{'fraction_non_alphanumeric': 0.013528748590755355, 'fraction_numerical': 0.0, 'mean_word_length': 5.481751824817518, '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}}
Gradient Elasticity Theory for a Mode III Crack in a Functionally Graded Material

Anisotropic strain gradient elasticity theory is applied to the solution of a mode III crack in a functionally graded material (FGM). The theory includes both volumetric and surface energy terms, and a particular form of the moduli variation. The crack boundary value problem is solved by means of Fourier transform and a hypersingular integral equation of the Fredholm type. The solution naturally leads to a cusping crack, which is consisteut with Barenblatt's cohesive zone theory, but without the assmuption regarding existence of interatomic forces. The numerical implementation is discussed and examples are given, which provide insight into the cracking phenomenon in FGMs governed by strain gradient elasticity with characteristic lengths associated to volumetric and surface strain energy terms.