A Computational Framework for Phase-field Modeling
Memorandum rept. 1 Oct 2009-30 Sep 2010
ARMY RESEARCH LAB ABERDEEN PROVING GROUND MD COMPUTATIONAL AND INFORMATION SCIENCES DIR
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As part of the Directors Research Initiative, phase-field theory and simulation software are developed. The theory addresses mechanical twinning in crystalline solids with equilibrium equations obtained via a variational principle in the null temperature limit. Numerical solutions to weak forms of governing equations are obtained via conjugate gradient energy minimization and the finite element FE method. Two fundamental problems in materials physics are considered. The first addresses homogeneous nucleation of a twin in a magnesium Mg single crystal. Critical shear strains for nucleation obtained numerically using the phase-field approach are in fair agreement with those obtained analytically in the sharp-interface limit. The second addresses twin nucleation in calcite CaCO3 single crystals subjected to indentation loading. Long, thin, asymmetric twins with sharp cusp-like tips are observed in the numerical simulations and are in qualitative agreement with experiments. All results obtained are predictive the model does not require calibration or fitting of material parameters.
- Physical Chemistry
- Numerical Mathematics
- Computer Programming and Software