Modern continuum mechanics is the topic of this book. After its introduction it will be applied to a few typical systems arising in the environmental sciences and in geophysics. In large lake/ocean dynamics peculiar effects of the rotation of the Earth will be analyzed in linear/nonlinear processes of a homogenous and inhomogenous water body. Strong thermomechanical coupling paired with nonlinear rheology affects the flow of large ice sheets (such as Antarctica and Greenland) and ice shelves. Its response to the climatic forcing in an environmental of greenhouse warming may significantly affect the life of future generations.

The mechanical behavior of granular materials under quasistatic loadings requires non-classical mixture concepts and encounters generally complicated elastic-plastic-type constitutive behavior. Creeping flow of soils, consolidation processes and ground water flow are described by such theories. Rapid shearing flow of granular materials lead to constitutive relations for the stresses which incorporate rate independent behavior of Mohr-Coulomb type together with dispersive stress contributions due to particle collisions. Rockfalls, sturzstroms, snow and ice avalanches, but also debris flow and sea ice drifting can be described with such formulations.