This dissertation presents a numerical model constructed to investigate the dynamics and structures of the Earth’s mantle. Deformation of the Earth’s mantle, which is composed of solid silicate minerals, is strongly governed by the constitutive relation-ship among multiple length-scale structures and properties. To explain the realistic consti-tutive behavior of the silicate mantle, an Internal State Variable (ISV) theory that is an advanced and novel constitutive approach for history-dependent elastoviscoplasticity was applied. The ISV constitutive model was, in turn, implemented into a three-dimensional geodynamic code, TERRA3D, which uses the Finite Element method developed for the mantle convection problem. The sequential studies performed in this dissertation are presented in the follow-ing order: i) a comprehensive summary of the mantle material structures (compositions and microstructural features) and its mechanical properties (elasticity and rheology), ii) a development of a recrystallization and grain size dependent ISV constitutive model for the polycrystalline materials such as minerals and metals, which explains comprehensive mineral physics occurring under the conditions of pressure, temperature, and strain rate within the mantle and their history dependence, and iii) an application of the recrystalli-zation and grain size dependent ISV model to the Earth’s mantle convection problem us-ing the TERRA3D for an investigation of the grain size and dynamic recrystallization efect on the mantle dynamics. The applied ISV constitutive model within the TERRA3D Finite Element frame-work captures the subscale dynamics (dislocation density evolution, dynamic and static recrystallization, grain growth, and grain refinement) and their effect on the large-scale rheology and dynamics of the Earth’s mantle. The numerical investigations reveal that the potential for the mechanical instability and weakening within the mantle arises from the kinetics of grain size and recrystallization and their rheological effect. This mechanical instability leads to the mantle convection entering the episodic overturn regime. The TERRA3D-ISV mantle convection model herein also provides some insightful discover-ies regarding the dynamics and structures within the mantle, explaining its complex rhe-ology caused by the kinetics of recrystallization, grain size, hardening, dislocation recov-ery, and diffusion in the geological settings.

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