Impact cracks

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Impact cracks

Postby gonegahgah » Thu Apr 08, 2021 10:31 am

If you hit glass it radially cracks but if you hit a concrete post it forms a line crack perpendicular to the length (probably naturally due to the alignment of the materials).

Just curious how cracks would travel in 4D materials?
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Re: Impact cracks

Postby 개구리 » Thu Apr 08, 2021 4:21 pm

nD objects will preferentially crack along n-1D facets with the least curvature. I understand this as the curved dimensions wanting to "straighten out" under stress and thus pulling apart the surface along straight dimensions. Cracks propagate symmetrically on the square faces of the cube and the curved "face" of the sphere because both have no dimension more curved than the other. In the case of cubes and other polyhedra, there is no facial curvature at all. Cylinders will crack symmetrically on their disk caps but will prefer to crack along their lengths on the curved face. Similarly, in 4D the spherinder will crack symmetrically on its ball caps but will prefer to crack along its length on the curved cell. The same can be said for the torinder. The tesseract and other polychora, as well as the glome and the duocylinder, will crack symmetrically, because they have no least-curved cell. The cubinder, and other prisminders, will prefer to crack along their "circumferences", on their cylindrical cells.

This all ignores special behavior around edges/ridges and vertices, and assumes the materials are homogenous and anisotropic.
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