Note related to M. Batista’s “Comment on ‘Explicit solutions in Cartesian coordinates for an elliptic hole in an infinite elastic plate’ by M. Oore and S. Oore”

We thank M. Batista for his valuable contribution [1] to verify the exactness of our solution and his insight to further streamline the approach.

To provide historical context, in our article [2], we achieve the objective of deriving the Cartesian coordinate solutions for an elliptic hole from Inglis’ original multiple-term curvilinear results [3] and show they are consistent with Gao’s [4] general solution. Our results facilitate a trivial solution to the stress field near a crack from which KI is obtained. We find it interesting that the crack stress field solution was “hidden” all along in Inglis’ 1913 elliptic hole solution [3] decades before it was independently and fully developed by others. It is worth mentioning that Inglis’ work on elliptical holes was motivated by the need to understand how cracks affect the strength of materials. This was prompted by his investigation of crack findings in ships.

In summary, our results in Oore and Oore [2] show that the stress field due to a crack can be derived as a special case of Inglis’ elliptical hole solution. It is noted that the solution of a cracked plate under biaxial loading was also calculated by Gao [4] based on his general solution for an elliptic hole.