There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Biofibres and Biocomposites

Permeability of the woven fabrics

The paper investigates feasibility of application of embedded element technique to damage modelling of textile composites on an example of a woven laminate. The geometrical model of yarns is imported to Abaqus form WiseTex software. The yarns and matrix meshes are superimposed using embedded element technique. Damage initiation and development under tensile loading and the resulting stress strain curve is simulated using continuous damage mechanics approach based on Puck damage criterion and Zinoviev-type damage variables. The results show acceptable agreement with the damage modelling based on continuous mesh and with experimental data.

Meso-scale damage modelling of textile composite using the embedded element technique and contact algorithm

Determination of local fibers orientation in composite material from micro-CT data

The paper describes the incorporation of variability of preform permeability data into a mould filling simulation software (PAM-RTM from ESI-group). This implementation allows preventing bad gate and vent locations within more difficult injection set-ups. The input for the statistical parameters of the local permeability scatter is obtained from a large number of permeability measurements [1]. Alternatively, the permeability can also be calculated if the internal textile geometry is known [2,3]. Stochastic input for those textile models is obtained by using micro CT measurements [4]. This geometrical data serves as input for our textile modeling software WiseTex, which provides textile model for permeability calculation software. Assigning permeability values to each element in a finite element model can be done in a totally random way [5]. This approach can lead to very large differences in permeability between neighboring elements. This is not very realistic, because a textile reinforcement can be considered as a continuum hence preform permeability in neighboring points should be correlated. We have implemented this correlation, using the following general approach: 1. Consider local distribution of permeability with an unknown standard deviation sl. 2. Consider a correlation function with an unknown distance parameter a. 3. Run Monte-Carlo simulations of flow through a rectangular preform 4. Identify sl and a for the preform by comparison of results of (3) with a measured scatter of flow parameters. The parameter sl and a will then be used to simulate a distribution of permeability over a 3D shaped preform for a part under consideration. [1] Hoes K. et al, Statistical distribution of permeability values of different porous materials, ECCM 10, 2002 [2] Belov, E.B et al., Modelling of permeability of textile reinforcements: Lattice Boltzmann method, ECCM 10, 2002 [3] Lomov S.V. et al, submitted to SAMPE Europe 2004 [4] Desplentere F. et al, Geometrical characterization of 3-D warp interlaced fabrics, Sampe USA, 2003 [5] Long, et al, Modelling strategies for textile composites, ICCM 14, 2003

Stepan Vladimirovitch Lomov

Papers

Permeability of the woven fabrics

Meso-scale damage modelling of textile composite using the embedded element technique and contact algorithm

Determination of local fibers orientation in composite material from micro-CT data

Mold filling simulations for RTM: influence of the scatter of perform permeability

Correlations between damage initiation thresholds in textile composites and fatigue life limits