Variational problems of crack equilibrium and crack propagation

  • Khanh Chau Le
Part of the International Centre for Mechanical Sciences book series (CISM, volume 447)


Let us start with the well-known principle of minimum energy in linear elastostatics. For simplicity we restrict ourselves to the 2-D plane strain problems by considering a homogeneous elastic body of cylindrical shape, whose generator is directed along the x 3-axis. Let the cross section of the body occupy a 2-D regular open region B of the (x 1, x 2)-plane, and assume that all quantities we are looking for depend only on x 1 and x 2. The boundary of B, ∂B, is decomposed into two curves ω and τ such that
$$\partial B = {\partial _\omega } \cup {\partial _\tau },{\partial _\omega } \cap {\partial _\tau } = \emptyset $$
The part ω of the boundary is clamped, so the displacement is zero there, while on the remaining part τ the external traction τ is prescribed (see Fig. 1).


Stress Intensity Factor Displacement Field Energy Release Rate Displacement Gradient Dynamic Stress Intensity Factor 
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© Springer-Verlag Wien 2004

Authors and Affiliations

  • Khanh Chau Le
    • 1
  1. 1.Lehrstuhl für Allgemeine MechanikRuhr-Universität BochumBochumGermany

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