Issue 33

M.A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 33 (2015) 368-375; DOI: 10.3221/IGF-ESIS.33.40 372 Figure 4 : Hyper-sphere translations along 1 i i n n     , caused by the path 1 1 i i i P P P      . Dynamic filtering eliminates i P  because it does not alter the translation direction. The initial locations 1 P  of the peg and 1 O  of the hyper-sphere center must coincide with the first loading point from the load history in the 6D stress or strain space. As seen in Fig. 5(a), no hyper-sphere translation happens while the peg moves inside it, therefore points 2 P  through 1 i P   are filtered out, in a process called static filtering (because it does not involve hyper-sphere translations). When the peg reaches for the first time the hyper-sphere border and tries to move outside it, the translation direction i n  must be defined. A simple translation direction rule assumes here that i n  is determined from the segment that joins the current hyper-sphere center i O  and the next peg location 1 i P   , i.e. 1 ( ) i i i i n P O b       , see Fig. 5(a). Other improved rules for the translation direction of the hyper-sphere center could be defined. Figure 5 : Hyper-surface location (a) during its first translation and (b) during a load kinking. In summary, static filtering happens while the next peg location 1 i P   is not outside the current hyper-sphere, i.e. b i  r in Fig. 3, while dynamic filtering happens during hyper-sphere translations where b i > r , a i  0 , and d i  r . Besides the initial 1 P  , the only points that are not filtered out are the ones where some significant path kinking happens due to d i > r , and the ones where a load “reversal” forces a change of more than 90 o in the hyper-surface translation direction, i.e. 1 0 i i n n      and therefore a i < 0 . In these kinking or reversal cases, the new hyper-surface translation direction could be determined by the simple rule 1 ( ) i i i i n P O b       .