THE MONOTONE METHOD OF FRACTIONAL PARTICLES FOR TWO-DIMENSIONAL ELASTOPLASTIC FLOWS
V. A. Shmelyev, I. E. Cherednichenko, Yu. V. Yanilkin
VANT. Ser.: Mat. Mod. Fiz. Proc 2023. Вып.2. С. 3-15.
The paper describes the main algorithms of the two-dimensional method of fractional particles for the simulation of elastoplastic flows in the Lagrangian-Eulerian LEGAK code. The method is used to resolve the problem of the equation approximation accuracy in the convective transport stage for mixed cells, while eliminating the disadvantage of the classic method of particles, namely, the solution non-monotonicity caused by the discrete transport of mass and accompanying quantities from one cell to another. The sudden fracture and compaction model and Kanel’s model have been implemented on the base of the monotone method of fractional particles. The first model was tested on the problem of adiabatic compression and expansion of a plane layer, the second one was tested on the problem of colliding copper plates. And, also, the both models were tested on the problem of a steel sphere impacting a composite barrier. The results obtained confirm that the implemented method allows improving the accuracy of describing the material elastoplastic straining and fracturing processes within the continuum mechanics on immobile meshes. Keywords: elastoplastic flow, model of sudden fracture, Kanel´s model, brittle spall, damage measure, the monotone method of fractional particles, numerical simulation.
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