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A TECHNIQUE FOR SOLVING TIME-DEPENDENT ELASTIC-PLASTIC PROBLEMS ON IRREGULAR MULTIFARIOUS LAGRANGIAN GRIDS

S.S. Sokolov
VANT. Ser.: Mat. Mod. Fiz. Proc 2002. Вып.4. С. 23-36.

In solving multidimensional time-dependent elastic-plastic problems the numerical methods of Whilkins type have received wide acceptance. Finite difference and finite elements methods are the most universal ones. The wide spectrum of solved problems makes it difficult to cover all of them by a unique method particularly in one-dimension. Finite-difference methods, based mostly on regular quadrilateral hexagon Lagrangian, Eulerian-Lagrangian and Eulerian grids are progressing most rapidly in solving elastic-plastic problems.
The paper deals with Lagrangian technique for computing multidimensional time-dependent elastic-plastic problems on non-regular Lagrangian grids. In two dimensions a technique, based on Lagrangian gas dynamic DMK technique uses a non-regular difference grid consisting of convex polygons with arbitrary vertex number remaining convex during a problem solution. In three dimensions a technique, based on Lagrangian gas dynamic TMK technique uses a non-regular convex multifarious Lagrangian grid of arbitrary configuration. In 3D and 2D techniques explicit finite-difference schemes are used to approximate equations.
The described techniques are implemented in TMK and DMK program complexes, allowing the solution of continuum mechanics problems with severe distortions in areas with complicated geometry.



NUMERICAL SIMULATION OF ISOTROPIC DESTRUCTION OF ELASTIC-PLASTIC, MEDIA IN MIMOZA TECHNIQUE

A.A. Sadovoy, N.V. Sokolova
VANT. Ser.: Mat. Mod. Fiz. Proc 2002. Вып.4. С. 37-44.

A large amount of microdeffects of different types are formed during dynamical destruction of elastic-plastic materials. A separate description of each microfailure is very laborious and practically impossible. Therefore mechanics of continual (or scattered) destruction has been developed recently, which governing equations introduce some internal variables, characterizing microfailure development. MIMOZA technique implements a kinetic model for viscous plastic NAG destruction, updated to enable the description of destructed materials. Numerical simulation results for some experiments based on it are presented.










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