磁电弹性材料中圆弧形裂纹的反平面断裂问题  

Anti-Plane Fracture Problem of Circular Arc Crack in Magnetoelectroelastic Composites

作　　者：刘欣宇 刘官厅[1,2] LIU Xinyu;LIU Guanting(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematics,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2024年第1期17-26,共10页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目“压电准晶材料弹塑性断裂力学模型及广义复变方法研究”(12162027);内蒙古自治区高等学校科学技术研究自然科学重点资助项目“准晶压电材料纳米缺陷断裂力学问题研究”(NJZZ22574);教育部重点实验室无穷维哈密顿系统及其算法应用(内蒙古师范大学)资助项目“哈密顿方法在稀土、石墨烯、准晶等新材料力学问题中的应用”(2023KFZD02)。

摘　　要：利用广义复变函数理论和保角映射技术,研究磁电弹性复合材料中圆弧形裂纹在无穷远处受到沿磁电极化方向的磁/电载荷和反平面机械载荷的共同作用下的反平面问题,给出应力场及位移场的精确解析解,并获得在磁电全非渗透及全渗透边界条件下圆弧裂纹尖端场强度因子和能量释放率的解析解。基于数值解进行数值分析,由数值结果表明:控制圆弧形裂纹半弦长与弓高比值的减少,可以提高材料的可靠性能;在两种边界条件下,机械载荷的不断增加最终会促进裂纹的扩展;在磁电全渗透边界条件下,裂纹扩展不受磁/电载荷的影响,但与材料常数和机械载荷的大小水平有关;在磁电全非渗透边界条件下,正(负)磁/电载荷的增加会阻碍裂纹扩展。Based on conformal mapping technique and generalized complex function theory,the anti-plane problem of circular arc crack in magnetoelectric composites were studied systematically for the first time,which is subjected to both magnetic/electrical and anti-plane mechanical loads at infinity.Research has found that a decrease in the ratio of half chord length to arch height of circular arc crack will improve the reliability of material.In addition,under two boundary conditions,the continuous increase in mechanical load will ultimately promote crack propagation.Under the magnetoelectric permeable boundary conditions,crack propagation is not affected by magnetic/electric load,but is related to material constant and mechanical load.However,under the impermeable boundary conditions of magnetoelectricity,an increase in positive(negative)magnetic/electrical loads can hinder crack propagation.

关 键 词：磁电弹性复合材料 圆弧形裂纹 反平面问题 复变函数方法 

分 类 号：O343[理学—固体力学]