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S. Kim, S. Jin, J.-W. Hong, "Ellipsoidal Kinematic Reconstruction for the Neighborhood Deformation Tracking in Nonlocal Analyses", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Thirteenth International Conference on Engineering Computational Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 13, Paper 2.3, 2026, doi:10.4203/ccc.13.2.3

Keywords: nonlocal method, large deformation, peridynamics, thermomechanics, heat conduction, ellipsoidal mapping.

Abstract

Nonlocal methods such as peridynamics are effective for the analysis of large deformations, yet the simplification of the geometric evolution of the neighborhood often leads to physical inconsistencies. In this study, an ellipsoidal kinematic reconstruction method is proposed to accurately capture the changes in the shape and volume of the neighboring area of each node. The proposed method identifies specific marker nodes along the initial Cartesian axes and decouples the rigid body rotation from the stretching of the support domain through a hierarchical rotation decomposition. This alignment provides a stable basis for an ellipsoidal mapping to quantify the stretch ratios and the change of the nodal volume. To verify the accuracy of the rotation and volume tracking, rigid body rotation and axial stretching tests are performed. The results demonstrate the precise recovery of rotation angles and the local volume ratio even under significant nodal irregularity, confirming the robustness and coordinate invariance of the framework. Consequently, the ellipsoidal kinematic reconstruction method establishes a reliable kinematic foundation for nonlocal models. This method is applicable to the thermomechanical analysis of peridynamics to ensure physical consistency and stability under large deformations.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 13 PROCEEDINGS OF THE THIRTEENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: P. Iványi, J. Kruis and B.H.V. Topping Paper 2.3 Ellipsoidal Kinematic Reconstruction for the Neighborhood Deformation Tracking in Nonlocal Analyses S. Kim¹, S. Jin² and J.-W. Hong¹ ¹Civil and Environmental Engineering, KAIST, Republic of Korea ²Department of Mechanical Engineering, Pukyong National University, Republic of Korea doi:10.4203/ccc.13.2.3 Full Bibliographic Reference for this paper S. Kim, S. Jin, J.-W. Hong, "Ellipsoidal Kinematic Reconstruction for the Neighborhood Deformation Tracking in Nonlocal Analyses", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Thirteenth International Conference on Engineering Computational Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 13, Paper 2.3, 2026, doi:10.4203/ccc.13.2.3 Keywords: nonlocal method, large deformation, peridynamics, thermomechanics, heat conduction, ellipsoidal mapping. Abstract Nonlocal methods such as peridynamics are effective for the analysis of large deformations, yet the simplification of the geometric evolution of the neighborhood often leads to physical inconsistencies. In this study, an ellipsoidal kinematic reconstruction method is proposed to accurately capture the changes in the shape and volume of the neighboring area of each node. The proposed method identifies specific marker nodes along the initial Cartesian axes and decouples the rigid body rotation from the stretching of the support domain through a hierarchical rotation decomposition. This alignment provides a stable basis for an ellipsoidal mapping to quantify the stretch ratios and the change of the nodal volume. To verify the accuracy of the rotation and volume tracking, rigid body rotation and axial stretching tests are performed. The results demonstrate the precise recovery of rotation angles and the local volume ratio even under significant nodal irregularity, confirming the robustness and coordinate invariance of the framework. Consequently, the ellipsoidal kinematic reconstruction method establishes a reliable kinematic foundation for nonlocal models. This method is applicable to the thermomechanical analysis of peridynamics to ensure physical consistency and stability under large deformations. download the full-text of this paper (PDF, 6697 Kb) go to the previous paper return to the table of contents return to the volume description
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