Aim. To compare the effect of brushing motion on torsional and cyclic fatigue resistance of TF Adaptive instruments after clinical use. Methods. 20 packs of TFA small sequence (Sybro-nEndo, Orange, CA, USA) were used for this study and divided into two groups. Each instrument prepared one resin tooth, consisting in 4 canals with a complex anatomy. In group A, no brushing motion was performed. In group B, after the green instrument reached the working length, brushing motion with circumferential filing was performed for 15 seconds in each canal (overall 1 minute). All the instruments were then subjected to cyclic fatigue test and mean values and standard deviation for time to fracture were evaluated. Data were subjected to one-way analysis of variance and Bonferroni t-test procedure with a significance set at P < 0.05. Results. No instruments were broken during preparation of root canals. Two TF Adaptive green and 5 yellow showed unwinding after intra-canal clinical use. No statistically significant differences were found between green instruments of both groups (P > 0.05), while a statistically significant difference was found between the yellow instruments (P < 0.05), with group B showing an higher resistance to cyclic fatigue. Conclusions. A prolonged passive brushing motion did not adversely affected mechanical resistance of the instrument used for this purpose. Resistance to both deformations and cyclic fatigue of the second instrument within the TFA small sequence was enhanced by the coronal flaring provided by the brushing action of the first instrument used.
Generalized Standard Materials are governed by maximal cyclically monotone operators and modeled by convex potentials. Géry de Saxcé's Implicit Standard Materials are modeled by biconvex bipotentials. We analyze the intermediate class of n-monotone materials governed by maximal nmonotone operators and modeled by Fitzpatrick's functions. Revisiting the model of elastic materials initiated by Robert Hooke, and insisting on the linearity, coaxiality and monotonicity properties of the constitutive law, we illustrate that Fitzpatrick's representation of n-monotone operators coming from convex analysis provides a constructive method to discover the best bipotential modeling a n-monotone material. Giving up the symmetry of the linear constitutive laws, we find out that n-monotonicity is a relevant criterion for the materials characterization and classification.2000 Mathematics Subject Classification. Primary: 74D10 and 47H05 and Secondary: 47H04.
Eine Verallgemeinerung der Hypothese der normalen Dissipation wurde von de Saxcé durch die Einführung des Bipotentials erreicht. In diesem Beitrag werden einige mathematische Eigenschaften des Bipotentials untersucht.
A new formulation of the constitutive law of materials based on the concept of bipotential was introduced by de Saxcé. This concept is able to describe non‐associated laws and to suggest robust numerical algorithms. Materials that admit a bipotential to model their behaviour constitute the class of Implicit Standard Materials (ISM). This class contains, as a sub‐class, the Generalized Standard Materials (GSM). In this paper, we present a bipotential expressing the coaxiality of two tensors with preservation of the order of the eigenvalues. We call it Hill's bipotential. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
In this paper, we constructed relationships with the differents 2D elasticity tensor invariants. Indeed, let ${\bf A}$ be a 2D elasticity tensor. Rotation group action leads to a pair of Lax in linear elasticity. This pair of Lax leads to five independent invariants chosen among six. The definite positive criteria are established with the determined invariants. We believe that this approach finds interesting applications, as in the one of elastic material classification or approaches in orbit space description.
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