A Novel Peridynamic Topology Optimization Formulation for Fractured Structures
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Peridynamics (PD) is a nonlocal continuum mechanics theory introduced by Silling in 2000 [1], which allows the natural appearance and propagation of cracks without additional special treatments. This is a result of the PD equations of motion, where local derivatives are replaced with integrals over each point horizon, comparatively with the classical theory. Its numerical implementation can be done as a typical meshless point collocation scheme. Peridynamics has been applied to numerous fields, ranging from multiphysics [2], fatigue prediction [3], multibody system dynamics [4] and topology optimization [5]. Despite still being largely unexplored, this intersection between peridynamics and topology optimization has recently shown high potential. In this work we present a novel density-based topology optimization peridynamic formulation. The simple isotropic material with penalization interpolation scheme is used and a consistent sensitivity analysis is presented. The peridynamic model used in this work is the bond-based prototype microelastic material, for computational efficiency. Results show that peridynamics presents itself as a good candidate for approaching topology optimization problems. On the one hand, as it is illustrated in the results, it provides a consistent regularization as far as mesh independence is concerned, due to the feature of nonlocality. Moreover, the importance of the use of a convenient surface correction factor is also illustrated by the results. Results are also analysed considering different gradient-based optimization algorithms as well as different levels of grid refinement. The formulation is also applied to optimization of structures under fracture conditions. REFERENCES [1] Silling, S. A.,” Reformulation of elasticity theory for discontinuities and long-range forces”. Journal of the Mechanics and Physics of Solids, 48(1), 175-209 (2000). [2] Vieira, F. S., and Aurélio L. A., "A peridynamic model for electromechanical fracture and crack propagation in piezoelectric solids." Computer Methods in Applied Mechanics and Engineering 412 (2023): 116081. [3] Silling, Stewart Andrew, and Abe Askari. Peridynamic model for fatigue cracking. No. SAND2014-18590. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States), 2014. [4] Vieira, F., Pagaimo, J., Magalhães, H., Ambrósio, J., & Araújo, A. "A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems." Multibody System Dynamics (2023)