Consistency Checks for Power-Law Calibration Functions
SourceRecently, considerable numerical effort has been devoted to obtaining solutions to crack problems in incompressible J2 deformation theory materials of pure power-law type (ε ∞ σn). Following Il'yushin's observation of the scalability of such solutions, many investigators have conducted broad parametric studies on crack length and material exponent, and have tabulated normalized J and deformation magnitudes. Due to numerical difficulties such as slow convergence, incompressibility, or inadequate finite-element mesh refinement, the solutions do not always agree.
We outline the basis for a very stringent general test of the “quality” of proposed solutions by applying the well-known equivalence of J and energy difference rate with respect to crack length.
The test is applied to data available in the literature, and conclusions are drawn as to their accuracy.