Porous solids with a fluid pore content as well as real mixtures of liquids and gases belong both to the class of multi-phase materials. With a continuum theory for multiphasic media, the movement or flow of fluids in deformable porous solids can be described for arbitrary deformation processes and arbitrary material properties of the solid matrix. Moreover, it is possible to consider phase transitions and electrochemical reactions within such a theory. In this regard, a theoretical tool is provided that can be used to mathematically describe and numerically analyse a manifold of distinct materials, ranging from geomaterials over polymer and metal foams to biological tissues. For the numerical application, a system of strongly coupled partial differential equations has to be solved.

• Continuum-mechanical basics for the description of single- and multiphasic materials: state of motion, deformation measures, stress states
• Balance relations for multi-phase materials: master balances, special balances for mass, momentum, moment of momentum, energy and entropy
• Caloric state variables and energy potentials
• Fundamentals of materials theory for multiphasic media
• Thermodynamics and constitutive equations
• The fluid-saturated, materially incompressible deformable porous solid
• Elastic material properties of the solid skeleton
• Plastic behaviour of the solid skeleton (optional)