含唇形延伸裂缝的磁电弹性体的反平面问题  

Antiplane problem of magnetoelectric elastomers with lip shaped extended cracks

作　　者：郭宗华 郭怀民[2] GUO Zong-hua;GUO Huai-min(College of Mathematics Science,Shandong University,Jinan 250000,China;College of Mathematics Science,Baotou Teacher’s College,Baotou 014030,China)

机构地区：[1]山东大学,数学科学学院,济南250000 [2]包头师范学院,数学科学学院,包头014030

出　　处：《计算力学学报》2025年第1期68-74,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(12162027,12361076);内蒙古自然科学基金(2021MS01001)资助项目。

摘　　要：磁电弹性材料是一种新型智能材料,广泛应用于智能器件和设备的制造和安装。本文基于Muskhelishvili理论,构建了唇形延伸裂缝的缺陷模型。利用保角变换技术和Stroh型公式,研究了含唇形延伸裂缝的磁电弹性材料的力学行为,得出了部分磁电渗透边界条件下裂缝端点处场强度因子和能量释放率的解析表达式。数值算例描述了缺陷的几何尺寸、耦合系数对磁、电、弹性场SIF和SERR的影响规律。结果表明,增加裂缝的长度会促进扩展,增加唇口的高度会抑制裂缝的扩展。当唇口两边的延伸裂缝长度变为零时,所得结果可退化为经典的唇口裂纹问题,当唇口的高度变为零时,结果可退化为Griffith裂纹问题,进一步检验了结论的正确性和有效性。Magnetoelectroelastic materials are a new type of intelligent material widely used in the manufacturing and installation of intelligent devices and equipment.Based on Muskhelishvili theory,this paper constructs a defect model for secondary cracks.By using conformal transformation technology and Stroh type formulas,the mechanical behavior of magneto-electroelastic material containing lip-type extended cracks is studied,and the analytical expressions of the field intensity factors and energy release rate at the crack tip under the partial magnetoelectric permeability boundary condition are obtained.The numerical examples describe the influence of the geometric size of defects on the SIF and SERR of magnetic,electrical,and elastic fields.The results indicate that increasing the length of the crack will promote its expansion,while increasing the height of the lip will suppress its expansion.When the length of the extended crack on both sides of the lip becomes zero,the obtained results can degenerate into the classic lip crack results.The results can degenerate into the Griffith crack results as the height of the lip becomes zero,which further verifies the correctness and effectiveness of the model.

关 键 词：磁电弹性体 唇形延伸裂缝 场强度因子 能量释放率 保角变换 

分 类 号：TB330.1[一般工业技术—材料科学与工程] O346.1[理学—固体力学]