Journal of Theoretical and Applied Mechanics, Sofia, Vol.48 No.2 (2018) pp. 24-49 DOI: 10.2478/jtam-2018-0009 DYNAMIC RESPONSE OF A CRACKED VISCOELASTIC ANISOTROPIC PLANE USING BOUNDARY ELEMENTS AND FRACTIONAL DERIVATIVES TSVIATKO V. RANGELOV 1∗ ,PETIA S. DINEVA 2 , GEORGE D. MANOLIS 3 1 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria 2 Institute of Mechanics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria 3 Department of Civil Engineering, Aristotle University, Thessaloniki, GR-54124, Greece [Received 31 October 2017. Accepted 11 January 2018] ABSTRACT: The aim of this study is to develop an efficient numerical tech- nique using the non-hypersingular, traction boundary integral equation method (BIEM) for solving wave propagation problems in an anisotropic, viscoelastic plane with cracks. The methodology can be extended from the macro-scale with certain modifications to the nano-scale. Furthermore, the proposed ap- proach can be applied to any type of anisotropic material insofar as the BIEM formulation is based on the fundamental solution of the governing wave equa- tion derived for the case of general anisotropy. The following examples are solved: (i) a straight crack in a viscoelastic orthotropic plane, and (ii) a blunt nano-crack inside a material of the same type. The mathematical modelling effort starts from linear fracture mechanics, and adds the fractional derivative concept for viscoelastic wave propagation, plus the surface elasticity model of M. E. Gurtin and A. I. Murdoch, which leads to nonclassical boundary condi- tions at the nano-scale. Conditions of plane strain are assumed to hold. Follow- ing verification of the numerical scheme through comparison studies, further numerical simulations serve to investigate the dependence of the stress inten- sity factor (SIF) and of the stress concentration factor (SCF) that develop in a cracked inhomogeneous plane on (i) the degree of anisotropy, (ii) the pres- ence of viscoelasticity, (iii) the size effect with the associated surface elasticity phenomena, and (iv) finally the type of the dynamic disturbance propagating through the bulk material. KEY WORDS: In-plane waves, viscoelasticity, fractional derivatives, anisotropy, cracks, nano-scale, surface elasticity, boundary elements, SIF, SCF. * Corresponding author e-mail: rangelov@math.bas.bg