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Numerical Solution of Integro-Differential Equations Modelling the Dynamic Behavior of a Nano-Cracked Viscoelastic Half-Plane Cover

Numerical Solution of Integro-Differential Equations Modelling the Dynamic Behavior of a Nano-Cracked Viscoelastic Half-Plane

Open Access
|Dec 2020

References

  1. 1. Arroyo, M. T. V., T. Belytschkho. An Atomistic-Based Finite Deformation Membrane for Single Layer Crystalline Films. – J. Mech. Phys. Solids, Vol. 50, 2002, pp. 1941-1977.10.1016/S0022-5096(02)00002-9
  2. 2. Dineva, P. S., T. Rangelov. Wave Scattering by Cracks at Macro- and Nano-Scale in Anisotropic Plane by BIEM. – J. Theor. Appl. Mech., Vol. 46, 2016, No 4, pp. 19-35.10.1515/jtam-2016-0019
  3. 3. Dong, C. Y., E. Pan. Boundary Element Analysis of Inhomogeneities of Arbitrary Shapes with Surface and Interface Effects. – Eng. Anal. Bound. Elem., Vol. 35, 2011, pp. 996-1002.10.1016/j.enganabound.2011.03.004
  4. 4. Gradshteyn, I. S., I. M. Ryzhik. Tables of Integrals, Series, and Products. New York, Academic Press, 1965.
  5. 5. Gurtin, M. E., A. I. Murdoch. A Continuum Theory of Elastic Material Surfaces. – Arch. Ration. Mech. Anal., Vol. 57, 1975, pp. 291-323.10.1007/BF00261375
  6. 6. MATHEMATIKA. Champaign, Illinois, Wolfram Research, 1987.
  7. 7. Mainardi, F. Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. London, UK, Imperial College Press, 2010.10.1142/p614
  8. 8. Makrou, A. A., G. D. Manolis. A Fractional Derivative Zener Model for the Numerical Simulation of Base Isolated Structures. – Bull. Earthquake Eng., Vol. 14, 2016, No 1, pp. 283-295.10.1007/s10518-015-9801-7
  9. 9. Manolis, G. D., P. S. Dineva, T. V. Rangelov, F. Wuttke. Seismic Wave Propagation in Non-Homogeneous Elastic Media by Boundary Elements. – In: Solid Mechanics and Its Applications. Vol. 240. Cham, Switzerland, Springer International Publishers, 2017.10.1007/978-3-319-45206-7
  10. 10. Rangelov, T. V., P. S. Dineva. Dynamic Fracture Behavior of a Nano-Crack in a Piezoelectric Plane. – ZAMM, Z. Angew. Math. Mech., Vol. 97, 2017, No 11, pp. 1393-1405.10.1002/zamm.201700072
  11. 11. Rangelov, T. V., P. S. Dineva, G. D. Manolis. BIEM Analysis of a Graded Nano-Cracked Elastic Half-Plane under Time-Harmonic Waves. – ZAMM, Vol. 100, 2020, 100:e202000021. https://doi.org/10.1002/zamm.20200002110.1002/zamm.202000021
  12. 12. Rangelov, T. V., P. S. Dineva, G. D. Manolis. Dynamic Response of a Cracked Viscoelastic Anisotropic Plane Using Boundary Elements and Fractional Derivatives. – J. Theor. Appl. Mech., Vol. 48, 2018, No 2, pp. 24-49.10.2478/jtam-2018-0009
  13. 13. Rangelov, T. V., G. D. Manolis. Time-Harmonic Elastodynamic Green’s Function for the Half-Plane Modelled by a Restricted Inhomogeneity of Quadratic Type. – J. Mech. Mater. Strut., Vol. 5, 2010, No 6, pp. 909-924.10.2140/jomms.2010.5.909
  14. 14. Schanz, M. Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach. Lecture Notes in Applied Mechanics. Vol. 2. Berlin, Springer, 2001.10.1007/978-3-540-44575-3
  15. 15. Sharma, P., S. Ganti, N. Bhate. Effect of Surfaces on the Size-Dependent Elastic State of Nano-Inhomogeneities. – Appl. Phys. Lett., Vol. 82, 2003, pp. 535-537.10.1063/1.1539929
DOI: https://doi.org/10.2478/cait-2020-0065 | Journal eISSN: 1314-4081 | Journal ISSN: 1311-9702
Language: English
Page range: 105 - 115
Submitted on: Sep 15, 2020
Accepted on: Oct 30, 2020
Published on: Dec 31, 2020
Published by: Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2020 Tsviatko V. Rangelov, Petia S. Dineva, George D. Manolis, published by Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.