期刊
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
卷 83, 期 7, 页码 929-954出版社
ELSEVIER
DOI: 10.1016/j.matpur.2004.02.004
关键词
functions with bounded deformation; free discontinuity problems; brittle fracture
A special displacement with bounded deformation is a function u: Omega subset of R-N --> R-N whose symmetrized gradient is a bounded measure which coincides, outside a (N - 1)-dimensional rectifiable jump set J(u), with a summable function e(u). We show that in dimension N = 2, when u and e(u) are square integrable, and the total length H-1 (J(u)) is finite, then such a displacement is approximated with a sequence (u(n))(ngreater than or equal to1) of piecewise continuous displacements whose jump sets J(un) are (relatively) closed, with u(n) and e(u(n)) converging strongly in L-2, respectively to u and e(u), and the lengths H-1(J(un)) converging to H-1 (J(u)). As an application, we approximate with a sequence of elliptic functionals a functional which appears in the theory of brittle fracture in linearized elasticity. (C) 2004 Elsevier SAS. All rights reserved.
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