This question deserves to be posed and clarified. It is at this price that we will be able to consider an improvement involving analyses including new concepts. The answer to this question is given below.
YES, FRACTURE MECHANICS IS BEAUTIFULLY COMPLETED. It has been suggested and demonstrated that a crack in an elastic loaded solid in the framework of elasticity may be viewed as a continuous distribution of infinitesimal dislocations (For a review, see Bilby and Eshelby, 1968). These authors provide an expression for G, the crack extension force per unit length of the crack front (or energy release rate), for steady motion. G is sum of terms that are products of stresses and values of the relative displacement of the faces of the crack at the tip of the crack. We find in recent works (Anongba, 2021 and 2022) that for a dislocation in the form of an arbitrary closed loop, there exists only one singularity in the dislocation stress fields, when calculating G. This singularity is of the Cauchy type: i.e., 1 / │r - r0│; r the position in the medium and r0 the position on the dislocation, where G is evaluated for instance. These are terms involving that singularity which contribute a non-zero value to G. All the other additional terms in the dislocation stress fields are bounded and contribute nothing. G can be calculated successfully (analytically) for any arbitrary closed forms of the crack front. In this sense, we may say that Fracture Mechanics is completed. Experiments would provide the accuracy of the various physical quantities involved in the mathematical results.
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