Non-singular solutions of GradEla models for dislocations: An extension to fractional GradEla

References

• Aifantis, E. C. [1992] “ On the role of gradients in the localization of deformation and fracture,” International Journal of Engineering Science 10, 1279–1299. Crossref, Google Scholar
• Aifantis, E. C. [2011] “ A note on gradient elasticity and non-singular crack fields,” Journal of Mechanical Behavior of Materials 20, 103–105. Crossref, Google Scholar
• Aifantis, E. C. [2011] “ Gradient Nanomechanics: Applications to deformation, fracture, and diffusion in nanopolycrystals,” Metallurgical and Materials Transactions A 42, 2985–2998. Crossref, Google Scholar
• Aifantis, E. C. [2014] “ On non-singular GRADELA crack fields,” Theoretical and Applied Mechanics Letters 4, 051005. Crossref, Google Scholar
• Aifantis, E. C. [2016] “ Internal length gradient (ILG) material mechanics across scales & disciplines,” Advances in Applied Mechanics 49, 1–110. Crossref, Google Scholar
• Aifantis, E. C. [2019] “ Fractional generalizations of gradient mechanics,” Handbook of Fractional Calculus with Applications (De Gruyter, Berlin) in press. Crossref, Google Scholar
• Erdelyi, A. [1954] Higher Transcendental Functions, Vol. 1 (McGraw Hill, New York). Google Scholar
• Eringen, A. C. [1983] “ On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” Journal of Applied Physics 54, 4703–4710. Crossref, Google Scholar
• Gradshteyn, I. M. Ryzhik [2007] Tables of Integrals, Series and Products, 7th edn. (Academic Press, New York). Google Scholar
• Gutkin, M. Yu. and Aifantis, E. C. [1996] “ Screw dislocation in gradient elasticity,” Scripta Materialia 35, 1353–1358. Crossref, Google Scholar
• Gutkin, M. Yu. and Aifantis, E. C. [1997] “ Edge dislocation in gradient elasticity,” Scripta Materialia 36, 129–135. Crossref, Google Scholar
• Gutkin, M. Yu. and Aifantis, E. C. [1999] “ Dislocations and disclinations in gradient elasticity,” Physica Status Solidi (b) 214, 245–284. Crossref, Google Scholar
• Isaksson, P. [2014] “ Approximation of mode I crack-tip displacement fields by a gradient enhanced elasticity theory,” Engineering Fracture Mechanics 117, 1–11. Crossref, Google Scholar
• Konstantopoulos, I. and Aifantis, E. C. [2013] “ Gradient elasticity applied to a crack,” Journal of Mechanical Behavior of Materials 22, 193–201. Crossref, Google Scholar
• Konstantopoulos, I. [2012] “Dislocations and cracks in gradient elasticity,” PhD Thesis. Aristotle University of Thessaloniki (in Greek). Google Scholar
• Lazar, M. and Maugin, G. [2005] “ Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity,” International Journal of Engineering Science 43, 1157–1184. Crossref, Google Scholar
• Lazar, M. and Maugin, G. [2006] “ Dislocations in gradient elasticity revisited,” Proceedings of Royal Society A 462, 3465–3480. Crossref, Google Scholar
• Lazar, M. and Polyzos, D. [2015] “ On non-singular crack fields in Helmholtz type enriched elasticity theories,” International Journal of Solids Structures 62, 1–7. Crossref, Google Scholar
• Lazar, M., Maugin, G. and Aifantis, E. C. [2005] “ On dislocations in a special class of generalized elasticity,” Physica Status Solidi (b) 242, 2365–2390. Crossref, Google Scholar
• Lazar, M. [2003] “ A non-singular solution of the edge dislocation in the gauge theory of dislocations,” Journal of Physics A: Mathematics and General 36, 1415–1437. Crossref, Google Scholar
• Lazar, M. [2012] “ Non-singular dislocation loops in gradient elasticity,” Physics Letters A 376, 1757–1758. Crossref, Google Scholar
• Lazar, M. [2013] “ The fundamentals of non-singular dislocations in the theory of gradient elasticity: Dislocation loops and straight dislocations,” International Journal of Solids Structures 50, 352–362. Crossref, Google Scholar
• Mindlin, R. [1964] “ Micro-structure in linear elasticity,” Archive for Rational Mechanics and Analysis 16, 52–78. Crossref, Google Scholar
• Mousavi, S. M. and Aifantis, E. C. [2015] “ A note on dislocation-based mode III gradient elastic fracture mechanics,” Journal of Mechanical Behavior Materials 20, 115–119. Crossref, Google Scholar
• Mousavi, S. M. and Aifantis, E. C. [2016] “ Dislocation-based gradient elastic fracture mechanics for in-plane analysis of cracks,” International Journal of Fracture 202, 93–110. Crossref, Google Scholar
• Mousavi, S. M. and Lazar, M. [2015] “ Distributed dislocation technique for cracks based on non-singular dislocations in nonlocal elasticity of Helmholtz type,” Engineering Fracture Mechanics 136, 79–95. Crossref, Google Scholar
• Po, G., Lazar, M., Seif, D. and Ghoniem, N. [2014] “ Singularity-free dislocation dynamics with strain gradient elasticity,” Journal Mechanics and Physics of Solids 68, 161–178. Crossref, Google Scholar
• Ru, C. Q. and Aifantis, E. C. [1993] “ A simple approach to solve boundary-value problems in gradient elasticity,” Acta Mechanica 101, 59–68. Crossref, Google Scholar
• Samko, S., Kilbas, A. and Marichev, O. [1993] Integrals and Derivatives of Fractional Order and Applications (Gordon and Breach, New York). Google Scholar
• Sneddon, I. N. [1951] Fourier Transforms (McGraw-Hill, New York). Google Scholar
• Tarasov, V. and Aifantis, E. C. [2014] “ Toward fractional gradient elasticity,” Journal of Mechanical Behavior Materials 23, 41–46. Crossref, Google Scholar
• Tarasov, V. and Aifantis, E. C. [2015] “ Non-standard extensions of gradient elasticity: Fractional non-locality, memory and fractality,” Communications in Nonlinear Science and Numerical Simulattion 22, 197–227. Crossref, Google Scholar