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

solidify planetary bodies and subsequently absorb high numbers of impacting bodies culminates in deep time required to produce the observed structure and impact crater record. Our work signifies an initial attempt to address the questions presented above and provide insights into the creation of the Solar System and possible catastrophic interactions occurring from the near passage of celestial objects related to the Earth. This first inception of the model aims to capture the body deformation induced by a passing object (moon, small planet, etc.) on a stable, orbiting object (Earth-like planet), in order to investigate factors contributing to the surface rise and overall deformation of the stationary body (Earth). Finite Element Analysis (FEA) on a planetary scale is cast in a Design of Experiments (DOE) framework to investigate the influence parameters on the Earth’s surface deformation during a near pass fly-by. In particular, we focus on the Earth’s deformations during near pass events as the size and position of the bodies are garnered from the current size and position of the Earth-Moon system. A complex thermomechanical Internal State Variable (ISV) elastic-plastic model is applied to allow for temperature dependent dissipation in the form of plastic deformation. Examination of the ISV parameters provide insights into the hardening and recovery related to dislocation mechanics and highlight certain areas pertaining to the highest rate of plastic deformation. Future model iterations will attempt to describe dissipation mechanisms from tidal and resonance heating and the angular momentum transfer that would occur given favorable conditions of a near pass event. METHODS 1. Design of Experiments (DOE) Methodology To provide a generalized understanding of the boundary conditions of our model, a split-level factorial DOE study is conducted to elicit the most essential aspects pertaining to a near pass event. The DOE presented herein studies the influence of five parameters related to the boundary conditions of a stationary object (body size, core material, and core/mantle thickness ratio) that represents the Earth and a passing object (object mass and passing distance) and the resulting influence on the stationary object’s surface elevation change during a near pass event. A full factorial investigation at two levels would consist of thirty-two (2 5 ) unique simulations. A DOE analysis using an L­ 8 array can obtain the desired first order influences while reducing the number of simulations to eight calculations. The relationship between a set of influences, {A}, and responses, {R}, can be described by a linear mapping through the parameter matrix, [P], which corresponds to the chosen orthogonal array (L 8 ), as the following: { } [ ] { } R P A = , (1) where {R}, {A}, and [P] are given in matrix form as: { } { } [ ] 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , , 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 R A R A R A R A R A P R A R A R A R A + − − − − − − −         + − − − + + + +         + − + + − − + +     + − + + + + − −     = = =     + + − + − + − +         + + − + + − + −     + + + − − + −             1 1 1 1 1 1 1 1 1 1                    +   + + + − + − + −     The magnitude of the set of influences, {A}, can be found by inverting the parameter matrix, [P], and solving { } [ ] { } 1 A P R − = . For this study, three sets of responses, each targeting the surface elevation change at a specific surface area of the stationary body (Earth) are investigated. Figure 1 shows the model parameters for the DOE setup along with targeted areas of interest. The targets of interest correspond to local elevation change occurring on the approach surface, the near-side surface, and the out-of-plane direction. Table 1 describes the simulation parameter values used for the DOE with five parameters and two levels for each parameter. The parameters were chosen to be of similar size and composition to the Earth/Moon system. 2. Internal State Variable Model for Mantle Material Many rheological mechanisms simultaneously operate in the Earth’s mantle during deformation events. While many conceptual theories exist for mantle materials, the exact mechanisms involved and their relationship to mantle strengthening and weakening are still relatively unknown, especially when considering high rate deformation events. Most commonly, power-law creep models have been used to describe the mechanical responses of rock material. Such models rely on uniformitarian assumptions of very slow rates and are limited to few deformation mechanisms. With this motivation, several authors (Baumgardner 2003; Sherburn et al. 2011) have developed mathematical models to accurately and realistically describe some of the rheological mechanisms and have applied them to global mantle simulations, specifically regarding the dynamics of the Earth’s mantle during the Genesis Flood. Most recently, Sherburn et al. (2013) implemented the Internal State Variable (ISV) constitutive model, a sophisticated constitutive model originally developed at Sandia National Laboratories (Bammann 1990; Bammann et al., 1993; Horstemeyer 2000). The authors show that the ISVmodel has a great capacity of capturing the material behavior of metals, polymers, and mantle rocks. Through the use of internal state variables, the ISV model can capture the mechanical history of a material and be used to predict mechanical properties such as strength and deformation. Furthermore, the ISV model has the capability to accurately capture the elasticity and plasticity of a material, including the hardening and the recovery mechanisms related to internal structure rearrangement. Sherburn et al. (2013) discovered that a crucial microstructural mechanism dominated the Genesis Flood event: dynamic recovery. When the dynamic recovery was turned on in the calibrated ISV model using lherzolite’s stress-strain data, simulations showed a significant strength weakening in the mantle. Because the catastrophic mantle deformation process during a near pass event would be much more dynamic than mantle motion we see today, the dynamic recovery or dislocation creep could be highly activated and greatly influence the resulting kinetics of planetary deformation. A pressure dependent ISV model was implemented by Cho et al. (2018) to capture the complex mechanical behavior of the Earth’s mantle in static and dynamic conditions. The ISV model is a strain-rate, pressure, and temperature dependent plasticity model that utilizes isotropic hardening as an internal state variable to describe dislocation pile up (hardening) and dislocation slip and Seely et al. ◀ Finite element analysis of a near impact event ▶ 2018 ICC 54