A Systematic Approach to Standard Dissipative Continua

Many isothermal dissipative continuum problems can be formulated in a variational setting using the concept of “standard dissipative continua”. A major advantage of this approach is that complex problems can be cast into a compact, thermodynamically consistent formulation based on a single space–time continuous functional together with a corresponding variational principle. Formulating the problem in terms of a functional provides an immediate avenue for performing spatial and temporal discretization, which are the prerequisites for a numerical solution. Within the present contribution, a novel systematic approach to standard dissipative formulations is proposed, with the main goal being the development and implementation of generic procedures and algorithms for the formulation as well as the computational solution of a subset of isothermal dissipative continuum problems. In order to demonstrate the capabilities of the approach, its application to example problems is discussed.