NON-SINGULAR METHOD OF FUNDAMENTAL SOLUTIONS FOR THE DEFORMATION OF TWO-DIMENSIONAL ELASTIC BODIES IN CONTACT

The development of an effective new numerical method for the simulation of the micromechanics of multi-grain systems in contact is developed in the present paper. The method is based on the Method of Fundamental Solutions (MFS) for two-dimensional plane strain isotropic elasticity and employs the Kelvin Fundamental Solution (FS). The main drawback of MFS is the presence of an artificial boundary, outside the physical boundary, for positioning the source points of the FS, which is difficult or impossible in multi-body problems. In order to remove the singularities of the FS the point sources are replaced by the distributed sources over circular disks. The values of the distributed sources are calculated in a closed form in the case of the Dirichlet boundary conditions. In the case of the Neumann boundary conditions the respective values of the derivatives of the FS are calculated indirectly from the considerations of the solution of simple displacement fields. A problem of two, four and nine bodies in contact is tackled. The newly developed method is verified based on a comparison with the classic MFS. The numerical method will form a part of the microstructure-deformation model, coupled with the macroscopic thermo-mechanics simulation system for continuous casting, hot rolling and heat treatment.