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Numerical simulation of the non‐linear crack problem with non‐penetration
Author(s) -
Kovtunenko Victor A.
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.449
Subject(s) - mathematics , isotropy , quasistatic process , finite element method , mathematical analysis , linear elasticity , numerical analysis , homogeneous , fracture mechanics , stress intensity factor , nonlinear system , structural engineering , materials science , physics , composite material , quantum mechanics , combinatorics , engineering
Here the numerical simulation of some plane Lamé problem with a rectilinear crack under non‐penetration condition is presented. The corresponding solids are assumed to be isotropic and homogeneous as well as bonded. The non‐linear crack problem is formulated as a variational inequality. We use penalty iteration and the finite‐element method to calculate numerically its approximate solution. Applying analytic formulas obtained from shape sensitivity analysis, we calculate then energetic and stress characteristics of the solution, and describe the quasistatic propagation of the crack under linear loading. The results are presented in comparison with the classical, linear crack problem, when interpenetration between the crack faces may occur. Copyright © 2004 John Wiley & Sons, Ltd.