Twinning in pressurized porous elastomers

For some time, it has been known that, under appropriate loading conditions, porous elastomers may develop instabilities in their macroscopic response. More recent theoretical work has shown that these composites may undergo ‘twinning’ or ‘domain formation,’ beyond the onset of such macroscopic instabilities. Here, motivated by interest in the possibility of using such porous elastomers for actuation purposes, we generalize this earlier work to account for pore pressure. For this purpose, we consider a class of two-dimensional (2D) porous elastomers consisting of random, isotropic distributions of aligned cylindrical pores in the elastomer. Exploiting the incompressibility of the elastomeric matrix, estimates are generated for the ‘principal’ or ‘mesoscopic’ and ‘relaxed’ or ‘macroscopic’ stored-energy functions of the porous elastomers with pressurized pores, by means of the earlier estimates for the unpressurized porous elastomers. Two specific cases are considered in detail: closed pores containing an ideal gas and open pores with direct pressure control. In the first case, it is found that, while the pressure generally stiffens the response, the onset of the instabilities and the associated twinned microstructures are insensitive to the pore pressure. In the second case, it is found that negative gauge pressures in the pores can be used to trigger the twinning instabilities, even at zero externally applied tractions. In either case, as previously found for the case of unpressurized pores, the response of the porous composite after twinning is perfectly soft in shear, which could prove extremely useful for actuation purposes. In addition, highly unusual behaviors, such as huge changes in shape, are predicted, even before the onset of twinning, by combining direct pressure control with appropriately selected (fixed) traction boundary conditions.