A novel peridynamic model enriched with the rotation effects of material points. (1st January 2022)

• Record Type: Journal Article
• Authors: Zhou, Xiaoping; Ma, Jianxiang
• Is Part Of: Engineering analysis with boundary elements. Volume 134(2022)
• Page Start: 591
• Page End: 611
• Publication Date: 2022-01-01
• Subjects: A novel peridynamic model -- Material point rotation -- Limitation of Poisson's ratio; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.11.006
• Languages: English
• ISSNs: 0955-7997

Abstract

Highlights: A novel peridynamic model enriched with rotation of material points is proposed. The translational and rotational governing equations of material points are obtained by the Lagrangian equation. The concept of rotational micropotentials is introduced into this proposed peridynamic model. The parameters of the proposed peridynamic model with rotation of material points are calibrated. The limitation problem of Poisson's ratio can be effectively solved by the proposed peridynamic model. Abstract: Combining the nonlocal properties of peridynamics and the viewpoint of material point rotation, a novel peridynamic model enriched with the rotation effects of material points is proposed. By considering the rotation of material points, the concept of rotational micropotential is introduced into this proposed peridynamic model. On this basis, the translational and rotational governing equations of material points obtained by the Lagrangian equation are proven to satisfy the conservation of linear momentum and angular momentum. Based on the linear assumption, the parameters of the novel peridynamic model with rotation effects of material points are calibrated, and its validity is verified. It can be seen from the numerical results that the limitation problem of Poisson's ratio can be effectively solved by the proposed peridynamic model. Compared with the traditional micropolar peridynamic model (MPPD), the proposed model directly decomposes the motion of material points into translation and rotation and does not need to introduce the shear modulus. This makes the mathematical formula more concise and the numerical calculations more efficient.