Dynamic Stress State of Auxetic Foam Medium Under the Action of Impulse Load

The paper presents studies on the application of the boundary integral equation method for investigation of dynamic stress state of negative Poisson’s ratio foam media with tunnel cavity under the action non-stationary loads. In case of the plane problem, the distribution of normalized hoop and radial stresses were obtained for the action of non-stationary impulse load, which was applied to the boundary of cavity cross-sections. For the solution of the non-stationary problem, the Fourier transform for time variable was used. In Cosserat elasticity for the application of the boundary integral equation method the Fourier transform potential representations of displacements and microrotations were written. The fundamental functions of displacements and microrotations for the two-dimensional case of Cosserat continuum were built. For the solving of time-domain problem the system of singular integral equations was written. For numerical calculations the method of mechanical quadrature was applied. Numerical example shows the comparison of dynamic stress distribution in the foam medium with negative and positive Poisson’s ratio under the action of impulse load.