Finite element modeling of the cement-bone interface beneath the tibial tray of a total knee arthroplasty: Study of the stress shielding effect (modellazione agli elementi finiti dell'interfaccia cemento-osso sotto il piatto tibiale di protesi totale di ginocchio: Analisi dello stress shielding)

The goal of this thesis was the study of the cement-bone interface in the tibial component of a cemented total knee prosthesis. One of the things you can see in specimens after in vivo service is that resorption of bone occurs in the interdigitated region between bone and cement. A stress shielding effect was investigated as a cause to explain bone resorption. Stress shielding occurs when bone is loaded less than physiological and therefore it starts remodeling according to the new loading conditions. µCT images were used to obtain 3D models of the bone and cement structure and a Finite Element Analysis was used to simulate different kind of loads. Resorption was also simulated by performing erosion operations in the interdigitated bone region. Finally, 4 models were simulated: bone (trabecular), bone with cement, and two models of bone with cement after progressive erosions of the bone. Compression, tension and shear test were simulated for each model in displacement-control until 2% of strain. The results show how the principal strain and Von Mises stress decrease after adding the cement on the structure and after the erosion operations. These results show that a stress shielding effect does occur and rises after resorption starts.

Studio e progettazione di giunti incollati di tipo strutturale per applicazioni aeronautiche

Il presente elaborato è stato approfondito e sviluppato presso lo stabilimento della Blackshape Aircraft S.p.A. sito in Monopoli (Bari). L’obiettivo è stato principalmente orientato sull’individuazione di un metodo di progettazione di giunzioni incollate fra laminati in CFRP basato su di un modello matematico in grado di prevederne la resistenza. Per realizzare tale studio sono stati necessari approfondimenti preliminari relativi al comportamento meccanico dei laminati in materiale composito e agli studi condotti da Hart-Smith sulla teoria degli incollaggi. E’ stato determinato un metodo analitico per il calcolo della lunghezza di sovrapposizione degli aderenti. Il criterio di resistenza del giunto individuato, basato sulla teoria del cedimento multiassiale di Von Mises, è stato approvato dalla Agenzia Europea per la Sicurezza Aerea, EASA. A livello numerico-pratico è stato preso in esempio il giunto fra i gusci di fusoliera relativi al nuovo velivolo Blackshape con certificazione VLA (Very Light Aircraft).

Numerical assessment on the effective mechanical stimuli for matrix-associated metabolism in chondrocyte-seeded constructs

The self-regeneration capacity of articular cartilage is limited, due to its avascular and aneural nature. Loaded explants and cell cultures demonstrated that chondrocyte metabolism can be regulated via physiologic loading. However, the explicit ranges of mechanical stimuli that correspond to favourable metabolic response associated with extracellular matrix (ECM) synthesis are elusive. Unsystematic protocols lacking this knowledge produce inconsistent results. This study aims to determine the intrinsic ranges of physical stimuli that increase ECM synthesis and simultaneously inhibit nitric oxide (NO) production in chondrocyte-agarose constructs, by numerically re-evaluating the experiments performed by Tsuang et al. (2008). Twelve loading patterns were simulated with poro-elastic finite element models in ABAQUS. Pressure on solid matrix, von Mises stress, maximum principle stress and pore pressure were selected as intrinsic mechanical stimuli. Their development rates and magnitudes at the steady state of cyclic loading were calculated with MATLAB at the construct level. Concurrent increase in glycosaminoglycan and collagen was observed at 2300 Pa pressure and 40 Pa/s pressure rate. Between 0-1500 Pa and 0-40 Pa/s, NO production was consistently positive with respect to controls, whereas ECM synthesis was negative in the same range. A linear correlation was found between pressure rate and NO production (R = 0.77). Stress states identified in this study are generic and could be used to develop predictive algorithms for matrix production in agarose-chondrocyte constructs of arbitrary shape, size and agarose concentration. They could also be helpful to increase the efficacy of loading protocols for avascular tissue engineering. Copyright (c) 2010 John Wiley \& Sons, Ltd.

A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales

Nonlinear computational analysis of materials showing elasto-plasticity or damage relies on knowledge of their yield behavior and strengths under complex stress states. In this work, a generalized anisotropic quadric yield criterion is proposed that is homogeneous of degree one and takes a convex quadric shape with a smooth transition from ellipsoidal to cylindrical or conical surfaces. If in the case of material identification, the shape of the yield function is not known a priori, a minimization using the quadric criterion will result in the optimal shape among the convex quadrics. The convexity limits of the criterion and the transition points between the different shapes are identified. Several special cases of the criterion for distinct material symmetries such as isotropy, cubic symmetry, fabric-based orthotropy and general orthotropy are presented and discussed. The generality of the formulation is demonstrated by showing its degeneration to several classical yield surfaces like the von Mises, Drucker–Prager, Tsai–Wu, Liu, generalized Hill and classical Hill criteria under appropriate conditions. Applicability of the formulation for micromechanical analyses was shown by transformation of a criterion for porous cohesive-frictional materials by Maghous et al. In order to demonstrate the advantages of the generalized formulation, bone is chosen as an example material, since it features yield envelopes with different shapes depending on the considered length scale. A fabric- and density-based quadric criterion for the description of homogenized material behavior of trabecular bone is identified from uniaxial, multiaxial and torsional experimental data. Also, a fabric- and density-based Tsai–Wu yield criterion for homogenized trabecular bone from in silico data is converted to an equivalent quadric criterion by introduction of a transformation of the interaction parameters. Finally, a quadric yield criterion for lamellar bone at the microscale is identified from a nanoindentation study reported in the literature, thus demonstrating the applicability of the generalized formulation to the description of the yield envelope of bone at multiple length scales.

Directional statistics: introduction

In many of the natural and physical sciences, measurements are directions, either in two or three dimensions. The analysis of directional data relies on specific statistical models and procedures, which differ from the usual models and methodologies of Cartesian data. This chapter briefly introduces statistical models and inference for this type of data. The basic von Mises-Fisher distribution is introduced and nonparametric methods such as goodness-of-fit tests are presented. Further references are given for exploring related topics such as correlation and regression.

Dr. Marcus Landau, Wien [Illustration] : rühmlich bekannter Litteraturhistoriker (Bleistiftzeichnung)

Helena von Mises

Selbstporträt

Helena von Mises

Judenknabe [Illustration]

Helena von Mises

Armensuppe [Illustration]

Helena von Mises

Beratung [Illustration]

Helena von Mises

Ruthenischer Bauer [Illustration]

Helena von Mises

Magnetic susceptibility anisotropy in deformed sediments of ODP Leg 110

The anisotropy of magnetic susceptibility documents the generation of tectonically produced fabrics in sediments that macroscopically show no evidence of this disruption. The fabric observed in initial accretion is largely produced by overprinting of the original sedimentary susceptibility anisotropy by an E-W horizontal tectonic shortening and vertical extension. The response of the sediments to stress during initial accretion is variable, particularly near the sediment surface, and appears to reflect the inhomogeneous distribution of strain rate in the overthrust sequence. The susceptibility anisotropy of sediments possessing scaly fabric is consistent with the strong orientation of Phyllosilicates seen in thin section, producing a Kmin normal to the scalyness. The slope sediments deposited on the accreted sequence are also affected by tectonic shortening. The accreted sequences at Sites 673 and 674 show a complex history of fabric modification, with previous tectonic fabrics overprinted by later fabric modifications, pointing to continued tectonic shortening during the accretion process. The form of the susceptibility anisotropy axes at Sites 673 and 674 is consistent with NESW shortening, probably reflected in the NW-SE surface expression of the out-of-sequence thrusts. The susceptibility anisotropy appears to document a downhole change in the trend of shortening from E to W at the surface to more NESW at depth, probably as a result of the obliquely trending basement ridge, the Tiburon Rise.

Dynamic Response of Wind Turbines to Theoretical 3D Seismic Motions Taking into Account the Rotational Component

We study the dynamic response of a wind turbine structure subjected to theoretical seismic motions, taking into account the rotational component of ground shaking. Models are generated for a shallow moderate crustal earthquake in the Madrid Region (Spain). Synthetic translational and rotational time histories are computed using the Discrete Wavenumber Method, assuming a point source and a horizontal layered earth structure. These are used to analyze the dynamic response of a wind turbine, represented by a simple finite element model. Von Mises stress values at different heights of the tower are used to study the dynamical structural response to a set of synthetic ground motion time histories

Failure locus of polypropylene nonwoven fabrics under in-plane biaxial deformation

The failure locus, the characteristics of the stress–strain curve and the damage localization patterns were analyzed in a polypropylene nonwoven fabric under in-plane biaxial deformation. The analysis was carried out by means of a homogenization model developed within the context of the finite element method. It provides the constitutive response for a mesodomain of the fabric corresponding to the area associated to a finite element and takes into account the main deformation and damage mechanisms experimentally observed. It was found that the failure locus in the stress space was accurately predicted by the Von Mises criterion and failure took place by the localization of damage into a crack perpendicular to the main loading axis.