By Marcin Marek Kaminski

Computational Mechanics of Composite Materials lays pressure at the merits of mixing theoretical developments in utilized arithmetic and mechanics with the probabilistic method of experimental info in assembly the sensible wishes of engineers.



Programs for the probabilistic homogenisation of composite constructions with finite numbers of parts let composites to be handled as homogeneous fabrics with less complicated behaviours. 

Treatment of defects within the interfaces inside of heterogeneous fabrics and people bobbing up in composite gadgets as an entire through stochastic modelling. 

New types for the reliability of composite structures.


Novel numerical algorithms for powerful Monte-Carlo simulation.

Computational Mechanics of Composite Materials might be of curiosity to educational and training civil, mechanical, digital and aerospatial engineers, to fabrics scientists and to utilized mathematicians requiring actual and usable types of the behaviour of composite materials.

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Extra info for Computational Mechanics of Composite Materials: Sensitivity, Randomness, and Multiscale Behaviour

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The closed form probabilistic moments of the homogenised tensor make it possible to derive explicitly the sensitivity gradients with respect to the expected values and standard deviations of the original material properties of a composite. Probabilistic methods in homogenisation [116,120,141,146,259,287,378] obey (a) algebraic derivation of the effective properties, (b) Monte-Carlo simulation of the effective tensor, (c) Voronoi-tesselations of the RVE together with the relevant FEM studies, (d) the moving-window technique.

The alternative stochastic second order approach to the cell problem solution, where the SFEM analysis should be applied to calculate the effective characteristics, is displayed below. Various effective elastic characteristics models proposed in the literature are extended below using the stochastic perturbation technique and verified numerically with respect to probabilistic material parameters of the composite components. The entire homogenisation methodology is illustrated with computational examples of the two-component heterogeneous bar, fibre-reinforced and layered unidirectional composites as well as the heterogeneous plate.

All non-homogeneities introduced are divided into two groups: the stochastic interface defects (SID), which have non-zero intersections with the interface boundaries, and the volumetric stochastic defects (VSD) having no common part with any interface or external composite boundary. Further, the interphases are deterministically 36 Computational Mechanics of Composite Materials constructed around all interface boundaries using probabilistic bounds of geometric dimensions of the SID considered. Finally, the stochastic geometry is replaced by random elastic characteristics of composite constituents thanks to a probabilistic modification of the spatial averaging method (PAM).

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