The fracture mechanics community may be interested in a new evaluation of a J-Integral for a fundamental geometry: an elliptical hole in a perfectly plastic material under the Tresca yield condition for plane stress loading conditions. The analysis is exact and involves only elementary functions. This makes the problem suitable as a classroom example or as a homework problem for a graduate level course in fracture mechanics. See J. Elasticity (2008) 92:217-226. http://www.springerlink.com/content/102932/
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nonproportional loading
A large deformation extension of this particular elliptical hole problem by the author has been published in the Journal of Elasticity, 99, 117-130 (2010). To the best of the author’s knowledge this is the first analytical nonproportional plasticity solution to a crack problem.