超弹性Kirchhoff-Love板壳的相场断裂研究  

Study on fracture of hyperelastic Kirchhoff-Love plates and shells by phase field method

作　　者：彭帆 马维力 马玉娥[2] 黄玮[2] 李显方[3] PENG Fan;MA Weili;MA Yu′e;HUANG Wei;LI Xianfang(School of Science,Chang′an University,Xi′an 710064,China;School of Aeronautics,Northwestern Polytechnical University,Xi′an 710072,China;School of Civil Engineering,Central South University,Changsha 410075,China)

机构地区：[1]长安大学理学院,陕西西安710064 [2]西北工业大学航空学院,陕西西安710072 [3]中南大学土木工程学院,湖南长沙410075

出　　处：《西北工业大学学报》2024年第4期597-605,共9页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(12372086);陕西省自然科学基金(2023-JC-QN-0010);中央高校基本科研业务费(300102123106)资助。

摘　　要：板壳这类薄壁结构在诸多工程领域得到广泛应用,预测其断裂行为对工程结构的完整性设计和强度评估具有重要意义。超弹性板壳断裂行为的数值仿真需同时考虑复杂的运动学描述、超弹性本构关系、几何非线性和断裂损伤对弹性常数的退化,因此具有一定的挑战性。将Kirchhoff-Love(K-L)板壳理论与断裂相场法结合,采用T样条对位移场和相场的一、二阶偏导进行数值离散,满足了K-L板壳理论对形函数C^(1)连续的要求,建立了超弹性K-L板壳相场断裂模型的等几何分析数值格式,模拟了超弹性K-L板壳在均布载荷和位移加载下的断裂失效行为,研究了高斯曲率对超弹性K-L壳断裂性能的影响。数值模拟结果表明:所建立的数值格式可以有效地捕捉板壳在均布载荷下的复杂裂纹扩展路径,模拟得到的位移场可以有效地反映材料的裂纹分布情况;具有负高斯曲率的薄壳在承受内压作用时具有较好的断裂性能,可以承受更大的内压。Thin walled structures such as plates and shells are widely used in many engineering fields.To Predict its fracture behavior is of great significance for integrity design and strength evaluation of engineering structures.Numerical simulation of the fracture behavior of hyperelastic plates and shells is a challenge due to complex kinematic description,hyperelastic constitutive relationship,geometric nonlinearity and the degradation on elastic parameter caused by fracture damage.Combining Kirchhoff Love(K-L)shell theory with the fracture phase field method,and numerically discretizing the first and second order partial derivatives of displacement field and phase field by using T-splines and meeting the requirements of K-L plate and shell theory for the C^(1) continuity of the shape function,a model for the isogeometric analysis numerical formulation of the phase field fracture in hyperelastic K-L plates and shells is established.The fracture failure behavior of hyperelastic K-L plates and shells under the uniform load and displacement load is simulated,and the effect of the Gaussian curvature on the fracture behavior of hyperelastic K-L shells is studied.The simulation results show that the present numerical scheme can effectively capture the complex crack propagation path of plates and shells under the uniform load,and the displacement field can effectively reflect the crack distribution of materials.The thin shell with negative Gaussian curvature shows the excellent fracture performance under the internal pressure,and can withstand the greater internal pressure.

关 键 词：超弹性 板壳 相场 断裂 等几何分析 

分 类 号：O341[理学—固体力学]