A smoothed variable horizon peridynamics and its application to the fracture parameters evaluation
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O R I G I NA L PA P E R
M. Imachi · T. Takei · M. Ozdemir · S. Tanaka · S. Oterkus · E. Oterkus
A smoothed variable horizon peridynamics and its application to the fracture parameters evaluation
Received: 15 April 2020 / Revised: 19 July 2020 / Accepted: 15 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract Peridynamics has attractive features for solving several fracture mechanics problems. On the other hand, to ensure the accuracy, a large amount of particles (material points) is required. Introduction of variable horizon is an alternative approach by changing the horizon size over the problem domain. In the present study, we propose a novel variable horizon concept. It is known that an undesired “ghost” force arises along the transition region of different horizons. In order to suppress the ghost force, the gradual variation in the horizon size over a certain region, called smoothing length, is introduced between different scale particle distributions. Efficiency of the smoothed variable horizon peridynamics is demonstrated by several numerical studies employing the ordinary state-based peridynamics. As a basic case, a linear displacement field is considered. It is observed that the proposed approach significantly reduces the ghost forces along the interface of different spatial discretizations. Additionally, the dynamic stress intensity factors of stationary cracks are carefully examined. The path independence of the fracture parameters in the variable horizon peridynamics is ensured. The efficiency of the presented method is then discussed. It is monitored that introduction of the smoothing length concept significantly reduces the computational costs in the peridynamic modeling.
M. Imachi · T. Takei · S. Tanaka (B) Graduate School of Advanced Science and Engineering, Hiroshima University, 4-1, Kagamiyama 1-chome, Higashi-Hiroshima 739-8527, Japan E-mail: [email protected] M. Imachi TechnoStar Co., Ltd, 7-1-1, Akasaka, Minato-ku, Tokyo 107-0052, Japan E-mail: [email protected] T. Takei ITOCHU Techno-Solutions Corporation (CTC), North Gate Bldg., 3-1-3, Umeda, Kita-ku, Osaka-shi, Osaka 530-0001, Japan E-mail: [email protected] M. Ozdemir Department of Naval Architecture and Marine Engineering, Ordu University, Ordu, Turkey E-mail: [email protected] S. Oterkus · E. Oterkus Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow, UK E-mail: [email protected] E-mail: [email protected]
M. Imachi et al.
1 Introduction Peridynamics (PD) is a new continuum mechanics formulation that has been popular in recent years. PD was proposed as a non-local reformulation of classical elasticity equations by Silling [1]. The equation of motion in PD is an integro-differential equation inherently avoiding the partial differentiations, which cannot be evaluated for discontinuities in a traditional manner. In the PD framework, cracks are taken into account in a straightforward way by simply eliminati
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