Ivestigation of the Dynamic Stress State of Foam Media in Cosserat Elasticity

Abstract

The paper presents studies on the application of the boundary integral equation method for investigation of dynamic stress state of foam media with tunnel cavities in Cosserat continuum. For the solution of the non-stationary problem, the Fourier transform for time variable was used. The potential representations of Fourier transform displacements and microrotations are written. The fundamental functions of displacements and microrotations for the two-dimensional case of Cosserat continuum are built. Thus, the fundamental functions of displacement for the time-domain problem are derived as the functions of the two-dimensional isotropic continuum and the functions, which are responsible for the effect of shear-rotation deformations. The method of mechanical quadrature is applied for numerical calculations. Numerical example shows the comparison of distribution of dynamic stresses in the foam medium with the cavity under the action of impulse load accounting for the shear-rotation deformations effect and without accounting for this effect.

Моделювання Динамічного Напруженного Стану Пінистих Матеріалів За Дії Концентрованого Навантаження

“…Solution of the non-stationary problem. For the solving non-stationary problem Fourier transforms for time variable [5] and modification boundary integral equation method [6] were used. The representations for transforms of displacements and microrotations are written [6]:…”

“…where UU  are the fundamental functions for displacements and mictrorotations [6], pj, mk are unknown functions.…”

“…Inserting the representations of displacements ( 5) and microrotations (6) to the force and couple stress formulas (3) we obtain the integral dependencies for absent of couple forces:…”

“…Calculations of the hoop stress transforms on the boundary of the cavity of the medium are performed by formulas [6]. Substituting in these formulas the potential representations for displacements (5) and microrotations (6), selecting irregular parts and completing limit transition the transforms of the hoop stresses on the boundary are written:     for plane strain). Modified discrete Fourier transform is used for calculation of originals of the dynamic hoop and radial stresses [5].…”

“…Numeric calculation.Within the framework of the Cosserat elasticity, based on the developed boundary integral equation method [6] for elastic foam medium, we investigate the distribution of dynamic hoop stresses at the boundary of a circular cross-section cavity. Numerical calculations are performed for the case of the dynamic stress state of the medium is caused by the action of the system of concentrated nonstationary forces (1) (2) j j j P P iP  .…”