Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Smolin A.   Psakhie S.G.  

Modelling materials deformation and fracture based on coupled discrete-continual approach

Reporter: Smolin A.

Coupled discrete-continual approach allows joining the advantages of the both methods using mesh for the regions with small deformations and placing particles in the highly distorted regions. The movable cellular automaton method, which has been successfully applied to simulate deformation and fracture of materials, is used to describe a discrete part of the specimen. As a mesh method one can use the finite element or finite difference one. For the purpose of the coupling it is important that for Lagrangian formulation of a dynamical problem the difference analogue of the equation of motion in the mesh method could be written in the form of forces, acting from the surrounding cells on a mesh node. The interface boundary between the particle and mesh regions is assumed to be plane and specified on the pre-processor stage. The centres of particles at the interface are rigidly bound with corresponding mesh nodes or edges. The information exchange is performed via sending coordinates and velocities from the mesh part to the interface automata and using forces from these automata to compute the corresponding nodes acceleration. The suggested approach was applied to study processes taking place at contact patch under of friction.

Abstracts file: Smolin_A_Yu_abstract.doc
Full text file: Smolin_Psakhie.pdf

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