By W. Olszak, L. àuklje (eds.)
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This ebook contains lecture notes of a summer time university named after the overdue Jacques Louis Lions. The summer time college used to be designed to alert either Academia and to the expanding function of multidisciplinary equipment and instruments for the layout of advanced items in a variety of components of socio-economic curiosity.
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Extra info for Limit Analysis and Rheological Approach in Soil Mechanics
However, although it is necessary, that locations of the image in the hodograph is such, that c is positive or negative depending on the interval, this is not yet suffIcient. L the case ofinterval (1), where a > 0 and, 13 > O. ) shows, that it is necessary for c to be positive. ) aa + I3b ~ 0 and this implies a ~ - pb/a. Since all three quantities a; 13 ; b are positive in this case, it follows that there exist negative values of a that satisfy c ~ O. as b ~ - a a/13 ,the possibility is shown that also b can be negative.
This is a fallacy, originated by applying indiscriminantly a general principle, valid in mechanics. The general rule in question is, that in an isotropic medium the tensors of strain and incremental stress are coaxial, if there exists an unique functional relationship between the two. Application cf this rule is not allowed in this case, because the rule is no more valid, when a material is in the limit stress state. When a material is in the limit state of stress, strains can develop although stresses remain constant.
Is shown in Fig. 2b and Fig. 2c shows the intersection by the meridional plane. p (17) Z. Mroz and Cz. cctg f) b) \I \,t'