Computational Materials Science: The Simulation of Materials, Microstructures and PropertiesModeling and simulation play an ever increasing role in the development and optimization of materials. Computational Materials Science presents the most important approaches in this new interdisciplinary field of materials science and engineering. The reader will learn to assess which numerical method is appropriate for performing simulations at the various microstructural levels and how they can be coupled. This book addresses graduate students and professionals in materials science and engineering as well as materials-oriented physicists and mechanical engineers. |
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Page 29
... derivatives . Equations which involve unknown functions that depend on only one independent variable are referred to ... derivatives of the unknown functions in the equation . Equations involving only the first derivatives are referred ...
... derivatives . Equations which involve unknown functions that depend on only one independent variable are referred to ... derivatives of the unknown functions in the equation . Equations involving only the first derivatives are referred ...
Page 31
... derivatives in each of the independent variables , each of the derivatives having equal sign when grouped on the same side of the equation . hyperbolic partial differential equation parabolic partial differential equation elliptic ...
... derivatives in each of the independent variables , each of the derivatives having equal sign when grouped on the same side of the equation . hyperbolic partial differential equation parabolic partial differential equation elliptic ...
Page 33
... derivatives , are often referred to as finite difference techniques . Most of the finite difference simulations addressed in this book are discrete not only in time but also in space . Finite difference methods approximate the derivatives ...
... derivatives , are often referred to as finite difference techniques . Most of the finite difference simulations addressed in this book are discrete not only in time but also in space . Finite difference methods approximate the derivatives ...
Contents
Material Constants | 1 |
Molecular Dynamics | 7 |
GinzburgLandauType Phase Field Kinetic Models | 10 |
Copyright | |
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Common terms and phrases
according allows amounts applications approach approximate assumed atoms average boundary calculated cell cellular Chapter classical components concentration concept considered constant coordinates crystal defects defined density depends derivatives described differential equations diffusion discrete dislocation displacement distribution elastic electron energy ensemble equilibrium et al evolution examples expression field Figure finite difference finite element force formulation function given grain grain boundary growth independent instance integral interaction interface introduced kinetic lattice macroscopic materials science matrix means mechanics Metall method microstructure models molecular dynamics Monte Carlo motion obtained orientation original parameters particle phase physical plasticity position possible potential predictions problem properties Raabe random recrystallization referred represents rules sampling scale segments simple simulations solution solving space spatial statistical step strain stress structure techniques tensor theory transformation typically usually values variables various vector volume written