000015161 001__ 15161
000015161 005__ 20161115100213.0
000015161 04107 $$aeng
000015161 046__ $$k2016-08-21
000015161 100__ $$aBerdichevsky, Victor
000015161 24500 $$aThe variational principle for probabilistic measure, Hashin- Shtrikman bounds and beyond

000015161 24630 $$n24.$$p24th International Congress of Theoretical and Applied Mechanics - Book of Papers
000015161 260__ $$bInternational Union of Theoretical and Applied Mechanics, 2016
000015161 506__ $$arestricted
000015161 520__ $$2eng$$aNumerical studies reveal the enormous complexity of local fields in composites with random microstructures. There is no doubt that the local fields can be described adequately only in probabilistic terms. Such description is needed not only for characterization of the state of a composite, but also for prediction of microstructure evolution due to plasticity, fatigue, or fracture, where the path of evolution is controlled by the local fields. At the moment, the probabilistic characteristics of local fields are sought by statistical analysis of a huge number of numerical simulations conducted for different realizations of microstructures. Apparently, a more practical way is desirable. In this talk it is discussed the possibility of using for such purposes the variational principle for probabilistic measure constructed in (Berdichevsky, J. Appl. Math. Mech., 1987). We derive classical results of homogenization theory and obtain statistical characteristics of local fields which were not available previously.

000015161 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000015161 653__ $$a

000015161 7112_ $$a24th International Congress of Theoretical and Applied Mechanics$$cMontreal (CA)$$d2016-08-21 / 2016-08-26$$gICTAM2016
000015161 720__ $$aBerdichevsky, Victor
000015161 8560_ $$ffischerc@itam.cas.cz
000015161 8564_ $$s143201$$uhttps://invenio.itam.cas.cz/record/15161/files/TS.SM04-3.02.pdf$$yOriginal version of the author's contribution as presented on CD,  page 1914, code TS.SM04-3.02
.
000015161 962__ $$r13812
000015161 980__ $$aPAPER