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

annihilation (recovery). The strain rate, pressure, and temperature dependence can be captured with sufficient experimental data for fitting. For this work, the ISV coefficients found in Cho et al. (2018) for polycrystalline olivine were used for the mantle material. The complete formulation for the ISV elastic-plastic model can be found in the same reference. The pressure dependent ISV model provides pressure sensitive descriptions of the yield surface and hardening equations, along with the bulk and shear modulus, to capture pressure effects on the dislocation mechanisms required for the extremely high pressures found in the Earth’s mantle. Regarding the yield surface in the present ISV constitutive model, Drucker-Prager shear failure yield surface and von Mises pressure insensitive yield surface were combined with Transitional yield surface to avoid numerical singularities (Hammi et al. 2016). This yield function describes that initially the elastic limit increases as pressure increases, but the elastic limit becomes insensitive to the pressure when the rock aggregate is fully compacted, as shown in several lab experiments (Kavner 2007). Dislocation motion is also influenced by hydrostatic pressure. When the pressure increases, the activation barrier also increases; consequently, the dislocation mobility is somewhat suppressed. In the free energy concept, the pressure dependence of dislocation dynamics can be modeled via an activation volume (Karato 2012). Also, the current ISV formulism uses a pressure and temperature dependent shear modulus for the hardening moduli, and the shear modulus is estimated by 3rd-order Birch-Murnaghan equation of state. In this manner, the present ISV constitutive model captures the pressure dependent material’s behavior, which counteracts against temperature effects. 3. Finite Element Analysis Setup For this work, the finite element programABAQUS/Standard v14.2 was used as the numerical code of choice. First, to validate the surface deformation predicted by the model, a simple Earth-Moon system was simulated to predict the surface deflection observed on the Moon by the Earth’s gravitational pull. Both objects were stationary to simulate tidal locking between the Earth and Moon. The Moon sized object was first loaded under self-gravity then subjected to a gravitational body force according to Newton’s law of gravitational acceleration and the resulting surface deformation was determined. The detailed procedures for the development and application of the self-gravity body force and the distributed gravitational body force are provided in theAppendix for reference. Figure 1 depicts the two-dimensional geometry, orientation, and trajectory of the stationary (Earth) and passing objects although the simulations were performed on a three-dimensional mesh. For the DOE simulations, the passing object travels within the x-y plane and begins at an x-distance of 1.4E10 m and travels at 7000 m/s in the negative x-direction. Table 2 lists material constants used for the olivine mantle/core and iron core. Due to the high pressure environment of the iron core, an elastic model was used to describe the core’s material properties. The mantle material model was the ISV model for polycrystalline olivine described above. For a detailed study of the near pass phenomena, the kinetics of a large object fly-by on a non-rotating two-layer model Earth were investigated for two cases. The first case is a Lunar scale mass (7.34 x 10 22 kg) passing at a velocity of 5,000 m/s at a peri-apsis distance (point of nearest passage) of 45,000 km between mass centers. The second case is an Earth scale mass (5.97 x 10 24 kg) passing at a velocity of 20,000 m/s and a peri-apsis distance of 45,000 km between mass centers. For both cases the passing body followed a simplified linear path with constant velocity in the equatorial plane of the model Earth. The fly-by simulations occurred in two steps: first, a body force was applied to the stationary object to represent a self-gravitational load; second, a subsequent fly-by of a near pass object, modeled as a point mass, was passed by the stationary body at the prescribed velocity. The detailed procedures for the development and application of the self-gravity body force and the distributed body force due to the fly-by object are provided in the Appendix for reference. The following is a short description of the boundary conditions implemented for the simulation. To apply the self-gravity body force, an analytical expression based on the element radial distance was developed using Newton’s law of gravitational acceleration. For the two-layer model, the self-gravity expression for the mantle became more complicated as it accounted for gravitational forces from the denser iron core and the olivine mantle. The distributed force expression for the gravitational force between the stationary and fly-by object used the ABAQUS user subroutine DLOAD. As shown in Figure 1, the passing fly-by object traveled at a constant velocity in a simplified linear path past the stationary object. Using the DLOAD routine, the position of the passing object was calculated at each time step and the distance was used in Newton’s gravitational equations to calculate the resulting body forces on the stationary object. In order to remove the center of mass motion that was created from the pull of the passing object, the ABAQUS inertia relief command was used and only body deformation was allowed. All geometries resulting from the DOE setup are meshed with three-dimensional, twenty-noded, continuum, quadratic, brick elements with reduced integration (C3D20R). The global size of elements for each simulation was 250 km. Post-processing of the simulation data was performed with ABAQUS/CAE v14.4. To study the effect of self-gravity, pressure Seely et al. ◀ Finite element analysis of a near impact event ▶ 2018 ICC 56 Layer Material Material Model Temperature (K) Density (kg/m 3 ) Shear Modulus (GPa) Bulk Modulus (GPa) Mantle Olivine ISV 350 3345 80 130 Core Olivine Elastic 750 4500 80 130 Core Iron Elastic 2000 13000 176 1425 Table 2. Material constants for the mantle/core material used for the design of experiments simulation matrix. The ISV relates to the plasticity internal state variable constitutive model.