# Lherzolite

## Contents |

### Background

A mantle convection has been one of the hardest and most controversial parts of geology. In 1980, Dziewonski and Anderson performed an important study using a seismological method to explore the inner earth^{[1]}. This PREM (Preliminary Reference Earth Model) study showed that the mantle is made of a solid material that has viscosity. Moreover, sophisticated GPS technology that allows observation of the oceanic floor demonstrated that the earth’s plates are moving with a velocity of approximately 10 cm/yr. Therefore, many geophysicists studied and model the mantle’s convection mechanisms. However, mantle convection still remains a largely unsolved problem.

Engineering society has developed a material modeling technique. Integrated Computational Material Engineering (ICME) has been developed as one of the effective material modeling methods. The ICME modeling method is expected to give better accuracy for mantle convection problem.

### Multiscale Modeling for Lherzolite

#### Structural Scale Research

By using FEA simulation, structural scale mantle modeling can be implemented. ISV constants needed for simulation will be obtained from lower length scales' simulations and experimental data for Lherzolite.

#### Macroscale Research

At the macroscale, FEA simulations with ISV model equations will be performed then validated and verified. Through these processes, the material model is validated and verified with by quantifying uncertainty. A validated and verified lherzolite material model can be used to simulate structural deformation.

#### Mesoscale Research

In this scale, slip systems of lherzolite can be modeled directly using Finite Element Analysis. Through this modeling, information of plastic spin, texture, yield surfaces, isotropic hardening, and kinematic hardening can be gained for the polycrystalline rock^{[2]}. Also, averaged information can be compared with the macro scale continuum material.

#### Microscale Research

The plastic deformation of crystals occurs by dislocation processes when the material is subjected to stress. The mantle convection mechanism is closely related to the dislocation and recovery process of the rock materials such as lherzolite. Dislocation-Dynamics (DD) simulations will be applied to explore the dislocation phenomena of lherzolite. Dislocation segments respond to driving forces with a mobility function which is extracted from lower length scale, atomistic simulations.

#### Nanoscale Research

Atomistic simulations need information about the interaction potentials of atoms. Total energy information can be given either by lower length scale DFT calculations or experimental data. To calculate the interaction potentials, the embedded atom method (EAM) or modified embedded atom method (MEAM) will be used. Atomistic simulations give mobility functions that are related to dislocations. For the next higher length scale, Dislocation Dynamics will use this mobility function to simulate dislocation mechanisms. Also, for the EAM or MEAM calculation and validation, energy and elastic moduli results from lower length scale and electronics scale will be used.

#### Electronic Structure Research

In the electronic scale, the basic principles are related to quantum mechanics. Actually, every material is formed by electron’s interactions among neighboring atoms. This interaction is also related to energy. Through the simulation of the electronics scale, one can find the interfacial energy term and elastic moduli of the materials. Density Functional Theory (DFT) will be used as an electronic scale simulation tool. DFT’s principle expresses an interacting system of fermions using its density.

### References

- ↑ Dziewonski, A. M., Anderson, D. L., “Preliminary reference Earth model”, Physics of the Earth and Planetary Interiors, Vol. 25 (1981), pp. 297-356.
- ↑ Horstemeyer, M. F., “Integrated computational Materials Engineering (ICME) For Metals”, A John Wiley & Sons, Inc.(New Jersey, 2012), pp.98-111, 146-159, 164-185