize the mismatch between computed and measured set-paths. Thus, important process characteristics are calculated realistically, enabling the computer aided assessment of the weld quality.
Contact force path in total hip arthroplasty: effect of cup medialisation in a whole-body simulation
(2020)
Background:
Cup medialisation down to the true acetabular floor in total hip arthroplasty with a compensatory femoral offset increase seems to be mechanically advantageous for the abductor muscles due to the relocation of the lever arms (body weight lever arm decreased, abductor lever arm increased). However, limited information is currently available about the effects of this reconstruction type at the head cup interface, compared to an anatomical reconstruction that maintains the natural lever arms. Through a whole-body simulation analysis, we compared medialised versus anatomical reconstruction in THA to analyse the effects on: (1) contact force magnitude at the head cup interface; (2) contact force path in the cup; and (3) abductor activity.
Methods:
Musculoskeletal simulations were performed to calculate the above-mentioned parameters using inverse dynamics analysis. The differences between the virtually implanted THAs were calculated to compare the medialised versus anatomical reconstruction.
Results:
Cup medialisation with compensatory femoral offset increase led to: (1) a reduction in contact force magnitude at the head cup interface up to 6.6%; (2) a similar contact force path in the cup in terms of sliding distance and aspect ratio; and (3) a reduction in abductor activity up to 17.2% (gluteus medius).
Conclusions:
In our opinion, these potential biomechanical gains do not generally justify a fully medialised reconstruction, especially in younger patients that are more likely to undergo revision surgery in their lifetime. Cup medialisation should be performed until sufficient press fit and bony coverage of a properly sized and oriented cup can be achieved.
Based on electromyographic data and force measurements within the shoulder joint, there is an indication that muscle and resulting joint reaction forces keep increasing over an abduction angle of 90°. In inverse dynamics models, no single parameter could be attributed to simulate this force behaviour accordingly. The aim of this work is to implement kinematic, kinetic and muscle model modifications to an existing model of the shoulder (AnyBody™) and assess their single and combined effects during abduction up to 140° humeral elevation. The kinematics and the EMG activity of 10 test subjects were measured during humeral abduction. Six modifications were implemented in the model: alternative wrapping of the virtual deltoid muscle elements, utilization of a three element Hill model, strength scaling, motion capture driven clavicle elevation/protraction, translation of the GH joint in dependency of the acting forces and an alteration of the scapula/clavicle rhythm. From the six modifications, 16 different combinations were considered. Parameter combinations with the Hill model changed the resultant GH joint reaction force and led to an increase in force during abduction of the humerus above 90°. Under the premise of muscle activities and forces within the GH joint rising after 90° of humeral abduction, we propose that the Hill type muscle model is a crucial parameter for accurately modelling the shoulder. Furthermore, the outcome of this study indicates that the Hill model induces the co-contraction of the muscles of the shoulder without the need of an additional stability criterion for an inverse dynamics approach.
Common Schanz screw systems can be used to stabilize pelvic ring fractures. In order to accommodate for different patient’s requirements, implants can be placed in cranio-caudal direction into the os ilium (T1), or into the supraacetabular bone canal, and thus, in dorso-ventral direction (T2). Whereas both techniques are currently used, no data of the biomechanical behavior is available up to this date. The aim of this study is to analyze, whether T2 shows biomechanical advantages with respect to tissue and implant stresses due to the enlarged bone-implant interface. Forces acting on the pelvis were analyzed using motion capture data of a gait cycle obtained by the utilization of a musculoskeletal simulation program. A three dimensional finite element (FE) model of the pelvis with grayscale-based material properties was generated. The muscle and joint reaction forces at toe-off were applied to the FE model and instable pelvis fractures were implemented. The osteosynthesis systems were positioned within the model in order to enable the comparison between the two different surgical techniques. Stresses and displacements were analyzed for bone tissue, fracture zone and implant.
T2 lead to approx. 30% larger displacements in the fracture zone. Von-Mises stresses were larger for T2 in the implant (80 MPa vs. 227 MPa), whereas T1 leads to larger stresses in the bone tissue (200 MPa vs. 140 MPa).
Both implantation techniques showed a good biomechanical behavior. Differences could be found with respect to tissue strains and deformations in the fracture zone. If bone quality or fracture healing are of concern, T2 or T1 should be used, respectively. However, both techniques seem to be applicable for cases with no special requirements. Further analyses aim to investigate the behavior under cyclic loading.
Measuring functional outcome after total hip replacement with subject-specific hip joint loading
(2012)
Total hip replacement is an often-performed orthopedic surgical procedure; the amount of procedures undertaken will increase since our life expectancy is growing. In order to optimize function, hip biomechanics should be restored to as near normal as possible. The goal of this pilot study was to determine whether or not it is feasible to compute the vectorial hip reaction force pathways on the head of the prosthesis and the force angles relative to the cup of the prosthesis that occur during gait in total hip replacement patients, serving as an objective measurement of the functional outcome following hip replacement. A three-dimensional gait analysis, measuring ground reaction forces and kinematics, was performed. The data retrieved from the gait analysis was used as the input for the musculoskeletal model to compute vectorial joint reaction forces for data processing. To evaluate the position and orientation of the joint reaction forces, the force path, as well as the force angles for the operated and non-operated joint, has been calculated during the stance phase of the specific leg. The force path for subject 2 on the non-operated side is only located in the posterior-lateral quarter, as is the force path for subject 1. In contrast to this subject, the force path for subject 2 at the operated hip joint can be found only within the anterior quarter of the head of the implant, where it is nearly equally distributed in the medio-lateral half of the prosthesis head. The force-inclination angles on the cup of subject 1, with respect to the plane of the socket face, indicates that the force vector is mainly positioned in the same quadrant when compared with subject 2 (in a cup-fixed coordinate system). The force-anteversion angle behaves similarly to the force-inclination angle, even when the effects are not as pronounced. The proposed methods in this article are aiming to define two functional outcomes of total hip replacement that are related to wear and rim loading. It is accepted that wear is not only a function of time, but a function of use. Owing to the methods listed in this article, we are able to determine a) the applied force and b) the sliding distance (force pathway) in a subject-specific manner. The computed hip-reaction force angles and the distance to the rim cup are a measurement for cup or rim loading, and occurs in the so-called safe-zones. This method may well give us insight into the biomechanical situation during gait, after receiving total hip replacement, that we need to fully understand the mechanisms acting on a hip joint and to prove a possible increase of functional outcome after receiving total hip replacement.
The mechanical complications of osteosyntheses after hip fractures are previously investigated by mostly static or dynamic uniaxial loading test systems. However, the physiologic loading of the hip joint during a normal gait is a multiplanar, dynamic movement. Therefore, we constructed a system to test osteosyntheses for hip fractures under physiologic multiplanar loading representative of normal gait. To evaluate the testing system, 12 femora pairs were tested under 25,000 cycles with two standard osteosyntheses (Proximal Femoral Nail Antirotation/Gamma3 Nail). For angular movement, the varus collapse to cut out (∝CO) (∝CO=4.8°±2.1° for blade and ∝CO=7.8°±3.8° for screw) was the dominant failure mode, and only slight rotational angle shifts (∝Rot) (∝Rot=1.7°±0.4° for blade and ∝Rot=2.4°±0.3° for screw) of the femoral head around the implant axis were observed. Angular displacements in varus direction and rotation were higher in specimens reinforced with screws. Hence, the cut out model and the migration directions showed a distinction between helical blade and hip screw. However, there were no significant differences between the different implants. The new setup is able to create clinical failures and allows to give evidence about the anchorage stability of different implant types under dynamic gait motion pattern.
Finite element (FE)–based studies of preoperative processes such as folding,pleating, and stent crimping with a comparison with experimental inflation tests are not yet available. Therefore, a novel workflow is presented in which residual stresses of balloon folding and pleating, as well as stent crimping, and the geometries of all contact partners were ultimately implemented in an FE code to simulate stent expansion by using an implicit solver. The numerical results demonstrate that the incorporation of residual stresses and strains experienced during the production step significantly increased the accuracy of the subsequent simulations, especially of the stent expansion model. During the preoperative processes, stresses inside the membrane and the stent material also reached a rather high level. Hence, there can be no presumption that balloon catheters or stents are undamaged before the actual surgery. The implementation of the realistic geometry, in particular the balloon tapers, and the blades of the process devices improved the simulation of the expansion mech-anisms, such as dogboning, concave bending, or overexpansion of stent cells. This study shows that implicit solvers are able to precisely simulate the mentioned preoperative processes and the stent expansion procedure without a preceding manipulation of the simulation time or physical mass.
Musculoskeletal simulations of lumbar spine loading rely on a geometrical representation of the anatomy. However, this data has an inherent inaccuracy. This study evaluates the influence of defined geometrical parameters on lumbar spine loading utilising five parametrised musculoskeletal lumbar spine models for four different postures. The influence of the dimensions of vertebral body, disc, posterior parts of the vertebrae as well as the curvature of the lumbar spine was studied. Additionally, simulations with combinations of selected parameters were conducted. Changes in L4/L5 resultant joint force were used as outcome variable. Variations of the vertebral body height, disc height, transverse process width and the curvature of the lumbar spine were the most influential.
These parameters can be easily acquired from X-rays and should be used to morph a musculoskeletal lumbar spine model for subject-specific approaches with respect to bone geometry. Furthermore, the model was very sensitive to uncommon configurations and therefore, it is advised that stiffness properties of discs and ligaments should be individualised.