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Dynamic fracture behavior of nanocracked graded magnetoelectroelastic solid

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Abstract

Time-harmonic SH-wave scattering by a nanocrack in a continuously inhomogeneous magnetoelectroelastic (MEE) plane with exponentially dependent material parameters and under conditions of anti-plane strain is studied. A non-hypersingular, traction-based boundary integral equation method (BIEM) for solution of the problem under consideration is presented. The BIEM formulation combines classical elastodynamic theory for the graded bulk MEE solid with non-classical boundary conditions and the localized constitutive law for the MEE matrix–nanocrack interface within the framework of the Gurtin–Murdoch theory. The presented parametric study reveals the degree of dependence of the dynamic fracture characteristics on the size of the nanocrack, surface and bulk material properties, coupled nature of the magnetoeletroelasticity, properties of the incident wave as frequency, wave length and wave propagation direction, dynamic interaction between the nanocrack, incident wave and coupled magneto-electro-elastic graded continuum.

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References

  1. Chatzigeorgiou, G., Javili, A., Steinmann, P.: Surface magnetoelasticity theory. Arch. Appl. Mech. 85, 1265–1288 (2015)

    MATH  Google Scholar 

  2. Wang, S., Yang, H., Gao, C., Chen, Z.: In-plane stress analysis of two nanoscale holes under surface tension. Arch. Appl. Mech. 90, 1363–1372 (2020)

    Google Scholar 

  3. Wang, M., Ye, W.: Size-dependent elastic field of nano-inhomogeneity: from interface effect to interphase effect. Arch. Appl. Mech. 90, 1319–1333 (2020)

    Google Scholar 

  4. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A., Ford, R.G.: Functionally Graded Materials. Processing and Applications, Design. Kluwer Academic Publishers, London (1999)

    Google Scholar 

  5. Manolis, G.D., Dineva, P.S., Rangelov, T.V., Wuttke, F.: Seismic Wave Propagation in Non-homogeneous Elastic Media by Boundary Elements. Solid Mechanics and its Applications, vol. 240. Springer, London (2017)

    MATH  Google Scholar 

  6. Dineva, P., Marinov, M., Rangelov, T.: Dynamic fracture of a nano-cracked finite exponentially inhomogeneous piezoelectric solid. Arch. Appl. Mech. 89, 1317–1332 (2019)

    MATH  Google Scholar 

  7. Dineva, P., Gross, D., Müller, R., Rangelov, T.: Dynamic Fracture of Piezoelectric Materials. Solutions of Time-Harmonic Problems via BIEM. Solid Mechanics and Its Applications, vol. 212. Springer, London (2014)

    Google Scholar 

  8. Robertson, H.D., Brenner, D.W., Mintmire, J.: Energetics of nanoscale graphitic tubules. Phys. Rev. B 45(21), 12592–12595 (1992)

    Google Scholar 

  9. Garg, A., Sinnott, S.B.: Effect of chemical functionalization on the mechanical properties of carbon nanotubes. Chem. Phys. Lett. 295, 273–278 (1998)

    Google Scholar 

  10. Bao, H., Huang, Y., Yang, Z., Sun, Y., Bai, Y., Miao, Y., Chu, P., Xu, K., Ma, F.: Molecular dynamics simulation of nanocrack propagation in single-layer MoS2 nanosheets. J. Phys. Chemistry C. 122(2), 1 (2018)

    Google Scholar 

  11. Thai, H.T., Vo, T.P., Nguyen, T.K., Kim, S.E.: A review of continuum mechanics models for size-dependent analysis of beams and plates. Compos. Struct. 177, 196–219 (2017)

    Google Scholar 

  12. Sladek, J., Sladek, V., Wunsche, M., Kasala, J.: Gradient piezoelectricity for cracks under an impact load. Int. J. Fract. 210, 1 (2018)

    Google Scholar 

  13. Sladek, J., Sladek, V., Wunsche, M.: Crack analysis in magneto-electro-elastic solids by gradient theory. Mech. Adv. Mater. Struct. 27(15), 2 (2020)

    Google Scholar 

  14. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mach. Anal. 57, 291–323 (1975)

    MathSciNet  MATH  Google Scholar 

  15. Gurtin, M.E., Murdoch, A.I.: Surface stress in solids. Int. J. Solids Struct. 14, 431–440 (1978)

    MATH  Google Scholar 

  16. Parvanova, S.L., Manolis, G.D., Dineva, P.S.: Wave scattering by hanoheterogeneities embedded in a elastic matrix via BEM. Eng. Anal. Bound. Elem. 56, 57–69 (2015)

    MathSciNet  MATH  Google Scholar 

  17. Parvanova, S.L., Vasilev, G., Dineva, P.S.: Elastic wave scattering and stress concentration in a finite anisotropic solid with nanocavities. Arch. Appl. Mech. 87(12), 1947–1964 (2017)

    Google Scholar 

  18. Rangelov, T.V., Dineva, P.S., Manolis, G.D.: BIEM analysis of a graded nano-cracked elastic halfplane under time-harmonic wavess. Z. Angew. Math. Mech. 100, e202000021 (2020)

    Google Scholar 

  19. Rangelov, T., Dineva, P.: Dynamic fracture behavior of a nanocrack in a piezoelectric plane. ZAMM Z. Angew. Math. Mech. 97(11), 1393–1405 (2017)

    MathSciNet  Google Scholar 

  20. Zhang, P.W., Zhou, Z.G., Wang, B.: Dynamic behaviour of two collinear interace cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips. Appl. Math. Mech. 28, 615–625 (2007)

    MATH  Google Scholar 

  21. Zhang, P.W., Zhou, Z.G., Wu, L.Z.: Behaviour of three parallel non-symmetric mode III cracks in a functionally graded material plane. J. Mech. Eng. Sci. 222, 2311–2330 (2008)

    Google Scholar 

  22. Feng, W., Su, R.: Dynamic internal crack problem of a functionally graded magneto-electro-elastic strip. Int. J. Solids Struct. 43, 5196–5216 (2006)

    MATH  Google Scholar 

  23. Feng, W., Su, R.: Dynamic fracture behaviors of cracks in a functionally graded magneto-electro-elastic plate. Eur. J. Mech A/Solids 26, 363–379 (2007)

    MATH  Google Scholar 

  24. Sladek, J., Sladek, V., Solek, P., Pan, E.: Fracture analysis of cracks in magnetoelectro-elastic solids by the MLPG. Comput. Mech. 42, 697–714 (2008)

    MATH  Google Scholar 

  25. Sladek, J., Sladek, V., Solek, P., Zhang, C.: Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG. Int. J. Solids Struct. 47, 1381–1391 (2010)

    MATH  Google Scholar 

  26. Wunsche, M., Saez, A., Garcia-Sanchez, F., Zhang, C.: Cracks in magnetoelectroelastic solids under impact loading. Key Eng. Mater. 417–418, 377–380 (2010)

    MATH  Google Scholar 

  27. Rojas-Diaz, R., Saez, A., Garcia-Sanchez, F., Zhang, C.: Dynamic crack interactions in magnetoelectroelastic composite materials. Int. J. Fract. 157(1–2), 119–130 (2009)

    MATH  Google Scholar 

  28. Rojas-Diaz, R., Saez, A., Garcia-Sanchez, F., Zhang, C.: Analysis of cracked magnetoelectroelastic composites under time-harmonic loading. Int. J. Solids Struct. 47, 71–80 (2010)

    MATH  Google Scholar 

  29. Rangelov, T., Stoynov, Y., Dineva, P.: Dynamic fracture behavior of functionally graded magnetoelectroelastic solids by BIEM. Int. J. Solids Struct. 48, 2987–2999 (2011)

    Google Scholar 

  30. Liang, J.: The dynamic behaviour of two parallel symmetric cracks in functionally graded piezoelectric/piezomagnetic materials. Arch. Appl. Mech. 78, 443–464 (2008)

    MATH  Google Scholar 

  31. Zhou, Z.G., Wang, B.: An interface crack between two dissimilar functionally graded piezoelectric/piezomagnetic material half infinite planes subjected to the harmonic anti-plane shear stress waves. Int. J. Appl. Electromagn. Mech. 27, 117–132 (2008)

    MathSciNet  Google Scholar 

  32. Li, Y.D., Lee, K.Y.: Dynamic responses of a crack in a layered graded magnetoelectroelastic sensor subjected to harmonic waves. Acta Mech. 204, 217–234 (2009)

    MATH  Google Scholar 

  33. Dineva, P., Rangelov, T.: Wave scattering by cracks at macro- and nano-scale in anisotropic plane by BIEM. J. Theor. Appl. Mech. 46(4), 19–35 (2016)

    MATH  Google Scholar 

  34. Rangelov, T., Dineva, P., Manolis, G.: Dynamic response of a cracked viscoelastic anisotropic plane using boundary elements and fractional derivatives. J. Theor. Appl. Mech. 48(2), 24–49 (2018)

    MathSciNet  Google Scholar 

  35. Stoynov, Y., Dineva, P., Rangelov, T.: Wave scattering and stress concentration in a magneto-electro-elastic plate with a nano-crack by Boundary Integral Equations. J. Theor. Appl. Mech. 49, 203–223 (2019)

    Google Scholar 

  36. Hoagland, R.G., Daw, M.S., Hirth, J.P.: Some aspects of forces and fields in atomic models of crack tips. J. Mater. Res. 6, 2565–2571 (1991)

    Google Scholar 

  37. Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series, and Products. Academic Press, New York (1965)

    Google Scholar 

  38. Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity. Gordon and Breach Sci. Publ., New York (1988)

    Google Scholar 

  39. Soh, A.K., Liu, J.X.: On the constitutive equations of magnitoelectroelastic solids. J. Int. Mater. Syst. Struct. 16, 597–602 (2005)

    Google Scholar 

  40. Stoynov, Y., Rangelov, T.: Time-harmonic crack problems in magnetoelectroelastic plane by BIEM. J. Theor. Appl. Mech. 39(4), 73–92 (2009a)

    MathSciNet  Google Scholar 

  41. Zhang, C., Gross, D.: On Wave Propagation in Elastic Solids with Cracks. Comput. Mech. Publ., Southampton (1998)

    MATH  Google Scholar 

  42. Stoynov, Y., Rangelov, T.: Time-harmonic behaviour of anti-plane cracks in inhomogeneous magnetoelectroelastic solid. Comp. Rend. Acad. Bulg. Sci. 62(2), 175–186 (2009b)

    MATH  Google Scholar 

  43. Su, R.K.L., Sun, H.Y.: Numerical solution of two-dimensional anisotropic crack problems. Int. J. Solids Struct. 40, 4615–4635 (2003)

    MATH  Google Scholar 

  44. Li, X.F.: Dynamic analysis of a cracked magneto-electro-elastic medium under anti-plane mechanical and in-plane electric and magnetic impacts. Int. J. Solids Struct. 42, 3185–3205 (2005)

    MATH  Google Scholar 

  45. Shenoy, V.B.: Size-dependent rigidities of nanosized torsional elements. Int. J. Solids Struct. 39, 4039–4052 (2002)

    MATH  Google Scholar 

Download references

Acknowledgements

The first and third authors are partially supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICTinSES)”, contract No. DO1-205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria, by the Grant No. BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program (2014–2020) in Bulgaria and co-financed by the European Union through the European Structural and Investment Funds.

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Authors and Affiliations

  1. Institute of Mechanics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Petia Dineva

  2. Faculty of Applied Mathematics and Informatics, Technical University, Sofia, 1000, Bulgaria

    Yonko Stoynov

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Tsviatko Rangelov

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  1. Petia Dineva
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  2. Yonko Stoynov
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Correspondence to Tsviatko Rangelov.

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Dineva, P., Stoynov, Y. & Rangelov, T. Dynamic fracture behavior of nanocracked graded magnetoelectroelastic solid. Arch Appl Mech 91, 1495–1508 (2021). https://doi.org/10.1007/s00419-020-01835-8

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