Персона: Рябов, Павел Николаевич
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Localization of plastic flow in one-dimensional and two-dimensional problems
© 2021 Institute of Physics Publishing. All rights reserved.In this paper one-dimensional and two-dimensional models are used for investigation of the processes of adiabatic shear bands (ASB) formation. Significant characteristics of a localization process at different nominal strain-rates are studied in the series of the numerical simulations. The results obtained for one-dimensional and two-dimensional problems are compared.
2D Numerical Simulation of Adiabatic Shear Bands Formation
© 2022 American Institute of Physics Inc.. All rights reserved.In this work we suggest a mathematical model of motion of the elastoplastic materials with nonlinear plasticity constitutive law. We also propose an effective numerical method based on the Godunov-type scheme for simulation of such tasks on two-dimensional eulerian meshes. We test the proposed method on a benchmark problem that includes formation of the single adiabatic shear band (A S B) due to initial temperature perturbation. Then we study the formation of multiple adiabatic shear bands at high-speed shear deformation.
On Features of Formation of Localized Shear Bands in Depleted Uranium
Exploring the Efficiency of Neural Networks for Solving Dynamic Process Problems: The Fisher Equation Investigation
On collective behavior of shear bands in dipolar HY-100 steel and OFHC copper
© 2019 Author(s).The collective behavior of adiabatic shear bands in dipolar HY-100 steel and OFHC copper is studied. The mathematical model is formulated. The numerical algorithm which is based on the spiting method is suggested. This algorithm allows one to simulate the process of multiple or single band evolution taking into account dipolar effects. Also the method of dynamical adaptation of spatial grid nodes is applied in proposed numerical algorithm. The verification procedure was performed to show the efficiency and accuracy of proposed numerical method. The statistical properties of the processes of multiple shear bands formation in dipolar steel and copper are studied.
On Specific Features of an Approach Based on Feedforward Neural Networks to Solve Problems Based on Differential Equations
A finite volume method for numerical simulations of adiabatic shear bands formation
© 2021 Elsevier B.V.The aim of this paper is to develop an effective finite volume method for numerical simulation of the adiabatic shear bands (ASB) formation processes. A formation of ASB happens at high-speed shear strains of ductile materials. A numerical simulation of such problems using Lagrangian approach is associated with some problems, the main one of which is a mesh distortion at large deformations. We use Eulerian approach to describe a motion of the non-linear elasto-plastic material. More specifically, we consider a modification of a well-known hypoelastic Wilkins model. In this paper we suggest a numerical method for modeling of high-speed shear deformations on two-dimensional meshes. The method is verified on the three test problems suggested by other authors.
Dynamic domain decomposition method based on weighted Voronoi diagrams
Numerical studies of self-organization of shear bands in one and two dimensions
In the present manuscript we perform a numerical analysis of the self-organization processes of adiabatic shear bands formation in depleted uranium, aluminum alloy, and high-strength steel in one- and two-dimensional cases. Since the processes of shear bands formation are strongly nonlinear, three materials with significantly different parameters considered allow us to generalize obtained dependencies. For all materials, we investigate the evolution of stress, temperature and velocity fields from initial to final stage of localization. It is well known that localization processes occur during the high shear rate loads in the presence of initial microstructural defects in metallic materials. Starting with a random distribution of initial stress, which models microstructural defects, we obtained new dependencies for such significant parameters of the problem considered such as localization time and spacing between shear bands. The influence of initial plastic strain rate on these parameters was also studied. We obtain the linear dependence of localization time on initial strain rate and show that spatial dimension significantly influences on its value. Also, we introduce the method of shear bands selection during computations and present new statistical distributions for band spacing. We show that the interaction between shear bands significant influences on the spacing between them.