Advances in Continuum Modeling

Karlstad University

The PhD course contains: Non-dimensionalization and scaling. Extensive quantities and the link to the concept of measure. Local and global balance equations in terms of measure. Radon-Nikodym's theorem. Cauchy fluxes. Cauchy's and Piola-Kirchoff's stress tensors. Real and virtual work. Deformation tensor. Constitutive laws. Shock, Rankine-Hugoniot relations. Derivation of boundary conditions. General properties of Newtonian flows. Flows of inviscid fluids. Viscous flows and thermohydraulics. Chemical reactions. Derivation of combustion equations for mixtures. General equations for linear elasticity. Principle of virtual work and variantional formulations. Derivation of non-linear constitutive laws via asymptotic homogenization. Balance laws for extensive quantities in materials with microstructures.

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