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The structure is a rectangular paral-lelepiped made of reinforced concrete. The floor slab is 12.192m by 15.850m. The walls are placedon top of the slab and are 13.716m high. The floor slab and walls are 1.8288m thick. The floor slabis reinforced with #18 rebar at 0.3048-m spacing inside the lower and upper surfaces. The walls arereinforced with #18 rebar at 0.3048-m spacing inside the inner and outer surfaces. The rebar in the wallsextends 0.3048m into the floor slab. The structure is filled with water to a depth of 13.411m. A cubicyard of explosive is placed on the floor at the middle of the bottom side of one wall. The explosive hasa density of 1785.3 kg/m3 and detonation speed of 8747m/s. A cubic yard of this explosive has a massof about 1365.0 kg. It is detonated at time zero at the center of the side in contact with the floor. Figure 16 shows results from the EMU simulation of this scenario. In this figure, the concrete is green,the rebar is yellow, the liner is orange, the water is blue, and the explosive is purple. The view is a 0.5-mslice about a symmetry plane through the structure and explosive as shown in the graphic at time zero.The time simulated is about 9.8ms. The simulation took about 1.52 h using 8 processors, and the timesteps varied from 7.4µs to 13.6µs. The grid spacing is 0.229m, and there are 281,032 nodes in thecomputational model.The explosive is completely detonated by 0.12ms, and Figure 16 shows that the region containingthe explosive is voided by 0.33ms. By 1.0ms, the liner near the initial location of the explosive isfragmented considerably, and by 1.9ms the outer surface of the floor and concrete wall is slightly bulgednear the detonation region. Concrete is leaving the outer surfaces by 2.8ms as fracturing of the concretecontinues. There is no evidence of the liner near the detonation region at this time.By 4.4ms, most of the structure is fractured and the detonation gases have reached the surface ofthe water. Progression of structure damage is evident at the later times shown in this figure at 4.8ms,5.3ms, and 6.3ms. At 4.8ms, the liner has been completely removed. By 6.3ms, all the walls shown inthis figure are completely fragmented, and the water is essentially gone.
The fragmented materials aredispersing. Figure 17 shows internal damage to a concrete wall and its rebar reinforcement during the simulation.The wall shown in this figure is adjacent to the explosive and is the wall to the right in Figure 16. Noother materials are displayed to obscure the wall. This figure shows damage ranging from no damage(purple) to over 99% damage (orange).The sequence of times begins at 0.12ms when the explosive has completely detonated. The damagespreads until by 5.3ms the bonds in the concrete have completely failed. The spontaneous emergenceof cracks is particularly evident in this figure from 1.0ms until the entire wall is totally fragmented by5.3ms. The orange lines in these figures are damage over 99% at the locations of the rebar. They implythat the rebar fails before the concrete.9. Summary and conclusionsThis paper addressed extreme loading of structures using peridynamics. We reviewed peridynamic theoryand its implementation in the EMU computer code. The theory as implemented in EMU was illustratedwith examples of extreme loadings on reinforced concrete structures by impacts from aircraft. Whileperidynamic theory has been extended to model composite materials, fluids, and explosives, we discussedonly recent developments in modeling gases as peridynamic materials and the detonation model in EMU. Explosive loading of concrete structures was then illustrated. The examples illustrate the power of theperidynamics method in problems where deformation and fracture are expected. The work discussed inthis paper supports the conclusion that peridynamic theory is a physically reasonable and viable approachto modeling extreme loading of structures from impacts and explosions.Research and development in peridynamic theory is not completed. We are continuing our researchon modeling fluids, composite materials, and explosives. Recently, we extended modeling of gas deto-nation products to include use of the JWL equation of state [Dobratz and Crawford 1985]. To improveconfidence in EMU’s capability to model extreme loading, a verification and validation process is be-ing expanded. As the user base and number of code developers increase, attention is being given tosoftware-engineering issues to maintain and distribute the code. There is a long history of constitutivemodel development to represent stress-strain and yield behavior. We are investigating how this wealthof information can be adapted to the peridynamics paradigm and implemented in EMU.We envision future research and development addressing problems at both small scales and moreencompassing, extreme loading macroscale scenarios. Nanoscale to continuum coupling may be possibleusing peridynamics with methods such as the embedded atom method [Daw et al. 1993].Peridynamics has been demonstrated to be viable for analyzing fracture and failure due to loading atthe macroscale. We visualize its being viable for analyzing failure at the microscale and nanoscale also.At the macroscale, we see the possibility of including more phenomenology such as fire, heat transfer,material degradation, etc. to provide a more comprehensive methodology for vulnerability assessmentof critical structures.