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Numerical modeling of rock deformation 03 :: Continuum Mechanics

Goals of today. Understand the concept of Taylor series expansionDerive the conservation equations formasslinear momentumangular momentum. Conservation equations. The fundamental equations of continuum mechanics describe the conservation ofmasslinear momentumangular momentumenergyThere exi

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Numerical modeling of rock deformation 03 :: Continuum Mechanics

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    1. Numerical modeling of rock deformation 03 :: Continuum Mechanics www.structuralgeology.ethz.ch/education/teaching_material/numerical_modeling Fallsemester 2011 Thursdays 10:15 12:00 NO D11 & NO CO1 Marcel Frehner marcel.frehner@erdw.ethz.ch, NO E3 Assistant: Jonas Ruh, NO E69

    2. Goals of today Understand the concept of Taylor series expansion Derive the conservation equations for mass linear momentum angular momentum

    3. Conservation equations The fundamental equations of continuum mechanics describe the conservation of mass linear momentum angular momentum energy There exist several approaches to derive the conservation equations of continuum mechanics: Variational methods (virtual work) Based on integro-differential equations (e.g., Stokes theorem) Balance of forces and fluxes based on Taylor terms We use in this lecture the balance of forces and fluxes in 2D, because it may be the simplest and most intuitive approach.

    4. Conservation of mass Taylor series expansion Mass flux at left boundary Mass flux at right boundary Mass flux at bottom boundary Mass flus at top boundary

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