磁电弹性体中多条位错与Griffith裂纹

doi:10.19596/j.cnki.1001-246x.8016

计算物理 ›› 2020, Vol. 37 ›› Issue (2): 198-204.DOI: 10.19596/j.cnki.1001-246x.8016

磁电弹性体中多条位错与Griffith裂纹

郭怀民, 赵国忠

包头师范学院数学科学学院, 内蒙古包头 014030

收稿日期:2018-11-29 修回日期:2019-04-12 出版日期:2020-03-25 发布日期:2020-03-25
作者简介:GUO Huaimin (1969-),male,PhD,professor,research in computational mechanics,E-mail:804711984@qq.com
基金资助:
National Natural Science Foundation of China (11761054), Natural Science Foundation of Inner Mongolia Autonomous Region, China (2015Ms0108), Scientific Research Project of Higher Education Institutions of Inner Mongolia Autonomous Region(NJZZ16235), Training Plane of YinShan scholars of Bao Tou Teacher's College, Program for Young Talents of Inner Mongolia Autonomous Region, China (NJZZ12198), Science and Technology Development Foundation of CAEP (2015B010102)

Multiple Screw Parallel Dislocations and a Griffith Crack in Magnetoelectroelastic Body

GUO Huaimin, ZHAO Guozhong

Mathematics Science, Bao Tou Teacher's College, Baotou, Inner Mongolia 014030, China

Received:2018-11-29 Revised:2019-04-12 Online:2020-03-25 Published:2020-03-25
Supported by:
National Natural Science Foundation of China (11761054), Natural Science Foundation of Inner Mongolia Autonomous Region, China (2015Ms0108), Scientific Research Project of Higher Education Institutions of Inner Mongolia Autonomous Region(NJZZ16235), Training Plane of YinShan scholars of Bao Tou Teacher's College, Program for Young Talents of Inner Mongolia Autonomous Region, China (NJZZ12198), Science and Technology Development Foundation of CAEP (2015B010102)

摘要/Abstract

摘要： 根据本征方程，研究磁电弹性体中若干平行螺型位错与Griffith裂纹的相互作用.结合Muskhelishvili方法和算子理论，得到磁电弹性体中由位错和裂纹所诱导的应力场、电场和磁场的解析解.数值算例表明：在裂纹的端点及位错点上仍然存在应力的奇异性，离位错点越远处广义力越小，结论与已有的结果相符，证明了结论的正确性.当位错点与裂纹端点距离越近时，裂纹与位错间的应力场越小，并逐渐趋近于零.

关键词: 磁电弹性体, 平行位错, Griffith裂纹, Muskhelishvili方法

Abstract: Interactions among parallel screw dislocations and a Griffith crack in magnetoelectroelastic media are investigated in terms of fundamental equations. Combining Muskhelishvili techniques and operator theory, analytic solutions for stress fields, electric fields and magnetic fields induced by screw dislocation and crack in magnetoelectroelastic solid are derived. Numerical examples show that singularity of stress occurs at crack tip and dislocation core. Away from dislocation point, the generalized stress is smaller, which is verified with existing results. As dislocation point approaches crack tip, stress fields between crack and dislocation tends to zero.

Key words: magnetoelectroelastic body, parallel dislocation, Griffith crack, Muskhelishvili technique

中图分类号:

O346.5

郭怀民, 赵国忠. 磁电弹性体中多条位错与Griffith裂纹[J]. 计算物理, 2020, 37(2): 198-204.

GUO Huaimin, ZHAO Guozhong. Multiple Screw Parallel Dislocations and a Griffith Crack in Magnetoelectroelastic Body[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(2): 198-204.

参考文献

[1] NIRAULA O P, WANG B L. A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading[J]. Acta Mechanica, 2006, (187):151-168.
[2] HU K Q, CHEN Z T, ZHONG Z. Interface crack between magnetoelectroelastic and orthotropic half-spaces under in-plane loading[J]. Theoretical & Applied Fracture Mechanics, 2018, (96):285.
[3] ROGOWSKI B. The mode III cracks emanating from an elliptical hole in the piezo-electro-magneto-elastic materials[J]. Archive of Applied Mechanics, 2011, (87):1607-1620.
[4] MA P, SU R K L, FENG W J. Singularity of subsonic and transonic crack propagations along interfaces of magnetoelectroelastic bimaterials[J]. International Journal of Engineering Science, 2018, (129):21-33.
[5] YAO S L, CHENG C Z, NIU Z R. Thermo-elastic singular characteristic analysis on V-notches in orthotropic material[J]. Chinese J Comput Phys, 2016, 33(4):419-426.
[6] LIANG Y P, DING X, CHEN Y Q, YU H H. Application of scaled boundary finite element method in electromagnetic field problems[J]. Chinese J Comput Phys, 2017, 34(2):205-213.
[7] WANG X H, ZHENG X S, QIAO H, ZHANG X M. Analytical study of hypersinglar equations with constant element for 2D Helmholtz problems[J]. Chinese J Comput Phys, 2017, 34(6):666-672.
[8] TANG Q M, ZHEN T Y, LI D Y, GAO Q. Mechanical properties of graphene/hydroxyapatite composite materials:Numerical study[J]. Chinese J Comput Phys, 2018, 35(1):71-76.
[9] MOSHTAGH E, PAN E, ESKANDARI-GHADI M. Shear excitation of a multilayered magneto-electro-elastic half-space considering a vast frequency content[J]. International Journal of Engineering Science, 2018, (123):214-235.
[10] LI Y D, GUAN Y, SHAO Z Z. Multiple parallel cracks in a magnetoelectroelastic strip under in-plane magnetic/electric field and clamping-induced antiplane pre-deformation[J]. Acta Mechanica, 2016, (227):1-14.
[11] VIUN O, LOBODA V, LAPUSTA Y. Electrically and magnetically induced Maxwell stresses in a magneto-electro-elastic medium with periodic limited permeable cracks[J]. Archive of Applied Mechanics, 2016, (12):1-12.
[12] LIU L L, FENG W J, LIU J X. Transient thermal fracture analysis of a penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder[J]. Journal of Thermal Stresses, 2016, (11):1428-1441.
[13] RODRíGUEZ-TEMBLEQUE L, BURONI F C, SÁEZ A, et al. 3D coupled multifield magneto-electro-elastic contact modelling[J]. International Journal of Mechanical Sciences, 2016, (114):35-51.
[14] MA J, EL-BORGI S, KE L L, et al. Frictional contact problem between a functionally graded magnetoelectroelastic layer and a rigid conducting flat punch with frictional heat generation[J]. Journal of Thermal Stresses, 2016, (3):245-277.
[15] CHEN J, GUO J, PAN E. Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect[J]. Journal of Sound and Vibration, 2017, (400):550-563.
[16] AREFI M, ZENKOUR A M. Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates[J]. European Physical Journal Plus, 2017, (10):423.
[17] LUBARDA V A. Equilibrium position of screw dislocation near circular inhomogeneity at the tip of an elastic wedge[J]. Meccanica, 2017, (1):1-11.
[18] WANG X, SCHIAVONE P. Interaction between an edge dislocation and a circular inhomogeneity with a mixed-type imperfect interface[J]. Archive of Applied Mechanics, 2016, (1):1-12.
[19] HU K Q, KANG Y L, LI G Q. Moving crack at the interface between two dissimilar magnetoelectroelastic materials[J]. Acta Mechanica, 2006, (1):1-16.
[20] FENG W J, MA P, SU R K L. An electrically impermeable and magnetically permeable interface crack with a contact zone in magnetoelectroelastic bimaterials under a thermal flux and magnetoelectromechanical loads[J]. International Journal of Solids & Structures, 2012, (23):3472-3483.
[21] LV X, LIU G T. Interaction between many parallel screw dislocations and a semi-infinite crack in a magnetoelectroelastic solid[J]. Chinese Physics B, 2018, (7):074601.
[22] LIU G T, YANG L Y. Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal[J]. Chinese Phys B, 2017, (9):094601.
[23] MUSKHELISHVILI N I. Singular integral equations:Boundary problems of function theory and their application to mathematical physics[J]. P Noordhoff N, 1946, (2):256-291.
[24] SIH G C, CHEN E P. Dilatational and distortional behavior of cracks in magnetoelectroelastic materials[J]. Theor Appl Fract Mech, 2003, 40(1):1-21.

磁电弹性体中多条位错与Griffith裂纹

Multiple Screw Parallel Dislocations and a Griffith Crack in Magnetoelectroelastic Body

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

作者中心

审稿中心

期刊浏览

期刊介绍