Filtration devices may include a shape-memory material having a compressed run-in position or shape and an original expanded position or shape. The shape-memory material may include an open cell porous rigid polyurethane foam material held in the compressed run-in position at the temperature below glass transition temperature (Tg). The foam material in its compressed run-in position may be covered with a fluid-dissolvable polymeric film and/or a layer of fluid-degradable plastic. Once filtration devices are in place in downhole and are contacted by the fluid for a given amount of time at temperature, the devices may expand and totally conform to the borehole to prevent the production of undesirable solids from the formation.