@article{1126.74040,
author="Hinterm\"uller, M. and Kovtunenko, V.A. and Kunisch, K.",
title="{Constrained optimization for interface cracks in composite materials
    subject to non-penetration conditions.}",
language="English",
journal="J. Eng. Math. ",
volume="59",
number="3",
pages="301-321",
year="2007",
doi={10.1007/s10665-006-9113-7},
abstract="{Summary: A constrained problem for a composite material with an
    interface crack subject to non-penetration conditions is considered. The
    response of a composite consisting of two identical homogeneous orthotropic
    materials is described with respect to in-plane deformation. The coupling of
    the materials occurs at an interface with angle between their vertical
    planes of elastic symmetry. The model is not split into independent in-plane
    and anti-plane states. Well-posedness of the problem is proved by
    variational methods. For numerical computations, a semi-smooth Newton method
    is proposed and its convergence is studied. Using the proposed algorithms,
    numerical experiments for an interface crack under mode-3 loading are
    presented and analyzed with respect to the half-angle defining the
    coupling.}",
keywords="{semi-smooth Newton methods; variational methods; mode-3 loading}",
classmath="{*74R10 (Brittle fracture)
74E30 (Composite and mixture properties)
74G65 (Energy minimization)
}",
}