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Smoothed Finite Element Methods for Nonlinear Solid Mechanics Problems: 2D and 3D Case Studies
(2016)
The Smoothed Finite Element Method (SFEM) is presented as an edge-based and a facebased techniques for 2D and 3D boundary value problems, respectively. SFEMs avoid shortcomings of the standard Finite Element Method (FEM) with lower order elements such as overly stiff behavior, poor stress solution, and locking effects. Based on the idea of averaging spatially the standard strain field of the FEM over so-called smoothing domains SFEM calculates the stiffness matrix for the same number of degrees of freedom (DOFs) as those of the FEM. However, the SFEMs significantly improve accuracy and convergence even for distorted meshes and/or nearly incompressible materials.
Numerical results of the SFEMs for a cardiac tissue membrane (thin plate inflation) and an artery (tension of 3D tube) show clearly their advantageous properties in improving accuracy particularly for the distorted meshes and avoiding shear locking effects.
Soft Materials in Technology and Biology – Characteristics, Properties, and Parameter Identification
(2008)
Improved collapse loads of thick-walled, crack containing pipes and vessels are suggested. Very deep cracks have a residual strength which is better modelled by a global limit load. In all burst tests, the ductility of pressure vessel steels was sufficiently high whereby the burst pressure could be predicted by limit analysis with no need to apply fracture mechanics. The relative prognosis error increases however, for long and deep defects due to uncertainties of geometry and strength data.
Limit loads can be calculated with the finite element method (FEM) for any component, defect geometry, and loading. FEM suggests that published long crack limit formulae for axial defects under-estimate the burst pressure for internal surface defects in thick pipes while limit loads are not conservative for deep cracks and for pressure loaded crack-faces. Very deep cracks have a residual strength, which is modelled by a global collapse load. These observations are combined to derive new analytical local and global collapse loads. The global collapse loads are close to FEM limit analyses for all crack dimensions.
In the new European standard for unfired pressure vessels, EN 13445-3, there are two approaches for carrying out a Design-by-Analysis that cover both the stress categorization method (Annex C) and the direct route method (Annex B) for a check against global plastic deformation and against progressive plastic deformation. This paper presents the direct route in the language of limit and shakedown analysis. This approach leads to an optimization problem. Its solution with Finite Element Analysis is demonstrated for mechanical and thermal actions. One observation from the examples is that the so-called 3f (3Sm) criterion fails to be a reliable check against progressive plastic deformation. Precise conditions are given, which greatly restrict the applicability of the 3f criterion.
Structural design analyses are conducted with the aim of verifying the exclusion of ratchetting. To this end it is important to make a clear distinction between the shakedown range and the ratchetting range. The performed experiment comprised a hollow tension specimen which was subjected to alternating axial forces, superimposed with constant moments. First, a series of uniaxial tests has been carried out in order to calibrate a bounded kinematic hardening rule. The load parameters have been selected on the basis of previous shakedown analyses with the PERMAS code using a kinematic hardening material model. It is shown that this shakedown analysis gives reasonable agreement between the experimental and the numerical results. A linear and a nonlinear kinematic hardening model of two-surface plasticity are compared in material shakedown analysis.
This paper presents the direct route to Design by Analysis (DBA) of the new European pressure vessel standard in the language of limit and shakedown analysis (LISA). This approach leads to an optimization problem. Its solution with Finite Element Analysis is demonstrated for some examples from the DBA-Manual. One observation from the examples is, that the optimisation approach gives reliable and close lower bound solutions leading to simple and optimised design decision.
In: Technical feasibility and reliability of passive safety systems for nuclear power plants. Proceedings of an Advisory Group Meeting held in Jülich, 21-24 November 1994. - Vienna , 1996. - Seite: 43 - 55 IAEA-TECDOC-920 Abstract: It is shown that the difficulty for probabilistic fracture mechanics (PFM) is the general problem of the high reliability of a small population. There is no way around the problem as yet. Therefore what PFM can contribute to the reliability of steel pressure boundaries is demonstrated with the example of a typical reactor pressure vessel and critically discussed. Although no method is distinguishable that could give exact failure probabilities, PFM has several additional chances. Upper limits for failure probability may be obtained together with trends for design and operating conditions. Further, PFM can identify the most sensitive parameters, improved control of which would increase reliability. Thus PFM should play a vital role in the analysis of steel pressure boundaries despite all shortcomings.
Rezension zu: K. Zimmermann, Technische Mechanik – multimedial. Fachbuch Verlag Leipzig (2000)
(2002)
Extension fractures are typical for the deformation under low or no confining pressure. They 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. In this article, it is shown that the simple extension strain criterion makes unrealistic strength predictions in biaxial compression and tension. To overcome this major limitation, a new extension strain criterion is proposed by adding a weighted principal shear component to the simple criterion. The shear 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 extension failure modes, which are unexpected in the classical 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 leading to dilatancy. 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 stress CP. Different from compressive loading, tensile loading requires only a limited number of critical cracks to cause failure. Therefore, for tensile stresses, the failure criteria must be modified somehow, possibly by a cut-off corresponding to the CI stress. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
Pressure distribution to the distal biceps tendon at the radial tuberosity: a biomechanical study
(2020)
Purpose
Mechanical impingement at the narrow radioulnar space of the tuberosity is believed to be an etiological factor in the injury of the distal biceps tendon. The aim of the study was to compare the pressure distribution at the proximal radioulnar space between 2 fixation techniques and the intact state.
Methods
Six right arms and 6 left arms from 5 female and 6 male frozen specimens were used for this study. A pressure transducer was introduced at the height of the radial tuberosity with the intact distal biceps tendon and after 2 fixation methods: the suture-anchor and the cortical button technique. The force (N), maximum pressure (kPa) applied to the radial tuberosity, and the contact area (mm²) of the radial tuberosity with the ulna were measured and differences from the intact tendon were detected from 60° supination to 60° pronation in 15° increments with the elbow in full extension and in 45° and 90° flexion of the elbow.
Results
With the distal biceps tendon intact, the pressures during pronation were similar regardless of extension and flexion and were the highest at 60° pronation with 90° elbow flexion (23.3 ± 53.5 kPa). After repair of the tendon, the mean peak pressure, contact area, and total force showed an increase regardless of the fixation technique. Highest peak pressures were found using the cortical button technique at 45° flexion of the elbow and 60° pronation. These differences were significantly different from the intact tendon. The contact area was significantly larger in full extension and 15°, 30°, and 60° pronation using the cortical button technique.
Conclusions
Pressures on the distal biceps tendon at the radial tuberosity increase during pronation, especially after repair of the tendon.
Clinical relevance
Mechanical impingement could play a role in both the etiology of primary distal biceps tendon ruptures and the complications occurring after fixation of the tendon using certain techniques.
Purpose
The aim of this study was to compare several osteosynthesis techniques (intramedullary headless compression screws, T-plates, and Kirschner wires) for distal epiphyseal fractures of proximal phalanges in a human cadaveric model.
Methods
A total of 90 proximal phalanges from 30 specimens (index, ring, and middle fingers) were used for this study. After stripping off all soft tissue, a transverse distal epiphyseal fracture was simulated at the proximal phalanx. The 30 specimens were randomly assigned to 1 fixation technique (30 per technique), either a 3.0-mm intramedullary headless compression screw, locking plate fixation with a 2.0-mm T-plate, or 2 oblique 1.0-mm Kirschner wires. Displacement analysis (bending, distraction, and torsion) was performed using optical tracking of an applied random speckle pattern after osteosynthesis. Biomechanical testing was performed with increasing cyclic loading and with cyclic load to failure using a biaxial torsion-tension testing machine.
Results
Cannulated intramedullary compression screws showed significantly less displacement at the fracture site in torsional testing. Furthermore, screws were significantly more stable in bending testing. Kirschner wires were significantly less stable than plating or screw fixation in any cyclic load to failure test setup.
Conclusions
Intramedullary compression screws are a highly stable alternative in the treatment of transverse distal epiphyseal phalangeal fractures. Kirschner wires seem to be inferior regarding displacement properties and primary stability.
Clinical relevance
Fracture fixation of phalangeal fractures using plate osteosynthesis may have the advantage of a very rigid reduction, but disadvantages such as stiffness owing to the more invasive surgical approach and soft tissue irritation should be taken into account. Headless compression screws represent a minimally invasive choice for fixation with good biomechanical properties.
Human induced pluripotent stem cells (hiPSCs) have shown to be promising in disease studies and drug screenings [1]. Cardiomyocytes derived from hiPSCs have been extensively investigated using patch-clamping and optical methods to compare their electromechanical behaviour relative to fully matured adult cells. Mathematical models can be used for translating findings on hiPSCCMs to adult cells [2] or to better understand the mechanisms of various ion channels when a drug is applied [3,4]. Paci et al. (2013) [3] developed the first model of hiPSC-CMs, which they later refined based on new data [3]. The model is based on iCells® (Fujifilm Cellular Dynamics, Inc. (FCDI), Madison WI, USA) but major differences among several cell lines and even within a single cell line have been found and motivate an approach for creating sample-specific models. We have developed an optimisation algorithm that parameterises the conductances (in S/F=Siemens/Farad) of the latest Paci et al. model (2018) [5] using current-voltage data obtained in individual patch-clamp experiments derived from an automated patch clamp system (Patchliner, Nanion Technologies GmbH, Munich).
This paper develops a new finite element method (FEM)-based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple two-surface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the back-stress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature.
The impact of surgical staplers on tissues has been studied mostly in an empirical manner. In this paper, finite element method was used to clarify the mechanics of tissue stapling and associated phenomena. Various stapling modalities and several designs of circular staplers were investigated to evaluate the impact of the device on tissues and mechanical performance of the end-to-end colorectal anastomosis. Numerical simulations demonstrated that a single row of staples is not adequate to resist leakage due to non-linear buckling and opening of the tissue layers between two adjacent staples. Compared to the single staple row configuration, significant increase in stress experienced by the tissue at the inner staple rows was observed in two and three rows designs. On the other hand, adding second and/or third staple row had no effect on strain in the tissue inside the staples. Variable height design with higher staples in outer rows significantly reduced the stresses and strains in outer rows when compared to the same configuration with flat cartridge.
Influence of a freeze–thaw cycle on the stress–stretch curves of tissues of porcine abdominal organs
(2012)
The paper investigates both fresh porcine spleen and liver and the possible decomposition of these organs under a freeze–thaw cycle. The effect of tissue preservation condition is an important factor which should be taken into account for protracted biomechanical tests. In this work, tension tests were conducted for a large number of tissue specimens from twenty pigs divided into two groups of 10. Concretely, the first group was tested in fresh state; the other one was tested after a freeze-thaw cycle which simulates the conservation conditions before biomechanical experiments. A modified Fung model for isotropic behavior was adopted for the curve fitting of each kind of tissues. Experimental results show strong effects of the realistic freeze–thaw cycle on the capsule of elastin-rich spleen but negligible effects on the liver which virtually contains no elastin. This different behavior could be explained by the autolysis of elastin by elastolytic enzymes during the warmer period after thawing. Realistic biomechanical properties of elastin-rich organs can only be expected if really fresh tissue is tested. The observations are supported by tests of intestines.
Kyphoplasty of Osteoporotic Fractured Vertebrae: A Finite Element Analysis about Two Types of Cement
(2019)
A new in vitro tool to investigate cardiac contractility under physiological mechanical conditions
(2019)
Einschränkung von Taluskippung und -vorschub durch Sprunggelenkorthesen nach fibularer Bandruptur
(2013)
Die fibulare Bandruptur zählt zu einer der am häufigsten auftretenden Verletzungen des
Bewegungsapparats. In den meisten Fällen wird heute die konservativ frühfunktionelle Therapie mit Sprunggelenkorthesen allgemein bevorzugt. Im Rahmen der vorliegenden Studie wurden 14 verschiedene Sprunggelenkorthesen im Hinblick auf ihre Einschränkung von Taluskippung und Talusvorschub
untersucht. Zur Simulation einer fibularen Bandruptur wurde ein Unterschenkelmodell aus Holz mit Fußteil, mit angelegten Orthesen in einen Scheuba-Halteapparat eingespannt und mit 150 N seitlich sowie anterior-posterior belastet. Anhand der erstellten "gehaltenen" Röntgenaufnahmen konnten Taluskippung und Talusvorschub jeder einzelnen Orthese eindeutig bestimmt werden. Die meisten Orthesen erreichten zufriedenstellende Ergebnisse. Es stellte sich heraus, dass vor allem eine eng anliegende, im Gelenkbereich anatomisch angepasste Form vorteilhaft zu sein scheint.
Originalausgabe: Orthopädische Praxis Jg. 47. 2011 H. 11; S. 536-543. Mit freundlicher Genehmigung des Verlags Zusammenfassung: Auf der Basis von Patientenabfragen mittels Fragebogen zum Schmerzempfinden und zur Einschränkung bei Aktivitäten des alltäglichen Lebens wird die Langzeitwirkung der MBST® KernspinResonanz-Therapie bei Gonarthrose untersucht. An der Studie nahmen 39 Patienten teil, bei denen die Therapie bis zu vier Jahre zurückliegt. Neben einer Gesamtbetrachtung wird der Erfolg auch in Abhängigkeit von Alter, Geschlecht und sportlicher Aktivität analysiert. Insgesamt weist die Studie auf eine anhaltende Verbesserung des Gesundheitszustands mit zum Teil deutlicher Schmerzlinderung auch noch nach vier Jahren hin, jedoch mit einer leichten Schmerzzunahme gegen Ende des Untersuchungszeitraums von vier Jahren. Eine tendenziell positivere Wirkung bei Frauen, älteren Menschen oder auch sportlich nicht-aktiven Patienten lässt auf eine mögliche Beeinflussung des Erfolgs der Therapie durch (Über-)Belastung im Alltag schließen. Ein zusätzlich positiver Effekt der Therapie auf die Knochendichte ist ebenfalls denkbar, dies bleibt jedoch offen.
Analysis of the long-term effect of the MBST® nuclear magnetic resonance therapy on gonarthrosis
(2016)
An optimization method is developed to describe the mechanical behaviour of the human cancellous bone. The method is based on a mixture theory. A careful observation of the behaviour of the bone material leads to the hypothesis that the bone density is controlled by the principal stress trajectories (Wolff’s law). The basic idea of the developed method is the coupling of a scalar value via an eigenvalue problem to the principal stress trajectories. On the one hand this theory will permit a prediction of the reaction of the biological bone structure after the implantation of a prosthesis, on the other hand it may be useful in engineering optimization problems. An analytical example shows its efficiency.
Der vorliegende Artikel fokussiert sich auf die weibliche Belastungsinkontinenz als Insuffizienz der Speicherfunktion der Blase, auch wenn im klinischen Alltag die Harninkontinenz der Frau häufig verschiedene Ursachen hat und insbesondere eine Belastungsinkontinenz im Alter und bei neurologischer Komorbidität nur selten isoliert vorkommt.
Das kleine Becken der Frau ist sowohl als Funktions- als auch als strukturelle Einheit zu betrachten. Dabei unterliegen bei der Frau Blase, Harnröhre, Gebärmutter und Enddarm sowie die muskulären und ligamentösen Strukturen des kleinen Beckens durch Fertilitätsphase, mögliche Schwangerschaften, Geburten und Menopausen-Phase, über das „normale Altern“ hinaus, gravierenden Veränderungen.
This article focuses on female stress incontinence in the form of pelvic floor dysfunction and urethral sphincter deficiency, although isolated stress incontinence accounts for less than half of all incontinence cases. Especially in women of old age and those with neurological comorbidities, the causes of incontinence are mostly multifactorial. Also it has to be considered that the female bladder, urethra, uterus and rectum as well as the muscular and ligamentous structures of the female pelvis minor are affected by phases of fertility, possible pregnancies, births and menopause in addition to the normal ageing process.
Combining physiological relevance and throughput for in vitro cardiac contractility measurement
(2020)
Despite increasing acceptance of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) in safety pharmacology, controversy remains about the physiological relevance of existing in vitro models for their mechanical testing. We hypothesize that existing signs of immaturity of the cell models result from an improper mechanical environment. We cultured hiPSC-CMs in a 96-well format on hyperelastic silicone membranes imitating their native mechanical environment, resulting in physiological responses to compound stimuli.We validated cell responses on the FLEXcyte 96, with a set of reference compounds covering a broad range of cellular targets, including ion channel modulators, adrenergic receptor modulators and kinase inhibitors. Acute (10 - 30 min) and chronic (up to 7 days) effects were investigated. Furthermore, the measurements were complemented with electromechanical models based on electrophysiological recordings of the used cell types.hiPSC-CMs were cultured on freely-swinging, ultra-thin and hyperelastic silicone membranes. The weight of the cell culture medium deflects the membranes downwards. Rhythmic contraction of the hiPSC-CMs resulted in dynamic deflection changes which were quantified by capacitive distance sensing. The cells were cultured for 7 days prior to compound addition. Acute measurements were conducted 10-30 minutes after compound addition in standard culture medium. For chronic treatment, compound-containing medium was replaced daily for up to 7 days. Electrophysiological properties of the employed cell types were recorded by automated patch-clamp (Patchliner) and the results were integrated into the electromechanical model of the system.Calcium channel agonist S Bay K8644 and beta-adrenergic stimulator isoproterenol induced significant positive inotropic responses without additional external stimulation. Kinase inhibitors displayed cardiotoxic effects on a functional level at low concentrations. The system-integrated analysis detected alterations in beating shape as well as frequency and arrhythmic events and we provide a quantitative measure of these.
Successful bone sawing requires a high level of skill and experience, which could be gained by the use of Virtual Reality-based simulators. A key aspect of these medical simulators is realistic force feedback. The aim of this paper is to model the bone sawing process in order to develop a valid training simulator for the bilateral sagittal split osteotomy, the most often applied corrective surgery in case of a malposition of the mandible. Bone samples from a human cadaveric mandible were tested using a designed experimental system. Image processing and statistical analysis were used for the selection of four models for the bone sawing process. The results revealed a polynomial dependency between the material removal rate and the applied force. Differences between the three segments of the osteotomy line and between the cortical and cancellous bone were highlighted.