Problem of crack perturbation based on level sets and velocities | Zendy

Kovtunenko V.A. | Zendy; Kunisch K. | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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

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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research