李树忱, 马鹏飞, 王修伟, 刘祥坤. 基于非局部微分算子的近场动力学及固体材料应力数值模拟[J]. 工程力学, 2022, 39(11): 42-51. DOI: 10.6052/j.issn.1000-4750.2021.07.0520
引用本文: 李树忱, 马鹏飞, 王修伟, 刘祥坤. 基于非局部微分算子的近场动力学及固体材料应力数值模拟[J]. 工程力学, 2022, 39(11): 42-51. DOI: 10.6052/j.issn.1000-4750.2021.07.0520
LI Shu-chen, MA Peng-fei, WANG Xiu-wei, LIU Xiang-kun. PERIDYNAMICS AND NUMERICAL SIMULATION OF SOLID MATERIAL STRESS BASED ON NONLOCAL DIFFERENTIAL OPERATOR[J]. Engineering Mechanics, 2022, 39(11): 42-51. DOI: 10.6052/j.issn.1000-4750.2021.07.0520
Citation: LI Shu-chen, MA Peng-fei, WANG Xiu-wei, LIU Xiang-kun. PERIDYNAMICS AND NUMERICAL SIMULATION OF SOLID MATERIAL STRESS BASED ON NONLOCAL DIFFERENTIAL OPERATOR[J]. Engineering Mechanics, 2022, 39(11): 42-51. DOI: 10.6052/j.issn.1000-4750.2021.07.0520

基于非局部微分算子的近场动力学及固体材料应力数值模拟

PERIDYNAMICS AND NUMERICAL SIMULATION OF SOLID MATERIAL STRESS BASED ON NONLOCAL DIFFERENTIAL OPERATOR

  • 摘要: 在经典近场动力学模型的基础上引入非局部微分算子求解理论,建立近场动力学微弹性应力分析模型。在近场动力学模型物质点处进行泰勒级数展开,利用正交非局部函数构建微分算子的数值积分方程并且根据矩阵正交性求解函数未知系数,最终由平衡方程等价性建立近场动力学应力求解模型。采用所提出的方法对固体材料变形破坏过程中的应力进行模拟,并将计算结果与理论解对比以验证方法有效性,同时对粒子离散间距、泰勒项数及权函数的数值收敛性进行分析。结果表明:该文提出的方法可以较准确的反映完整及非完整固体脆性材料在荷载作用下的应力分布,并且离散间距及权函数对数值收敛结果具有显著影响,可为使用近场动力学方法模拟变形破坏时提供新的应力分析思路,有着较为广泛的应用前景。

     

    Abstract: Based on the classical peridynamic model, the nonlocal differential operator solution theory is introduced to establish the peridynamic micro-elastic stress analysis model. Taylor series expansion is carried out at the material point of the peridynamic model. The numerical integral equation of the differential operator is constructed by using the orthogonal nonlocal function, and the unknown coefficients of the function are solved according to the orthogonality of the matrix. Finally, the peridynamic stress solution model is established by the equivalence of the equilibrium equation. The proposed method is used to simulate the stress distribution in the deformation and failure process of solid materials, and the calculated results are compared with the theoretical solution to verify the effectiveness of the method proposed. At the same time, the numerical convergence of the particle discrete distance, Taylor term number and the weight function are analyzed. The simulation results show that the proposed method can accurately reflect the stress distribution of holonomic and nonholonomic solid brittle materials under loads. Moreover, the discrete distance and weight function have a significant influence on the numerical convergence. It can provide a new idea for stress analysis when using the extended peridynamics method to simulate deformation and failure and, has a wide application prospect.

     

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