Bayesian method approach for fatigue life distribution estimation of rubber components

The constantly increasing market requirements of high-quality vehicles compel automotive manufacturers to perform lifetime testing to verify the reliability levels of new products. A common problem is that only a small number of samples of a system\u27s component can be tested. In automotive applications, mechanical components subjected to cyclic loading have to be designed against fatigue. In this paper, the Bayesian estimation of lognormal distribution parameters (usually used to define the fatigue lifetime of rubber components) is studied to improve the accuracy of estimation while incorporating the available knowledge on the product. In particular, the finite element results and experts\u27 opinions are considered prior knowledge. For lifetime prediction by Finite Element Method (FEM), a model based on the Brown-Miller law was developed for the rubberlike boot seal material

Generator Matrix Elements For G2⊃SU(3)G_2 \supset SU(3) II

Basis states and generator matrix elements are given for the generic representation $(a,b)$ of $G_2$ in an $SU(3)$ basis.Comment: Latex, 17 pages, one figure using epsf published in J. Phys. A: Math. Gen 28 (1995) 2581-258

New three-dimensional model based on finite element method of bone nanostructure: single TC molecule scale level

At the macroscopic scale, the bone mechanical behavior (fracture, elastic) depends mainly on itscomponents nature at the nanoscopic scale (collagen, mineral). Thus, an understanding of themechanical behavior of the elementary components is demanded to understand the phenomenathat can be observed at the macroscopic scale. In this article, a new numerical model based on finiteelement method is proposed in order to describe the mechanical behavior of a single Tropocollagenmolecule. Furthermore, a parametric study with different geometric properties covering themolecular composition and the rate hydration influence is presented. The proposed model has beentested under tensile loading. While focusing on the entropic response, the geometric parametervariation effect on the mechanical behavior of Tropocollagen molecule has been revealed using themodel. Using numerical and experimental testing, the obtained numerical simulation results seemto be acceptable, showing a good agreement with those found in literature

A theory for bone resorption based on the local rupture of osteocytes cells connections: A finite element study

In this work, a bone damage resorption finite element model based on the disruption of the inhibitory signal transmitted between osteocytes cells in bone due to damage accumulation is developed and discussed. A strain-based stimulus function coupled to a damage-dependent spatialfunction is proposed to represent the connection between two osteocytes embedded in the bone tissue. The signal is transmitted to the bone surface to activate bone resorption. The proposed modelis based on the idea that the osteocyte signal reduction is not related to the reduction of the stimulus sensed locally by osteocytes due to damage, but to the difficulties for the signal in travelling along a disrupted area due to microcracks that can destroy connections of the intercellular network between osteocytes and bone-lining cells. To check the potential of the proposed model to predict the damage resorption process, two bone resorption mechano-regulation rules corresponding to twomechanotransduction approaches have been implemented and tested: 1) Bone resorption based on a coupled strain-damage stimulus function without ruptured osteocyte connections (NROC); and 2) Bone resorption based on a strain stimulus function with ruptured osteocyte connections (ROC). The comparison between the results obtained by both models, shows that the proposed model based on ruptured osteocytes connections predicts realistic results in conformity with previously published findings concerning the fatigue damage repair in bone

On character generators for simple Lie algebras

We study character generating functions (character generators) of simple Lie algebras. The expression due to Patera and Sharp, derived from the Weyl character formula, is first reviewed. A new general formula is then found. It makes clear the distinct roles of ``outside'' and ``inside'' elements of the integrity basis, and helps determine their quadratic incompatibilities. We review, analyze and extend the results obtained by Gaskell using the Demazure character formulas. We find that the fundamental generalized-poset graphs underlying the character generators can be deduced from such calculations. These graphs, introduced by Baclawski and Towber, can be simplified for the purposes of constructing the character generator. The generating functions can be written easily using the simplified versions, and associated Demazure expressions. The rank-two algebras are treated in detail, but we believe our results are indicative of those for general simple Lie algebras.Comment: 50 pages, 11 figure

Effect of material and structural factors on fracture behaviour of mineralised collagen microfibril using finite element simulation

Bone is a multiscale heterogeneous material and its principal function is to support the body structure and to resist mechanical loads without fracturing. Numerical modelling of biocomposites at different length scales provides an improved understanding of the mechanical behaviour of structures such as bone, and also guides the development of multiscale mechanical models. Here, a three-dimensional nano-scale model of mineralised collagen microfibril based on the finite element method was employed to investigate the effect of material and structural factors on the mechanical equivalent of fracture properties. Fracture stress and damping capacity as functions of the number of cross-links were obtained under tensile loading conditions for different densities and Young's modulus of the mineral phase. The results show that the number of cross-links and the density of mineral as well as Young's modulus of mineral have an important influence on the strength of mineralised collagen microfibrils which in turn clarify the bone fracture on a macroscale. © 2014 © 2014 Taylor & Francis

Finite element prediction of fatigue damage growth in cancellous bone

Cyclic stresses applied to bones generate fatigue damage that affects the bone stiffness and its elastic modulus. This paper proposes a finite element model for the prediction of fatigue damage accumulation and failure in cancellous bone at continuum scale. The model is based on continuum damage mechanics and incorporates crack closure effects in compression. The propagation of the cracks is completely simulated throughout the damaged area. In this case, the stiffness of the broken element is reduced by 98% to ensure no stress-carrying capacities of completely damaged elements. Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. The proposed model suggests that damage evolves over a real physical time variable (cycles). In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. In this approach, the real number of cycles is reduced (divided) into equivalent blocks of cycles. Damage accumulation is computed over the cycle blocks and then extrapolated over the corresponding real cycles. The results show a clear difference between local tensile and compressive stresses on damage accumulation. Incorporating stiffness reduction also produces a redistribution of the peak stresses in the damaged region, which results in a delay in damage fracture