The Proceedings of the Eighth International Conference on Creationism (2018)

contours were generated and pressure versus surface depth graphs were constructed. During the fly-by event, von Mises stress contours were generated at equal intervals from 0 seconds to 20,000 seconds in order to show the stress state changes. The surface displacement history on the approach face, the near-side face, and the out-of-plane direction (Poisson’s contraction) are plotted at several intervals throughout the fly-by. Contour plots of the plastic strain and isotropic hardening are also presented at equal intervals from 0 seconds to 20,000 seconds to provide insight into the hardening mechanisms involved during the near pass event. RESULTS/DISCUSSION 1. Model Validation with Earth-Moon System The model validation procedure for the near impact event includes comparing the pressure profiles and surface deformation of known quantities within the Earth-Moon system. Since the early solar system history is of interest, especially related to possible Earth- Moon interactions, careful attention is given to the pressure profile of the Earth due to self-gravity. The importance of capturing the self-gravity loading is expressed during the unloading of stress that occurs during a near pass event. If the stationary body is initially unloaded or loaded insufficiently, the magnitude of surface deformation will be difficult to determine. Figure 2 illustrates the simulated two-layer Earth pressure response due to self-gravity forces. The complete pressure profile is shown in Figure 2(b) and is compared to the Preliminary Earth Reference Model (PREM) pressure profile obtained from seismic data (Dziewonski and Anderson 1981). The PREM model is a popular one-dimensional model fit from seismic data of the Earth’s layers and the first model to account for attenuation and anisotropy within the Earth. However, the PREM model is a zeroth order approximation due to the ellipticity and lateral variations within layers of the Earth, which poorly represents some areas of the uppermost and lower mantle. Thus, the model represents averages over the heterogeneous structure of the Earth. The overall pressure profile of the Earth is well captured throughout the mantle and core. The transition from the rocky mantle to the iron core is captured in the model by the sudden increase in pressure at the core-mantle boundary. Figure 3 compares the pressure dependence of the density, bulk modulus, and shear modulus to the PREM model within the mantle. The density profile is well predicted through the mantle. The bulk modulus and shear modulus are observed to be pressure dependent and compare well to the PREM model up to a depth of 600 km. At around 600 km, the crystallographic structure of the mantle rock changes causing a rapid increase in bulk modulus and shear modulus, an effect not captured by our model and illustrates the complexity involved in capturing the compete mantle behavior. Although a precise fit of the moduli is not achieved, the pressure and density profiles are well predicted. The next step in the simulation process is to compare the simulated lunar pressure and lunar tidal bulge to the experimentally determined values. Figure 4 illustrates the simulated lunar pressure profile due to self-gravity loading. While the complete pressure profile of the moon has not been experimentally determined, the maximum pressure of the moon is estimated to be five to six GPa through seismic experiments (de Vries et al. 2010). The estimated maximum lunar pressure compares closely to our simulated maximum pressure of 6.6 GPa. Additionally, the lunar tidal bulge created by the gravitational pull of the Earth was calculated. From the simulation, the bulge was calculated to be 87.5 cm and is within the experimental uncertainty bounds of 52 cm ± 126 cm determined recently by NASA measurements (Mazarico et al. 2014). 2. Design of Experiments Results The results of the normalized influence of the parameters on the approaching face surface deformation are shown in Figure 5. Based on the results, the dominating influences are the passing object distance, stationary body size, and the core/material ratio. The greater influence of these three parameters indicates that the surface rise on the approaching face is greatly dependent on the increased self-gravity loading caused by a much denser iron core and a larger iron core radius. The presence of a large dense core produces large gravitational forces that must be overcome to unload the surface and cause deformation during a near pass event. The core materials, along with a passing body mass, moderately influence the surface rise as they are directly involved in Newton’s equation in determining the force between the two bodies. Figure Seely et al. ◀ Finite element analysis of a near impact event ▶ 2018 ICC 57 Figure 2. Internal pressure of a two-layer earth model (iron core, olivine mantle) due to self-gravity illustrating a) the finite element analysis pressure contour and b) the simulated internal pressure profile compared to the Preliminary Reference Earth Model (PREM) (Dziewonski and Anderson, 1981).