Vector level sets for description of propagating cracks in finite elements.

*(English)*Zbl 1032.74687Summary: A new level set method is developed for describing surfaces that are frozen behind a moving front, such as cracks. In this formulation, the level set is described in two dimensions by a three-tuple: the sign of the level set function and the components of the closest point projection to the surface. The update of the level set is constructed by geometric formulas, which are easily implemented. Results are given for growth of lines in two dimensions that show the method is very accurate. The method combines very naturally with the extended finite element method (XFEM) where the discontinuous enrichment for cracks is best described in terms of level set functions. Examples of crack growth simulations obtained by combining this level set method with the extended finite element method are given.

##### Keywords:

finite elements; crack propagation; fracture; vector level sets; extended finite elements; enriched finite elements
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\textit{G. Ventura} et al., Int. J. Numer. Methods Eng. 58, No. 10, 1571--1592 (2003; Zbl 1032.74687)

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