Constitutive equations are reported for the effect of porosity on the elastic moduli and longitudinal sound speed of polymer foams. These relations are grounded on the asymptotic homogenization method combined with the integration embedding scheme. Observations are analyzed on open-cell and closed-cell porous polymers manufactured by (1) foaming with chemical blowing agents, (2) foaming with inert gases, and (3) emulsion-templating foaming. Numerical analysis of experimental data shows that changes in the elastic moduli with porosity are correctly predicted by the governing relations for foams with spherical voids. Porous polydimethylsiloxane (PDMS) elastomers prepared by the emulsion-templating method provide an exception from this rule. The difference between these materials and the other cellular polymers is caused by production of hydrogen gas under curing, which induces severe deformation of pores. Simulation reveals that experimental data on cellular PDMS elastomers are described by the differential equations for foams with spheroidal voids whose aspect ratio depends on porosity.
INTRODUCTIONThe elastic response of polymer foams has attracted substantial attention, because these materials demonstrate excellent material properties (ease of processing, low production cost, high specific strength and energy adsorption, good chemical resistance, low density, dielectric constants, and thermal conductivity). Applications of polymer foams range from (1) composite core materials for sports equipment, interior panels in aircrafts and boats, 1 and automotive seat cushion constructions 2 to (2) materials for thermal isolation 3 and acoustic absorption, 4 to (3) porous template materials for purification of wastewater, 5 as well as filtration, gas sorption, catalysis, and separation, 6 to (4) drug delivery and protein encapsulation, 7 to (5) tissue scaffolds for growth of cells and artificial organs, 8 to (6) materials for endovascular procedures 9 and measurement of brain activity, 10 to (7) flexible and stretchable pressure 11 and temperature 12 sensors, to (8) lightweight devices for electromagnetic interference shielding, 13 to (9) porous electrodes for solid oxide fuel cells, 14 to (10) ferroelectrets for energy harvesting from vibration. 15