Smoothed Particle Hydrodynamics for the Linear and Nonlinear Analyses of Elastoplastic Damage and Fracture of Shell

It is a troublesome and focused problem of solid mechanics to solve shell structures with Smoothed particle hydrodynamics (SPH), which is a fully meshfree method. In this paper, an integral model of SPH shell is proposed to more accurately capture the nonlinear strain along the thickness direction. Though the idea is similar to the "Gaussian integral point" in Finite element method (FEM), it is absent and just the first presentation in SPH. Furthermore, focusing on the metal materials, a high-efficiency iteration algorithm for plasticity is derived and the plastic damage theory of Lemaitre–Chaboche is also introduced based on the studies of Caleyron et al. (2011). As for the dynamic fracture of SPH shell, the multiple line segments algorithm is proposed to treat crack adaptively, which overcomes the mesh dependency occurring in mesh method. These algorithms and theories are successfully applied in the integral model of SPH shell of elasticity, plastic damage and dynamic fracture. Finally, the linear and nonlinear analyses of geometry and material are carried out with FEM, the global model and the integral model of SPH shell to prove the feasibility and the accuracy of the integral model.

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