A biphasic transverse isotropic FEM model for cartilage

Articular cartilage is a viscoelastic, two-phase and fiber-strengthen tissue; it consists of a solid and a fluid phase. We describe this tissue using the Theory of Porous Media (TPM). Some simulation results are shown. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A constitutive model for continuous fiber reinforced polymer plies

In the present paper a constitutive model is reviewed which can be used to predict the non-linear behavior of continuous fiber reinforced laminates with polymeric matrix materials. The constitutive model considers stiffness degradation and plastic strain accumulation at the length scale of the individual plies (laminae). These effects are modeled via two different phenomenological approaches, however, their interaction is considered when the constitutive equations are solved by an implicit integration scheme. To demonstrate the predictive capabilities of the individual model parts, examples are given where the above mentioned effects are decoupled. This way, their impact on the laminate's response can be studied independently. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A RVE-based micro mechanical model for short fiber reinforced plastic materials including matrix damage and fiber fracture

The representative volume element (RVE) method is applied to a fiber reinforced polymer material undergoing matrix damage and fiber fracture. Results of RVE computations are compared to uniaxial tensile tests performed with the composite material. It is shown that the macroscopic behavior of the composite material can accurately be predicted by RVE computations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A three-dimensional progressive damage model for fiber reinforced composites with an implicit-explicit integration scheme

This contribution proposes a fully three dimensional “continuum damage model” (CDM) to describe the interlaminar and intralaminar failure mechanisms of transversely isotropic elastic-brittle materials under static loading. The constitutive model is derived from an energy function with independent damage variables for each damage mode. The evolution law is based on energy dissipation within the damage process, taking into account the critical energy release rate to weaken the effect of mesh dependent outcome. The onset of damage can be predicted with Cuntze's failure mode concept [1] as well as with Hashin's failure criteria. In this model linear stress decreasing is assumed. In addition, an implicit-explicit integration scheme, first proposed by Oliver [3] for isotropic damage models, is adapted to increase the stability and robustness of numerical simulations and to decrease the computational cost of material failure analyses. By comparing the results from implicit-explicit integration schemes and standard implicit integration schemes, a high level of agreement is found. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new model family for the strength distribution of fibers in relation to their length

Based on the weakest-link model, a family of fiber strength distributions is investigated assuming a two-stage failure process. At the first stage, a weakest link is formed (instantly or gradually), but at the second one the fracture of this link takes place. The gradual accumulation of flaws is described with the aid of Markov chain theory. The adequacy of the models considered is verified by checking them against experimental strength data for E-glass and flax fibers of various lengths. It is found that the models are not less accurate, but are even better, in a number of cases, than the model based on the known modified Weibull model with a power-law relation between the fiber length and the scale parameter. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 179–192, March–April, 2006.     

The effective heat conduction of short fibre reinforced materials considering the fibre distribution

This contribution focuses on the effective heat conductivity of short fibre reinforced materials. For this purpose, a representative volume element (RVE), which is able to represent all possible fibre orientation distributions, is introduced and modelled in ABAQUS. Subsequently, the effective heat conductivity of the RVE is derived, employing a numerical homogenisation scheme, and a phenomenological material model is fitted to those results. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A model for supply chain design considering the cost of quality

Recent studies have shown that the cost of quality (COQ) is of more strategic and economic importance than previously conceived. Whereas previous works have applied COQ as an internal performance measure within companies, the purpose of this paper is to present a model for supply chain design that computes the COQ as a global performance measure for the entire supply chain. In addition, rather than assume an exogenously given COQ curve, our model computes COQ in terms of internal operational decisions such as the error rate at inspection and fraction defective at manufacturing. The model can be used to design a logistic route that achieves a minimum total cost while maintaining an overall quality level and to evaluate the impact of investment in quality to increase overall profits. The behaviour of the model is illustrated with numerical examples that show how the COQ function changes depending on various parameters.     

A comparison of mean field homogenization schemes for short fiber reinforced thermoplastics

Different mean field homogenization methods are applied to a short glass fiber reinforced polybutylene terephthalate. The different models' predictions for the anisotropic effective elastic properties are assessed and compared to experimental data from tensile tests. Additionally, the estimation of fiber stresses and the influence of the fiber length distribution is studied. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of glass fiber inelasticity on the long-term strength of reinforced plastics subject to uniaxial tension along the fibers

Relationships are presented for determining the long-term strength of reinforced plastics subject to uniaxial tension by a constant load directed along the fibers; these relationships are based on the rheological characteristics of the components of the plastics. The proposed expressions agree quite well with experiment. Treatment of the experimental data by mathematical statistics showed that the relative strain at fracture remains constant; it does not depend either on the relative reinforcement content or on the applied load (i. e., on the time to fracture).Mekhanika Polimerov, Vol. 3, No. 4, pp. 719–725, 1967     

A random matrix model for the Gaussian distribution

Summary The Gaussian unitary ensemble is a random matrix model (RMM) for the Wigner law. While random matrices in this model are infinitely divisible, the Wigner law is infinitely divisible not in the classical but in the free sense. We prove that any variance mixture of Gaussian distributions -- whether infinitely divisible or not in the classical sense -- admits a RMM of non Gaussian infinitely divisible random matrices. More generally, it is shown that any mixture of the Wigner law admits a RMM. A key role is played by the fact that the Gaussian distribution is the mixture of Wigner law with the <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>2$-gamma distribution.     

A generalized model for static fatigue lifetime evaluation of optical fibers to reduce the model uncertainty

The mechanical reliability of silica-based optical fibers declines especially under the combination of applied stresses and severe chemical environment in service. It is of great concern to assess the mechanical reliability and lifetime based on the short-term accelerate testing and the relevant mechanism. The long-term lifetime prediction of optical fibers is sensitive to the form of kinetic model, yet no fair and common agreement has been reached on the best model. This study proposes a generalized lifetime model to search the best model in an expanded model space and hence can reduce model uncertainty. Following that, a procedure using the maximum likelihood estimation and the likelihood ratio test is conducted to determine the model structure. Furthermore, three sets of static fatigue lifetime data are used to illustrate the validity and superiority of the proposed framework. The result demonstrates that the proposed framework can reduce the uncertainty in model choice and is readily applicable to evaluation of static fatigue lifetime of optical fibers.     

A semiparametric Bayesian generalized linear mixed model for the reliability of Kevlar fibers

We analyze the reliability of NASA composite pressure vessels by using a new Bayesian semiparametric model. The data set consists of lifetimes of pressure vessels, wrapped with a Kevlar fiber, grouped by spool, subject to different stress levels; 10% of the data are right censored. The model that we consider is a regression on the log‐scale for the lifetimes, with fixed (stress) and random (spool) effects. The prior of the spool parameters is nonparametric, namely they are a sample from a normalized generalized gamma process, which encompasses the well‐known Dirichlet process. The nonparametric prior is assumed to robustify inferences to misspecification of the parametric prior. Here, this choice of likelihood and prior yields a new Bayesian model in reliability analysis. Via a Bayesian hierarchical approach, it is easy to analyze the reliability of the Kevlar fiber by predicting quantiles of the failure time when a new spool is selected at random from the population of spools. Moreover, for comparative purposes, we review the most interesting frequentist and Bayesian models analyzing this data set. Our credibility intervals of the quantiles of interest for a new random spool are narrower than those derived by previous Bayesian parametric literature, although the predictive goodness‐of‐fit performances are similar. Finally, as an original feature of our model, by means of the discreteness of the random‐effects distribution, we are able to cluster the spools into three different groups. Copyright © 2012 John Wiley & Sons, Ltd.     

A probabilistic model for the Solar System planetary distribution

The discovery of several extrasolar systems, each one characterized by its own planetary distribution around a central star, made the scientific interest addressed to the analysis of models permitting to predict, or at least estimate, the orbital features of the extrasolar planets. The main purpose of this work is to describe a mathematical model, inspired by quantum mechanics, able to provide a probability distribution of planets placing in a star system, mainly driven by the central star mass. More in detail, for any given eigenvalue of the model discrete spectrum, a distinct probability distribution with respect to the central star distance can be built. As per the Solar System, it has been possible to prove that both inner and outer planets belongs to two different spectral sequences, each one originated by the minimum angular momentum owned by silicate/carbonate and icy planetesimals respectively. In both sequences, the peak of the probability distributions almost precisely coincided with the average planets distance from Sun; furthermore, the eigenvalue spectrum of the inner planets thickens in an accumulation point corresponding to the asteroids belt, thus showing a striking similarity to the real matter distribution in the Solar System. From this point of view, the Titius–Bode law for the Solar System planets distribution is nothing but an exponential interpolation of the eigenvalues of both inner and outer sequences.     

Effect of parameters of the distribution of the length and orientation of short fibers on characteristics of the dynamic viscoelasticity of a polymer composite

Conclusion An algorithm for calculating the dynamic viscoelastic characteristics of a composite reinforced with short fibers was developed and realized in the form of a computer program. An analysis was made of the dependence of the characteristics of the composite on the volume content and length of its fibers, as well as on statistical distributions of fiber length and orientation in the material. It was shown that a change in the parameters of the statistical distributions has a significant effect on both the elastic and the dissi-pative properties of the composite. It was found that ignoring the statistical fiber-length distribution might lead to overestimation of the real component of the complex modulus and underestimation of the mechanical loss tangent.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 13–17, January–February, 1990.     

Strength and deformability of reinforced polymers in tension normal to the fibers

The strength and deformability of reinforced polymers in tension across the fibers is investigated. It is assumed that the polymer deforms as an ideal elastoplastic body. Relations are obtained for the nature of the deformation of the polymer between the fibers and the strength and deformability of the composite with allowance for the structural distribution of the components. Theoretical stress-strain diagrams are presented for composites with different reinforcement densities and resin elasticities. The theoretical values of the strength and deformation of reinforced polymers with the load applied across the fibers are compared with the results of experiments on model specimens of epoxy-Thiokol polymers.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 682–687, July–August, 1970.     

Relation between molecular orientation characteristics determined from birefringence and acoustic data and the effect of orientation on the strength of polycaprolactam fibers

The mean molecular orientation calculated from birefringence and acoustic data has been investigated in relation to the degree of stretching for polycaprolactam fiber. A correlation has been found between the characteristics calculated by these two independent methods. It is shown that the molecular orientation factor calculated from the speed of sound does not depend on crystallinity if the measurements are made below the glass transition temperature. It is confirmed that the strength of the fiber depends importantly on the degree of orientation of the molecular segments in the amorphous zones.Mekhanika Polimerov, Vol. 3, No. 1, pp. 3–7, 1967     

A numerical algorithm for simulation of the Q-switched fiber laser using the travelling wave model

We develop a finite-difference scheme for approximation of a system of nonlinear PDEs describing the Q-switching process. We construct it by using staggered grids. The transport equations are approximated along characteristics, and quadratic nonlinear functions are linearized using a special selection of staggered grids. The stability analysis proves that a connection between time and space steps arises only due to approximation requirements in order to follow exactly the directions of characteristics. The convergence analysis of this scheme is done in two steps. First, some estimates of the uniform boundedness of the discrete solution are proved. This part of the analysis is done locally, in some neighborhood of the exact solution. Second, on the basis of the obtained estimates, the main stability inequality is proved. The second-order convergence rate with respect to the space and time coordinates follows from this stability estimate. Using the obtained convergence result, we prove that the local stability analysis in the selected neighborhood of the exact solution is sufficient.