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Problem of crack perturbation based on level sets and velocities
Author(s) -
Kovtunenko V.A.,
Kunisch K.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510354
Subject(s) - perturbation (astronomy) , coordinate system , mathematical analysis , mathematics , transformation (genetics) , penetration (warfare) , geometry , physics , biochemistry , chemistry , quantum mechanics , operations research , gene
Abstract We describe cracks with the help of a given velocity as zero‐level sets of a non‐negative function satisfying a transport equation. For smooth velocities this description is equivalent to the coordinate transformation of a domain containing the crack inside. Analytical examples of cracks described by smooth as well as discontinuous velocities are presented in 2D and 3D domains. Based on a level‐set formulation we consider the crack perturbation problem subject to a non‐penetration condition and derive the formula for the shape derivative.