A Robust Solution Procedure for Hyperelastic Solids with Large Boundary Deformation

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a solution procedure for Lagrangian finite element discretization of a static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the case in which the boundary condition is a large prescribed deformation, so that mesh tangling becomes an obstacle for straightforward algorithms. Our solution procedure involves a largely geometric procedure to untangle the mesh: solution of a sequence of linear systems to obtain initial guesses for interior nodal positions for which no element is inverted. After the mesh is untangled, we take Newton iterations to converge to a mechanical equilibrium. The Newton iterations are safeguarded by a line search similar to one used in optimization. Our computational results indicate that the algorithm is up to 70 times faster than a straightforward Newton continuation procedure and is also more robust (i.e., able to tolerate much larger deformations). For a few extremely large deformations, the deformed mesh could only be computed through the use of an expensive Newton continuation method while using a tight convergence tolerance and taking very small steps.Comment: Revision of earlier version of paper. Submitted for publication in Engineering with Computers on 9 September 2010. Accepted for publication on 20 May 2011. Published online 11 June 2011. The final publication is available at http://www.springerlink.co

Experimental observation of two-dimensional fluctuation magnetization in the vicinity of T_c for low values of the magnetic field in deoxygenated YBa_2Cu_3O_{7-x}

We measured isofield magnetization curves as a function of temperature in two single crystal of deoxygenated YBaCuO with T_c = 52 and 41.5 K. Isofield MvsT were obtained for fields running from 0.05 to 4 kOe. The reversible region of the magnetization curves was analyzed in terms of a scaling proposed by Prange, but searching for the best exponent $\upsilon$. The scaling analysis carried out for each data sample set with $\upsilon$=0.669, which corresponds to the 3D-xy exponent, did not produced a collapsing of curves when applied to MvsT curves data obtained for the lowest fields. The resulting analysis for the Y123 crystal with T_c = 41.5 K, shows that lower field curves collapse over the entire reversible region following the Prange's scaling with $\upsilon$=1, suggesting a two-dimensional behavior. It is shown that the same data obeying the Prange's scaling with $\upsilon$=1 for crystal with T_c = 41.5 K, as well low field data for crystal with $T_c$ = 52 K, obey the known two-dimensional scaling law obtained in the lowest-Landau-level approximation.Comment: 4 pages, 3 figure

Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.Comment: 5 pages Late

Test Method Variability in Slow Crack Growth Properties of Sealing Glasses

The crack growth properties of several sealing glasses were measured by using constant stress rate testing in ~2 and 95 percent RH (relative humidity). Crack growth parameters measured in high humidity are systematically smaller (n and B) than those measured in low humidity, and crack velocities for dry environments are ~100x lower than for wet environments. The crack velocity is very sensitive to small changes in RH at low RH. Biaxial and uniaxial stress states produced similar parameters. Confidence intervals on crack growth parameters that were estimated from propagation of errors solutions were comparable to those from Monte Carlo simulation. Use of scratch-like and indentation flaws produced similar crack growth parameters when residual stresses were considered

Back-Face Strain for Monitoring Stable Crack Extension in Precracked Flexure Specimens

Calibrations relating back-face strain to crack length in precracked flexure specimens were developed for different strain gage sizes. The functions were verified via experimental compliance measurements of notched and precracked ceramic beams. Good agreement between the functions and experiments occurred, and fracture toughness was calculated via several operational methods: maximum test load and optically measured precrack length; load at 2 percent crack extension and optical precrack length; maximum load and back-face strain crack length. All the methods gave vary comparable results. The initiation toughness, K(sub Ii) , was also estimated from the initial compliance and load.The results demonstrate that stability of precracked ceramics specimens tested in four-point flexure is a common occurrence, and that methods such as remotely-monitored load-point displacement are only adequate for detecting stable extension of relatively deep cracks

A systematic review of the applications of Expert Systems (ES) and machine learning (ML) in clinical urology.

BackgroundTesting a hypothesis for 'factors-outcome effect' is a common quest, but standard statistical regression analysis tools are rendered ineffective by data contaminated with too many noisy variables. Expert Systems (ES) can provide an alternative methodology in analysing data to identify variables with the highest correlation to the outcome. By applying their effective machine learning (ML) abilities, significant research time and costs can be saved. The study aims to systematically review the applications of ES in urological research and their methodological models for effective multi-variate analysis. Their domains, development and validity will be identified.MethodsThe PRISMA methodology was applied to formulate an effective method for data gathering and analysis. This study search included seven most relevant information sources: WEB OF SCIENCE, EMBASE, BIOSIS CITATION INDEX, SCOPUS, PUBMED, Google Scholar and MEDLINE. Eligible articles were included if they applied one of the known ML models for a clear urological research question involving multivariate analysis. Only articles with pertinent research methods in ES models were included. The analysed data included the system model, applications, input/output variables, target user, validation, and outcomes. Both ML models and the variable analysis were comparatively reported for each system.ResultsThe search identified n = 1087 articles from all databases and n = 712 were eligible for examination against inclusion criteria. A total of 168 systems were finally included and systematically analysed demonstrating a recent increase in uptake of ES in academic urology in particular artificial neural networks with 31 systems. Most of the systems were applied in urological oncology (prostate cancer = 15, bladder cancer = 13) where diagnostic, prognostic and survival predictor markers were investigated. Due to the heterogeneity of models and their statistical tests, a meta-analysis was not feasible.ConclusionES utility offers an effective ML potential and their applications in research have demonstrated a valid model for multi-variate analysis. The complexity of their development can challenge their uptake in urological clinics whilst the limitation of the statistical tools in this domain has created a gap for further research studies. Integration of computer scientists in academic units has promoted the use of ES in clinical urological research

Measuring Crack Length in Coarse Grain Ceramics

Due to a coarse grain structure, crack lengths in precracked spinel specimens could not be measured optically, so the crack lengths and fracture toughness were estimated by strain gage measurements. An expression was developed via finite element analysis to correlate the measured strain with crack length in four-point flexure. The fracture toughness estimated by the strain gaged samples and another standardized method were in agreement