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<p>Despite the significant capabilities of the conventional ordinary state-based peridynamic (OSB-PD) method in modeling brittle materials, this method neglects the effects of rotation and shear in the bonds between material points. Consequently, it is incapable of accurately modeling ductile, viscoelastic, and elastic-plastic materials. Moreover, the complex formulation of the non-ordinary state-based peridynamic (NOSB-PD) method leads to significant computational cost in macro-scale analyses, often requiring additional algorithms to ensure convergence. In this study, a new model that incorporates rotational springs within the finite element framework is developed based on an elastic-plastic formulation to address these limitations. In this model, each bond consists of three components: the left subunit, the middle spring, and the right subunit. In this method, the fundamental OSB-PD equation of motion is derived by incorporating improved bond force and momentum force terms. These terms are obtained by reformulating the strain energy equations in both the elastic and plastic phases for each of the three components. The accuracy of the proposed model is validated using the finite element method, experimental tests, and micromechanical analyses. The effects of various parameters such as crack location, crack propagation path, microcrack growth, loading speed rate, and number of material points are examined. The proposed model serves as a bridge between the ordinary state-based peridynamic (OSB-PD) and non-ordinary state-based peridynamic (NOSB-PD) methods. It reduces the computational cost associated with the NOSB-PD method by a factor of 4.11 and enhances the accuracy of the OSB-PD method, with an average improvement of 20% observed across different specimens due to the incorporation of bond rotation and shear effects. The model shows a prediction error of less than 4% when compared to experimental results. The capability of the model expands the applicability of peridynamics to a broader range of real-world engineering problems at the macro scale.</p>

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A new approach to involve bond rotation and plasticity in the ordinary state-based peridynamic method

  • 期刊论文

  • 发表日期：

    2025年9月17日

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  • Morteza Khomami Abadi,
  • Mohammad Zaman Kabir

摘要

Despite the significant capabilities of the conventional ordinary state-based peridynamic (OSB-PD) method in modeling brittle materials, this method neglects the effects of rotation and shear in the bonds between material points. Consequently, it is incapable of accurately modeling ductile, viscoelastic, and elastic-plastic materials. Moreover, the complex formulation of the non-ordinary state-based peridynamic (NOSB-PD) method leads to significant computational cost in macro-scale analyses, often requiring additional algorithms to ensure convergence. In this study, a new model that incorporates rotational springs within the finite element framework is developed based on an elastic-plastic formulation to address these limitations. In this model, each bond consists of three components: the left subunit, the middle spring, and the right subunit. In this method, the fundamental OSB-PD equation of motion is derived by incorporating improved bond force and momentum force terms. These terms are obtained by reformulating the strain energy equations in both the elastic and plastic phases for each of the three components. The accuracy of the proposed model is validated using the finite element method, experimental tests, and micromechanical analyses. The effects of various parameters such as crack location, crack propagation path, microcrack growth, loading speed rate, and number of material points are examined. The proposed model serves as a bridge between the ordinary state-based peridynamic (OSB-PD) and non-ordinary state-based peridynamic (NOSB-PD) methods. It reduces the computational cost associated with the NOSB-PD method by a factor of 4.11 and enhances the accuracy of the OSB-PD method, with an average improvement of 20% observed across different specimens due to the incorporation of bond rotation and shear effects. The model shows a prediction error of less than 4% when compared to experimental results. The capability of the model expands the applicability of peridynamics to a broader range of real-world engineering problems at the macro scale.