Gradient piezoelectricity for cracks under an impact load
Source abstract
Abstract
The flexoelectric effect on elastic waves is investigated in nano-sized cracked structures. The strain gradients are considered in the constitutive equations of a piezoelectric solid for electric displacements and the higher-order stress tensor. The governing equations with the corresponding boundary conditions are derived from the variational principle. The finite element method (FEM) is developed from the principle of virtual work. It is equivalent to the weak-form of derived governing equations in gradient elasticity. The computational method can be applied to analyze general 2D boundary value problems in size-dependent piezoelectric elastic solids with cracks under a dynamic load. The FEM formulation is implemented for strain-gradient piezoelectricity under a dynamic load.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Thermoelastic and Magnetoelastic Phenomena · Composite Structure Analysis and Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (49)
Show source-provided references
1. Aifantis E (1984) On the microstructural origin of certain inelastic models. ASME J Eng Mater Technol 106:326–33010.1115/1.3225725 ↗
2. Altan S, Aifantis E (1992) On the structure of the mode III crack-tip in gradient elasticity. Scripta Metall Mater 26:319–32410.1016/0956-716X(92)90194-J ↗
3. Aravas N, Giannakopoulos AE (2009) Plane asymptotic crack-tip solutions in gradient elasticity. Int J Solids Struct 46:4478–450310.1016/j.ijsolstr.2009.09.009 ↗
4. Argyris JH, Fried I, Scharpf DW (1968) The tuba family of plate elements for the matrix displacement method. Aeronaut J 72:701–70910.1017/S000192400008489X ↗
5. Askes H, Aifantis EC (2011) Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures. Int J Solids Struct 48:1962–199010.1016/j.ijsolstr.2011.03.006 ↗
6. Baskaran S, He X, Chen Q, Fu JF (2011) Experimental studies on the direct flexoelectric effect in alpha-phase polyvinylidene fluoride films. Appl Phys Lett 98:24290110.1063/1.3599520 ↗
7. Buhlmann S, Dwir B, Baborowski J, Muralt P (2002) Size effects in mesiscopic epitaxial ferroelectric structures: increase of piezoelectric response with decreasing feature-size. Appl Phys Lett 80:3195–319710.1063/1.1475369 ↗
8. Catalan G, Lubk A, Vlooswijk AHG, Snoeck E, Magen C, Janssens A, Rispens G, Rijnders G, Blank DHA, Noheda B (2011) Flexoelectric rotation of polarization in ferroelectric thin films. Nat Mater 10:963–96710.1038/nmat3141 ↗
9. Cross LE (2006) Flexoelectric effects: charge separation in insulating solids subjected to elastic strain gradients. J Mater Sci 41:53–6310.1007/s10853-005-5916-6 ↗
10. Exadaktylos G (1998) Gradient elasticity with surface energy: mode-I crack problem. Int J Solids Struct 35:421–45610.1016/S0020-7683(97)00036-X ↗
11. Exadaktylos G, Vardoulakis I, Aifantis E (1996) Cracks in gradient elastic bodies with surface energy. Int J Fract 79:107–11910.1007/BF00032929 ↗
12. Fannjiang AC, Chan YS, Paulino GH (2002) Strain gradient elasticity for antiplane shear cracks: a hypersingular integrodifferential equation approach. SIAM J Appl Math 62:1066–109110.1137/S0036139900380487 ↗
13. Garcia-Sanchez F, Zhang Ch, Sladek J, Sladek V (2007) 2-D transient dynamic crack analysis in piezoelectric solids. Comput Mater Sci 39:179–18610.1016/j.commatsci.2006.03.021 ↗
14. Georgiadis HG, Grentzelou CG (2006) Energy theorems and the J integral in dipolar gradient elasticity. Int J Solids Struct 43:5690–571210.1016/j.ijsolstr.2005.08.009 ↗
15. Gitman I, Askes H, Kuhl E, Aifantis E (2010) Stress concentrations in fractured compact bone simulated with a special class of anisotropic gradient elasticity. Int J Solids Struct 47:1099–110710.1016/j.ijsolstr.2009.11.020 ↗
16. Harden J, Mbanga B, Eber N, Fodor-Csorba K, Sprunt S, Gleeson JT, Jakli A (2006) Giant flexoelectricity of bent-core nematic liquid crystals. Phys Rev Lett 97:15780210.1103/PhysRevLett.97.157802 ↗
17. Houbolt JC (1950) A recurrence matrix solution for the dynamic response of elastic aircraft. J Aeronaut Sci 17:371–37610.2514/8.1722 ↗
18. Hu SL, Shen SP (2009) Electric field gradient theory with surface effect for nano-dielectrics. CMC Comput Mater Contin 13:63–87
19. Karlis GF, Tsinopoulos SV, Polyzos D, Beskos DE (2007) Boundary element analysis of mode I and mixed mode (I and II) crack problems of 2-D gradient elasticity. Comput Methods Appl Mech Eng 196:5092–510310.1016/j.cma.2007.07.006 ↗
20. Kogan ShM (1964) Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals. Sov Phys Solid State 5:2069–2070
21. Kuna M (2006) Finite element analyses of cracks in piezoelectric structures—a survey. Arch Appl Mech 76:725–74510.1007/s00419-006-0059-z ↗
22. Kuna M (2010) Fracture mechanics of piezoelectric materials—where are we right now? Eng Fract Mech 77:309–32610.1016/j.engfracmech.2009.03.016 ↗
23. Lam DCC, Yang F, Wang J (2004) Size-dependent fracture and higher order J-integral for solids characterized by strain gradient elasticity. Int J Fract 126:385–39810.1023/B:FRAC.0000031149.41516.15 ↗
24. Ma LH, Ke LL, Wang YZ, Wang YS (2017) Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models. Phys E 86:253–26110.1016/j.physe.2016.10.036 ↗
25. Mao S, Purohit PK (2015) Defects in flexoelectric solids. J Mech Phys Solids 84:95–11510.1016/j.jmps.2015.07.013 ↗
26. Mao S, Purohit PK (2014) Insights into flexoelectric solids from strain-gradient elasticity. J Appl Mech Trans ASME 81:08100410.1115/1.4027451 ↗
27. Mao S, Purohit PK, Aravas N (2016) Mixed finite-element formulations in piezoelectricity and flexoelectricity. Proc R Soc A Math Phys Sci 472:2015087910.1098/rspa.2015.0879 ↗
28. Maranganti R, Sharma P (2007) A novel atomistic approach to determine strain-gradient elasticity constants: tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir) relevance for nanotechnologies. J Mech Phys Solids 55:1823–185210.1016/j.jmps.2007.02.011 ↗
29. Maugin GA (1980) The method of virtual power in continuum mechanics: applications to coupled fields. Acta Mech 35:1–8010.1007/BF01190057 ↗
30. McMeeking RM (1999) Crack tip energy release rate for a piezoelectric compact tension specimen. Eng Fract Mech 64:217–24410.1016/S0013-7944(99)00068-5 ↗
31. Metrikine A, Askes H (2006) An isotropic dynamically consistent gradient elasticity model derived from a 2D lattice. Philos Mag 86:3259–328610.1080/14786430500197827 ↗
32. Meyer RB (1969) Piezoelectric effects in liquid crystals. Phys Rev Lett 22:918–92110.1103/PhysRevLett.22.918 ↗
33. Mindlin RD (1964) Micro-structure in linear elasticity. Arch Ration Mech Anal 16:51–7810.1007/BF00248490 ↗
34. Sharma P, Maranganti R, Sharma ND (2006) Electromechanical coupling in nanopiezoelectric materials due to nanoscale nonlocal size effects: Green function solution and embedded inclustions. Phys Rev B 74:01411010.1103/PhysRevB.74.014110 ↗
35. Shen SP, Hu SL (2010) A theory of flexoelectricity with surface effect for elastic dielectrics. J Mech Phys Solids 58:665–67710.1016/j.jmps.2010.03.001 ↗
36. Shi MX, Huang Y, Hwang KC (2000) Fracture in a higher-order elastic continuum. J Mech Phys Solids 48:2513–253810.1016/S0022-5096(00)00020-X ↗
37. Shvartsman VV, Emelyanov AY, Kholkin AL, Safari A (2002) Local hysteresis and grain size effects in Pb)Mg1/3Nb2/3)O-SbTiO3. Appl Phys Lett 81:117–11910.1063/1.1490150 ↗
38. Sladek J, Sladek V, Zhang Ch, Solek P, Starek L (2007a) Fracture analyses in continuously nonhomogeneous piezoelectric solids by the MLPG. CMES Comput Model Eng Sci 19:247–262
39. Sladek J, Sladek V, Zhang Ch (2007b) Dynamic crack analysis in functionally graded piezoelectric solids by meshless local Petrov–Galerkin method. Key Eng Mater 348–349:149–15210.4028/www.scientific.net/KEM.348-349.149 ↗
40. Sladek J, Sladek V, Zhang Ch, Solek P, Pan E (2007c) Evaluation of fracture parameters in continuously nonhomogeneous piezoelectric solids. Int J Fract 145:313–32610.1007/s10704-007-9130-1 ↗
41. Sladek J, Sladek V, Stanak P, Zhang Ch, Tan CL (2017) Fracture mechanics analysis of size-dependent piezoelectric solids. Int J Solids Struct 113:1–910.1016/j.ijsolstr.2016.08.011 ↗
42. Thai HT, Vo TP, Nguyen TK, Kim SE (2017) A review of continuum mechanics models for size-dependent analysis of beams and plates. Compos Struct 177:196–219. https://doi.org/10.1016/j.compstruct.2017.06.04010.1016/j.compstruct.2017.06.040 ↗
43. Vardoulakis I, Exadaktylos G, Aifantis E (1996) Gradient elasticity with surface energy: mode-III crack problem. Int J Solids Struct 33:4531–455910.1016/0020-7683(95)00277-4 ↗
44. Yaghoubi ST, Mousavi SM, Paavola J (2017) Buckling of centrosymmetric anisotropic beam structures within strain gradient elasticity. Int J Solids Struct 109:84–9210.1016/j.ijsolstr.2017.01.009 ↗
45. Yang J, Guo S (2005) On using strain gradient theories in the analysis of cracks. Int J Fract 133:L19–L2210.1007/s10704-005-7120-8 ↗
46. Yudin PV, Tagantsev AK (2013) Fundamentals of flexoelectricity in solids. Nanotechnology 24:43200110.1088/0957-4484/24/43/432001 ↗
47. Wünsche M, Garcia-Sanchez F, Saez A, Zhang Ch (2010) A 2D time-domain collocation-Galerkin BEM for dynamic crack analysis in piezoelectric solids. Eng Anal Bound Elem 34:377–38710.1016/j.enganabound.2009.11.004 ↗
48. Wünsche M, Zhang Ch, Garcia-Sanchez F, Saez A, Sladek J, Sladek V (2011) Dynamic crack analysis in piezoelectric solids with nonlinear electrical and mechanical boundary conditions by a time-domain BEM. Comput Methods Appl Mech Eng 200:2848–285810.1016/j.cma.2011.05.007 ↗
49. Zhu W, Fu JY, Li N, Cross LE (2006) Piezoelectric composite based on the enhanced flexoelectric effects. Appl Phys Lett 89:19290410.1063/1.2382740 ↗