Efficient Solution for Composites Reinforced by Particles
نویسنده
چکیده
A very effective method for some kind of problems is the Method of Fundamental Solutions (MFS). It is a boundary meshless method which does not need any mesh and in linear problems only nodes (collocation points) on the domain boundaries and a set of source functions (fundamental solutions, i.e. Kelvin functions) in points outside the domain are necessary to satisfy the boundary conditions. Another kind of source functions can be obtained from derivatives of the Kelvin source functions. Dipoles are the derivatives of Kelvin function in direction of acting force. Putting the dipoles into the particle, i.e. outside the domain of the matrix of composite material, they can very efficiently simulate the interaction of the particle with the matrix and with the other particles. A dipole satisfies both the force and moment equilibrium and so the models do not require any additional condition for the simulation of interactions. If the particles of reinforcing material are in the form of spheres, or ellipsoids, a triple dipole (i.e. dipoles in the direction of main axes of the particle) can give satisfactory accuracy for practical problems. It is given how the models can be used for homogenization of composite material. A novel method is used for evaluation of material properties of homogenized material in order to increase the numerical efficiency of the composite. The numerical results are compared with Mori-Tanaka analytic models with all rigid inclusions as well as for problems with elastic inclusions when the differences in stiffness of matrices and particle are small.
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