Mandel and Cryer problems of fluid-saturated foams with negative Poisson's ratio

Professor Lakes created foams with negative Poisson's ratio:; in 1987. Since then he has examined interesting and fantastic characteristics of such foams and proposed their realistic and future possible applications. The present study was motivated by our interest in how such a foam behaves for a sudden loading if it is saturated with fluid. To highlight mechanical interactions between elastic deformation of such a foam and diffusion of the saturating fluid, we solved four problems in a unified manner: 2D and 3D, Cryer and Mandel problems. It is found that for all these problems the pore fluid pressure near the sample center climbs up from its initial pressure and then declines and vanishes; its peak is much higher for negative Poisson's ratios, that is, much more remarkable Mandel-Cryer effect. Stress components such as tangential stress also show similar behavior, and the tangential stress has tension near the sample surface in spite of compressive loading. It is also found that for the step-like axial compression the Mandel cylinder sample laterally expands immediately after the loading, then shrinks and finally becomes thinner than its original thickness; a possible application is proposed.