# Variational problems of crack equilibrium and crack propagation

Chapter

## Abstract

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
The part

*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$$\partial B = {\partial _\omega } \cup {\partial _\tau },{\partial _\omega } \cap {\partial _\tau } = \emptyset $$

*∂*_{ 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).## Keywords

Stress Intensity Factor Displacement Field Energy Release Rate Displacement Gradient Dynamic Stress Intensity Factor
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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