Abstract
The eight noded quarter-point Serendipity quadrilateral isoparametric element is reexamined. The stresses are proven to be square-root singular on all rays in a small region adjacent to the crack tip and, as was previously shown, along the element sides. It is demonstrated that the element strain energy, and hence its stiffness, is bounded. The effect of element size in characterizing the square-root singular behavior is investigated through stress intensity factor calculations in the case of two geometries with crack tip elements of various dimensions. Workers in the field of fracture mechanics may now, without hesitation, employ this element for modeling crack tip singularities in linear elastic material.
Résumé
On réexamine la validité d'un élément quadrilatère isoparamétrique à huit noeuds quart-point de Serendipity. On prouve que les contraintes présentent une singularité du deuxième ordre sur tous les rayons situés dans une petite région adjacente à l'extrémité de la fissure et, comme on l'a montré précédemment, le long des bords de l'élément. On démontre que l'énergie de déformation de l'élément, et donc sa rigidité, est limitée. On étudie l'effet de la taille de l'élément sur la caractérisation de la singularité du deuxième ordre, en calculant le facteur d'intensité d'entaille dans le cas de deux géométries présentant des éléments de dimensions différentes à l'extrémité d'une fissure. Les spécialistes en mécanique de la rupture peuvent à présent, sans hésitation, utiliser cet élément pour modéliser les singularités qui se présentent à l'extrémité d'une fissure dans un matériau linéaire et élastique.
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Banks-Sills, L., Bortman, Y. Reappraisal of the quarter-point quadrilateral element in linear elastic fracture mechanics. Int J Fract 25, 169–180 (1984). https://doi.org/10.1007/BF01140835
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DOI: https://doi.org/10.1007/BF01140835