A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics

Abstract Introducing a crack in an elastic plate is challenging from the mathematical point of view and relevant within engineering context evaluating strength reliability structures. Accordingly, multitude associated works available to date, emanating both applied mathematics mechanics communities. Although considering same problem, given complex potentials prove be different, revealing various inconsistencies terms resulting stresses displacements. Essential information on near-tip fields opening displacements nonetheless available, while intuitive adaption required obtain full-field solutions. Investigating cause prevailing deficiencies inevitably leads critical review classical by Muskhelishvili or Westergaard. Complex mixed-mode loaded Griffith crack, sparing restrictive assumptions limitations validity, are finally provided, allowing for rigorous treatment. The entity whole illustrated distributions plane explicitly.