When a solid element is subjected to large deformations, the components of stress will vary as a result of material rotation. These changes need to be accounted for in formulating constitutive laws that involve the rate of change of stress. To formulate the Flow Element Method (FLEM), two coordinate systems are defined: global and local. The global system is prepared to describe displacements of nodes. A set of local coordinates contributes, in the global system, to evaluate correction terms. The results of a numerical application to a two-dimensional elastic block are shown, with potential application to a wide range of large deformation problems.
Quand un element solide subit la deformation grande, une rotation materiale entraîne une variation dell composants du tenseur des contraintes. Il est neccessaire de compter la variation dans la loi de comportement qui envolve la vitesse de changement du tenseur des contraintes. Pour la formulation de la Methode des Élementes Flottants (FLEM), duex systemes des coordonnees sont definis: global et local. Le systeme global est prepare à decrire les deplacements des nodes. Le systeme locale contribue, dans Ie systeme global, à calculer le terme de modification du tenseur des contraintes. Le resultat de l'application numerique au bloc elastique est presente avec l'applicabilite potential pour beauc~up de sortes de problemes subitant Ie cisallement grand.
Wenn ein Festkörper große Verformungen erfahrt, werden sich die Spannungskomponenten im allgemeinen als Folge der Materialrotation andern, Diese Veranderungen muessen bei der Formulierung der Zustandsgleichungen, welche die Rate der Spannungsandenmg beruecksichtigen. in Betracht gezogen werden. Zwei Systeme der Koordinaten warden gedefiniert: global und örtlish, fuer die Formuleirung der Fließ-Elemente-Methode (FLEM). Das globale System wird gevorbereit fuer die Beschreibung der Verschiebungen der Knoten. Das System der örtlishen Koordinaten, in dem globalen System, tragt das Korreckturglieder zu beruecksichtigen bei. Die numerischen Forgen eines elastischen Block werden gezeigt mit der potenten Auwendung fuer einen breite Breich der Probleme einer große Scherverformung.
In recent years, a number of numerical methods for the analysis of engineering problems have been developed. One of the most important components of these methods is the mathematical description of a relationship between stress and strain. Failures of rocks often result from shear bands, i.e. zones of localized shear deformation, where large deformations, including rotation, occur. Experimental observations demonstrate effects of the generations of shear bands on mechanical behaviors of rocks. In analyzing such problems, numerical methods should be formulated within the framework of large deformation theories. This is done by introduction of a rate-type constitutive relation in terms of an objective stress rate, which is invariant to rigid body rotations.
This paper describes a practical formulation of Flow Element Method (FLEM) (Kiyarna, H. et al., 1991) for large deformation analysis of continua. The basic idea of this numerical method has originated from the principle of Distinct Element Method (DEM) (Cundall, PA, 1971). The equation of motion is the governing expression for displacements of nodes, The explicit time-marching scheme of DEM is adopted to solve the equation.
