Energetical background of common approaches in geomechanics

Book chapter, 2018

As is well known, mechanics in general is based on three basic conservation laws, those of mass, momentum and energy. Of those, the first two can be derived from the last, when one considers the objectivity with respect to the observer as a prerequisite. A further energy related concept significant for modeling is the second law of thermodynamics. This chapter discusses several common methods and concepts used in geomechanics, with respect to their relationship to the first and second law of thermodynamics. The aim is to provide the reader with a better understanding of the underlying assumptions of these approaches. The various methodologies presented are subdivided into two categories, principles based on the concept of energy conservation and variational principles. In the first category the derivation of the mass, momentum etc. balance equations from the energy balance by means of assuming a change of observer and the derivation of the micromechanical formulation of stress measures are discussed, as well as a brief discussion on energy based upscaling. In the category of variational principles, the minimum potential energy, the maximum plastic work and the second order work are outlined. The virtual work method is omitted, as it has been discussed in more detail elsewhere in this book.