Product: ABAQUS/Explicit
This problem involves two rubber bladders filled with fluid and subjected to external axial compression. There is a fluid exchange between the two bladders so that fluid can move between them. The amount of mass transfer depends on the pressure differentials between the bladders. The bladders are modeled as short cylinders (with M3D4R elements) or spheres (with SAX1 elements) with a radius of 1.0 m and a wall thickness of 0.05 m. Ogden hyperelasticity (N=3) with the TEST DATA INPUT parameter is used for the rubber constitutive equation. The fluid cavity in the bladders is modeled using the *FLUID CAVITY option by defining surfaces on the inside of the bladders using the *SURFACE, TYPE=ELEMENT option. The fluid cavity's reference node must lie on the symmetry plane or the symmetry axis, respectively. The normals to the element-based surface must point into the fluid cavity to obtain the correct cavity volume. The ambient pressure is assumed to be 50.0 kPa, and the fluid is prepressurized to a gauge (additional) pressure of 8.2736 kPa. Static equilibrium requires that the rubber bladders also be subjected to a uniform initial stress of 165.972 kPa along the circumferential direction in the M3D4R elements and a uniform in-plane initial stress of 82.736 kPa in the spheres.
The transfer of fluid is modeled by using the *FLUID EXCHANGE option and specifying the BULK VISCOSITY parameter on the *FLUID EXCHANGE PROPERTY option. The viscous coefficient, 
, and the hydrodynamic resistance coefficient, 
, are chosen to be 10000.0 and 100.0, respectively. These resistance coefficients determine the mass flow rate at any time instant as a function of the pressure differential between the two bladders.
The problem is also analysed by modeling the fluid cavity with hydrostatic fluid elements. In the axisymmetric case FAX2 fluid elements are used, sharing the same nodes as the SAX1 elements. Fluid pressure and fluid volume inside each sphere can, thus, be obtained. In the three-dimensional case F3D4 fluid elements are placed on top of the membrane elements (they share the same nodes) and F3D3 elements are used to model the two ends of the cylinders so that the fluid inside each container is completely enclosed by the hydrostatic fluid elements. The transfer of fluid is modeled with an FLINK element connecting the two cavity reference nodes. Hydrostatic fluid elements do not contribute to the stable time increment calculation. The reference nodes of the fluid elements have only a single (pressure) degree of freedom and do not move with the structures.
The bladder systems are impacted by a rigid body at a constant downward velocity of 4.0 m/s. The total time of the event is 0.64 sec. Figure 2.5.1–1 gives the initial configuration of the three-dimensional model. Figure 2.5.1–2 shows the final deformed shape of the cylindrical rubber bladders. Figure 2.5.1–3 gives the initial configuration of the axisymmetric model. Figure 2.5.1–4 shows the final deformed shape of the spherical rubber bladders. The fluid pressures inside the two containers are plotted in Figure 2.5.1–5 and Figure 2.5.1–6. The pressures in the two bladders are almost the same, owing to the fluid link, which drives the flow of fluid if there is any pressure differential between the two bladders. The pressure in the cylinders rises more than the pressure in the spheres as the relative volume change in the spheres is less than in the cylinders. The pressure in the cylinders and the spheres shows oscillations that are caused by the stiffness associated with flattening of the spheres.
Three-dimensional membrane elements. The surface-based fluid cavity capability is used to model the fluid cavity.
Three-dimensional membrane elements using the general contact capability. The surface-based fluid cavity capability is used to model the fluid cavity.
Axisymmetric case where two rubber spheres instead of barrels are modeled. The surface-based fluid cavity capability is used to model the fluid cavity.
Three-dimensional membrane and fluid elements.
Three-dimensional membrane and fluid elements using the general contact capability.
Axisymmetric case where two rubber spheres instead of barrels are modeled. Hydrostatic fluid elements are used to model the fluid cavities.
