Addressing bar_COHESIVE_linear Issue on MAC

In the bar_COHESIVE_linear phase-field benchmark, an issue has been encountered on certain operating systems, such as macOS running on Apple processors like M1, resulting in (sporadical) ctest failures. However, successful execution has been observed on other operating systems, including most Linux, Windows, and Mac systems with Intel processors.

In this benchmark, a bar is subjected to tensile loading, and the anticipated physical behavior involves fracture nucleation at the center of the bar. However, the observed results indicate that, in the bar benchmarks, fracture tends to propagate along a row of elements (resulting in a plane with mesh size thickness or slab) instead of a row of nodes (resulting in a zero-thickness plane).

This discrepancy arises from the even number of elements (100 elements in x direction) in the direction of tensile loading in the previous mesh, which led to the absence of a row of elements precisely at the center of the bar. Consequently, the phase field sometimes nucleated at the nearest right row of elements to the center line and in other cases selected the left one, resulting in ctest failures. This challenge is attributed to the non-convex nature of the total energy functional concerning the unknowns (phase field and displacement).

To address this issue in the bar benchmark, we have modified the mesh to ensure the presence of a row of elements at the center line of the bar (101 elements in x direction). The results demonstrate that most operating systems can now reproduce consistent outcomes.