CISM • International Centre for Mechanical Sciences

Thermodynamics of Irreversible Processes in Material Systems

Advanced Courses
Thermodynamics is an efficient tool for the description of the development of the microstructure of a solid material system as well as the motion of defects. Within the framework of continuum mechanics a proper thermodynamic potential depending on external and internal state variables can be found to describe the state of a system. Internal state variables are assigned to properties, e.g., as concentrations of components, but can also be assigned to defects, e.g., cracks or dislocations. As a proper thermodynamic potential the Gibbs energy of a material system is introduced, relevant for systems under constant temperature and stresses. A central role plays the dissipation and the associated dissipation function. The dissipation is derived from the rate of the Gibbs energy. Correspondingly, a dissipation function is introduced, in terms of thermodynamic fluxes (fluxes of matter, of heat, etc.). Finally, the dissipation and the dissipation function are used to derive evolution equations for the internal variables by applying an extremum principle for irreversible processes. The Thermodynamic Extremal Principle (TEP) is demonstrated (related to prominent names such as Onsager, Prigogine, H. Ziegler et al.) yielding a variational formulation, which allows an explicit derivation of evolution equations for the internal variables. The according thermodynamic forces lead to the so-called configurational forces driving physico-chemical processes and defects. Applications to various fields of materials science are presented. For example, one can treat the development of the surface of a solid consisting of grains and interacting with the environment as grooving, together with its numerical realization. Systems characterized by distinct parameters, such as effective grain radii, as evolving quantities are dealt with, too. Particular emphasis is laid on phase transformations as diffusive transformations controlled by the interaction of chemical and mechanical processes. Martensitic (i.e. displacive) phase transformations are also investigated, based on the minimization of the mechanical energy contribution to the total energy of the system. Also the Phase Field Method (PFM) is outlined for multiphysics problems (chemistry, diffusion, electricity, magnetism, mechanics) with respect to its mathematical foundation and demonstrated for practical applications. A successful validation of the procedures, introduced for simulations, by numerical methods, applied in a wide field of actual problems, is a necessary condition for their practical usability. Therefore, also this topic will be dealt with in this course. Particularly, the implementation of the physical and mathematical framework into actual numerical codes shall be discussed in detail. Within this context also the concept of configurational forces is explained allowing an efficient numerical calculation of the driving forces on defects, such as cracks, dislocations and other objects. In conclusion, this course shall offer an overall view on the subject of thermodynamics of irreversible processes in materials starting from physical principles and proceeding via their mathematical formulations and numerical solutions on the way to their application.

F.D. Fischer, J. Svoboda, H. Petryk, Thermodynamic extremal principles for irreversible processes in Materials Science, Acta mater., 67, 1-20, 2014.

F.D. Fischer, K. Hackl, J. Svoboda, Improved thermodynamic treatment of vacancy-mediated diffusion and creep, Acta mater., 108, 347- 354, 2016.

K. Hackl, U. Hoppe, D. Kochmann, Variational modeling of microstructures in plasticity
In: J. Schröder, K. Hackl (Eds.): Plasticity and beyond: microstructures, crystal-plasticity and phase transitions, International Centre for Mechanical Sciences: Courses and lectures, 550, Springer, 65–129, 2014.

J. Besson, G. Cailletaud, J.-L. Chaboche, S. Forest, Non-Linear Mechanics of Materials. Solid Mechanics and its Applications. Springer Netherlands. ISBN: 9789048133567.

T. Waitz, T. Antretter, F.D. Fischer, N.K. Simha, H.- P. Karnthaler, Size Effects on the Martensitic Phase Transformation of NiTi Nanograins, J. Mech. Phys. Solids , 55, 419-444, 2007.

C. Kuhn, R. Müller, A discussion of fracture mechanisms in heterogeneous materials by means of configurational forces in a phase field fracture model. Comput. Methods Appl. Mech. Engng. 312, 95-116, 2016.

Thomas Antretter (Montanuniversität Leoben, Austria)

6 lectures on: Martensitic transformation, development of microstructures, kinetics based on thermodynamics, comparison with experiments and still existing solution concepts.

Franz Dieter Fischer (Montanuniversität Leoben, Austria)

5 lectures on: Introduction to thermodynamics of materials. Irreversible processes, thermodynamic potential, Gibbs energy, dissipation, dissipation function, extremal principles, configurational forces. Workshop with participants.

Klaus Hackl (Ruhr Universität Bochum, Germany)

6 lectures on: Formulation of variational concepts based on extremal principles, application to inelastic materials, application to the evolution of microstructures.

Ralf Müller (Technische Universität Kaiserslautern, Germany)

6 lectures on: Configurational Forces and Phase Field modelling, application to multiphysics problems in materials and to defects (as cracks, point defects, and dislocations), discussion in relation to evolution concepts.

Jiri Svoboda (Institute of Physics of Materials, Brno, Czech Republic)

6 lectures on: Thermodynamic Extremal Principle (TEP), application of TEP to diffusive and growth processes in continuous and in discrete form, discussion in relation to still existing evolution concepts.

The registration fee is 600.00 Euro + VAT*, where applicable (bank charges are not included). The registration fee includes a complimentary bag, four fixed menu buffet lunches (on Friday upon request), hot beverages, downloadable lecture notes and wi-fi internet access. Applicants must apply at least one month before the beginning of the course. Application forms should be sent on-line through the following web site: A message of confirmation will be sent to accepted participants. Applicants requiring assistance with the registration should contact the secretariat at the following email address Applicants may cancel their course registration and receive a full refund by notifying CISM Secretariat in writing (by email to no later than two weeks prior to the start of the course. Cancellation requests received during the two weeks prior to the start of the course will be charged a 50.00 Euro handling fee. Incorrect payments are also subject to a 50.00 Euro handling fee. A limited number of participants from universities and research centres who are not supported by their own institutions can be offered lodging and/or board, if available, in a reasonably priced hotel or student guest house. Requests should be sent to CISM Secretariat by July 10, 2018 along with the applicant's curriculum and a letter of recommendation by the head of the department or a supervisor confirming that the institute cannot provide funding. Preference will be given to applicants from countries that sponsor CISM. Information about travel and accommodation is available on the web site, or can be mailed upon request.

* Italian VAT is 22%.