{'fraction_non_alphanumeric': 0.026376146788990827, 'fraction_numerical': 0.014908256880733946, 'mean_word_length': 4.898648648648648, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Guided tearing: The ruler test

The physical rules governing the tearing of a packaging or of a piece of paper are not completely elucidated despite being common phenomena in daily life. Here, we investigate how the presence of a straight rigid object, a ruler, guides the fracture of a thin sheet within a wide range of pulling directions. In the case of thin isotropic brittle sheets, a simple geometrical analysis shows that fracture follows the direction of a tearing vector, which differs significantly from the pulling direction. In addition to geometry, bending energy or material anisotropy has to be implemented in the case of thicker or anisotropic sheets, to predict the direction of propagation. A generalization of the Wulff-type construction introduced by Takei et al. [Phys. Rev. Lett. 110, 144301 (2013)] accounts successfully for our experimental results.