Fracture of plane bundle of interacting elastic fibers. Statics

The plane set of N elastic fibres is invesigated. Each fibre interacts with the two nearest neighbours, the interaction force being proportional to the difference of the displacements. The dispersion relation has been written in explicit form. The displacement has been written as the sum of displacements corresponding to the subsequent N modes. The equations of statics are written as the set of N linear algebraic equations. The displacements and stress have been calculated and plotted against the distance for the case when one or two fibres are damaged in a bundle of five fibers, and for the damage of the boundary fiber in a bundle of 21 fibers.