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Steady-State Problems in a Cracked Anisotropic Domain

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Dynamic Fracture of Piezoelectric Materials

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 212))

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Abstract

We start with the uncoupled homogeneous case, which actually is for a homogeneous elastic anisotropic material. The accuracy and convergence of the numerical BIEM solution for evaluation of the SIFs is studied by comparison with existing solutions for elastic isotropic and orthotropic materials. In addition a parametric study for the wave field sensitivity regarding frequency, crack geometry and material anisotropy is presented.

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References

  1. Abuquerque EL, Sollero P, Aliabadi MH (2002) The Boundary Element Method applied to time dependent problems in anisotropic materials. Int J Solids Struct 39:1405–1422

    Google Scholar 

  2. Aliabadi AM, Brebbia CA (eds) (1993) Advances in BEM for fracture mechanics. Computational Mechanics Publications, Southampton

    Google Scholar 

  3. Ang WT, Clements DL, Cooke T (1999) A hyper-singular boundary integral equation for anti-plane crack problems for a class of inhomogeneous anisotropic elastic materials. Eng Anal Bound Elem 23:567–572

    Article  MATH  Google Scholar 

  4. Brebbia CA, Wenturini WS (eds) (1987) Boundary element techniques: applications in stress analysis and heat transfer. Computational Mechanics Publications, Southampton

    Google Scholar 

  5. Chan KS, Cruse TA (1986) Stress intensity factors for anisotropic compact-tension specimens with inclined cracks. Eng Fract Mech 23:863–874

    Article  Google Scholar 

  6. Chandra A, Hu KX, Huang Y (1995) A hybrid BEM formulation for multiple cracks in orthotropic elastic components. Comput Struct 56:785–797

    Article  MATH  Google Scholar 

  7. Dhawan GK (1982) Interaction of elastic waves by a Griffith crack in an infinite transversely-isotropic medium. Int J Fract 19:29–37

    Article  Google Scholar 

  8. Dhawan GK (1983) Interaction of SV-waves by a Griffith crack in an infinite transversely-isotropic medium. Int J Fract 20:103–110

    Google Scholar 

  9. Dineva P, Rangelov T, Gross D (2005) BIEM for 2D steady-state problems in cracked anisotropic materials. Eng Anal Bound Elem 29:689–698

    Article  MATH  Google Scholar 

  10. Dineva P, Gross D, Rangelov T (2006) Wave scattering in cracked piezoelectric materials—a BIEM approach. J Theor Appl Mech 36(2):65–88

    Google Scholar 

  11. Hua Z, Tian YF, Lan QT (1996) Composite materials dynamic fracture studies by generalized Shmuely difference algorithm. Eng Fract Mech 54:869–877

    Article  Google Scholar 

  12. Karim MR, Kundu T (1988) Transient surface response of layered isotropic and anisotropic half-spaces with interface-cracks: SH case. Int J Fract 37:245–262

    Google Scholar 

  13. Karim MR, Kundu T (1991) Dynamic response of an orthotropic half-space with a subsurface crack: in-plane case. ASME J Appl Mech 58:988–995

    Article  Google Scholar 

  14. Kundu T, Boström A (1992) Elastic wave scattering by a circular crack in a transversely isotropic solid. Wave Motion 15:285–300

    Article  MATH  Google Scholar 

  15. Lekhnitski SG (1963) Theory of elasticity of an anisotropic body. Holden-Day, San Francisco

    Google Scholar 

  16. Lekhnitski SG (1968) Anisotropic plates. Gordon and Breach, New York

    Google Scholar 

  17. Mathematica 6.0 for MS Windows (2008) Champaign, Illinois

    Google Scholar 

  18. MS Visual Studio (2005) Professional edition. Redmond, Washington

    Google Scholar 

  19. Ohyoshi T (1973a) Effect of orthotropy on singular stresses produced near a crack tip by incident SH-waves. ZAMM Z Angew Math Mech 53:409–411

    Article  MATH  Google Scholar 

  20. Ohyoshi T (1973b) Effect of orthotropy on singular stresses for a finite crack. ASME J Appl Mech 40:491–497

    Article  MATH  Google Scholar 

  21. Pageau SS, Biggers SB (1995) Finite element evaluation of free-edge singular stress fields in anisotropic materials. Int J Solids Struct 38:2225–2239

    Google Scholar 

  22. Pageau SS, Joseph PF, Biggers SB (1995) Finite element analysis of anisotropic materials with singular in-plane stress fields. Int J Solids Struct 32:571–591

    Google Scholar 

  23. Pan E, Amadei B (1996) Fracture mechanics analysis of cracked 2D anisotropic media with a new formulation of the boundary element method. Int J Fract 77:161–174

    Article  Google Scholar 

  24. Saez A, Ariza MP, Dominguez J (1997) Three-dimensional fracture analysis in transversely isotropic solids. Eng Anal Bound Elem 20:287–298

    Article  Google Scholar 

  25. Saez A, Dominguez J (1999) BEM analysis of wave scattering in transversely isotropic solids. Int J Numer Meth Eng 44(9):1283–1300

    Article  MATH  Google Scholar 

  26. Saez A, Dominguez J (2000) Far-field dynamic Green’s functions for BEM in transversely isotropic solids. Wave Motion 32:113–123

    Article  MATH  Google Scholar 

  27. Saez A, Dominguez J (2001) Dynamic crack problems in three-dimensional transversely isotropic solids. Eng Anal Bound Elem 25:203–210

    Article  MATH  Google Scholar 

  28. Sarkar J, Mandal SC, Ghosh M (1995) Diffraction of elastic waves by three coplanar Griffith cracks in an orthotropic medium. Int J Eng Sci 33(2):163–177

    Article  MATH  Google Scholar 

  29. Savin GN (1961) Stress concentration around holes. Pergamon Press, New York

    Google Scholar 

  30. Sih GC Liebowitz H (eds) (1968) Mathematical theory of brittle fracture. Academic Press, New York

    Google Scholar 

  31. Sih GC, Paris PC, Irwin GR (1965) On cracks in rectilinear anisotropic bodies. Int J Fract 1:189–203

    Article  Google Scholar 

  32. Snyder MD, Cruse TA (1975) BIE analysis of cracked anisotropy plates. Int J Fract 11:315–328

    Article  Google Scholar 

  33. Sommerfeld A (1949) Partial differential equations in physics. Academic Press, New York

    MATH  Google Scholar 

  34. Song C, Wolf J (2002) Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multimaterials with the scaled boundary finite-element method. Comput Struct 80:183–197

    Article  Google Scholar 

  35. Su RKL, Sun HY (2003) Numerical solution of two-dimensional anisotropic crack problems. Int J Solids Struct 40:4615–4635

    Google Scholar 

  36. Tan CL, Gao YL (1992) Boundary element analysis of plane anisotropic bodies with stress concentrations and cracks. Comput Struct 20:17–28

    Article  Google Scholar 

  37. Wang CY, Achenbach JD (1994) Elastodynamic fundamental solutions for anisotropic solids. Geophys Int J 118:384–392

    Article  Google Scholar 

  38. Wang CY, Achenbach JD (1995) Three-dimensional time-harmonic elastodynamic Green’s functions for anisotropic solids. Proc R Soc Lond A 449:441–458

    Article  MATH  MathSciNet  Google Scholar 

  39. Wang CY, Achenbach JD (1996) Lamb’s problem for solids of general anisotropy. Wave Motion 24:227–242

    Article  MATH  MathSciNet  Google Scholar 

  40. Zhang C (2000) Transient elastodynamic antiplane crack analysis of anisotropic solids. Int J Solids Struct 37:6107–6130

    Google Scholar 

  41. Zhao MH, Shen YP, Lin YJ, Liu GN (1988) The method of analysis of cracks in three-dimensional transversely-isotropic media: boundary integral equation approach. Eng Anal Bound Elem 21:169–178

    Article  Google Scholar 

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Correspondence to Tsviatko Rangelov .

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Dineva, P., Gross, D., Müller, R., Rangelov, T. (2014). Steady-State Problems in a Cracked Anisotropic Domain. In: Dynamic Fracture of Piezoelectric Materials. Solid Mechanics and Its Applications, vol 212. Springer, Cham. https://doi.org/10.1007/978-3-319-03961-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-03961-9_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03960-2

  • Online ISBN: 978-3-319-03961-9

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