Guanchu Cheng's picture

thermodynamics equilibrium state vs. steady state???

I am not clear about two concepts: thermodynamics equilibrium state and steady state. It's easy to conceive of the following different two osmosis processes regarding thermodynamics equilibrium state and steady state, respecitvely.

Zhigang Suo's picture

Freely jointed chain

A single strand of polymer is a chain of a large number of monomers.  The monomers are joined by covalent bonds, and two bonded monomers may rotate relative to each other.  At a finite temperature, the polymer rapidly changes from one configuration to another.  When the two ends of the polymer are pulled by a force, the distance between the two ends changes.  The polymer is known as an entropic spring.  These notes are developed as part of statistical thermodynamics to supplement the course on advanced elasticity

Mubeen's picture

Physical Foundations of Continuum Mechanics

After many publications and lecture notes, Prof. Ian Murdoch has finally organized much of that material in the form of a book.

I am very hopeful that like Prof. Murdoch's lectures, this monograph will also help the readers to develop a better understanding of the physical aspects of mechanics. It will be a valuable addition to the researchers' personal collection. 


more details in the flyer attached.


A new book: Introduction to Thermodynamics of Mechanical Fatigue

Michael M.
Khonsari; Mehdi
Amiri, CRC Press, Taylor & Francis Group, Boca Raton, FL. ISBN 9781466511798;jsessionid=u7oBhNWRWC...

Zhigang Suo's picture

Empirical observations of temperature

I have divided the old notes on temperature into three parts:

Our feeling of hotness comes from everyday experiences. These experiences indicate that many levels of hotness exist, and that all levels of hotness can be mapped to a real variable.

Zhigang Suo's picture

Principle of the conservation of energy

The world consists of moving parts: stars, planets, animals, electrons, protons, photons, etc. Their movements and interactions carry energy. Energy is a fundamental concept. We do not know how to define energy in terms of more fundamental concepts. We do know many ways to keep track of energy. For example, we know how to calculate the kinetic energy of a flying bullet, and the gravitational energy of a weight. We can measure the electrostatic energy in a capacitor, and the elastic energy in a spring. We can look up the values of energy in all kinds of food. We can find similar numbers for fuels—coal, oil, gas. Energy in foods and fuels are stored in chemical bonds.

Zhigang Suo's picture

Carnot Cycle

(Class notes for ES 181 Engineering Thermodynamics.  Also part of my notes on thermodynamics)  In 1824, Sadi Carnot (1796-1832) published a short book, Reflections on the Motive Power of Fire. (The book is now free online. You should try it out.) To construct an engine, Carnot noted, at least two reservoirs of energy of different temperatures are needed. He further noted that the engine loses efficiency whenever the working fluid of the engine exchanges energy with the rest of the world across a finite difference in temperature. To avoid such exchange of energy, he described a specific cycle—later known as the Carnot cycle—consisting of isothermal and adiabatic processes. Whenever the working fluid exchanges energy with either reservoir, the temperature of the working fluid is kept the same as that of the reservoir. Whenever the temperature of working fluid differs from the temperatures of the reservoirs, the working fluid is thermally insulated. He argued that this cycle is the most efficient of all cycles that convert heat to work by operating between two constant-temperature reservoirs of energy.

Andrew Bunger's picture

Postdoctoral Fellow - Geomechanical Modelling, Perth, Australia

CSIRO division of Earth Science and Resource Engineering is seeking a Postdoctoral Fellow to develop a coupled Thermo-Hydro-Chemo-Mechanical (THCM) reservoir model for application to Engineered Geothermal Systems. To read the position details and to apply please visit this link:


Zhigang Suo's picture

Temperature vs. chemical potential

For the third time I am teaching the graduate course on soft active materials.  This course is called Advanced Elasticity in the Catalog of Courses.  In the last several years, I have dropped several traditional topics, and focused on thermodynamics and finite deformation.  I have added several topics where both thermodynamics and finite deformation play significant roles, such as elastomeric gels and dielectric elastomers.

Libb Thims's picture

How to teach thermodynamics

This blog will give some wisdom guidance on how to teach thermodynamics, particularly in the opening weeks, to undergraduate engineering students. This blog started as a response post to nanomechanics engineer Zhigang Suo's 19 Dec 2010 request for suggestive advice on which textbook to use and how to teach thermodynamics, as he is apprehensive about teaching his first thermodynamics class (Engineering Science 181 Engineering Thermodynamics, Harvard). In any event, to give some quick advice on how to teach thermodynamics:

Zhigang Suo's picture

Teaching Engineering Thermodynamics to Undergraduate Students

I have just volunteered to teach engineering thermodynamics to undergraduates in the Fall semester of 2011.  The students will be from all fields of engineering, primarily mechanical engineering, environmental engineering, and bioengineering.  I have never taught this course before, and would love to hear from you about your experience, either as a student or as a teacher. 

Here is what I have found from the website about the course.

Engineering Science 181 Engineering Thermodynamics

Introduction to engineering thermodynamics with emphasis on classical thermodynamics. Topics:

Amit Acharya's picture

Microcanonical Entropy and Mesoscale Dislocation Mechanics and Plasticity

(Journal of Elasticity, Carlson memorial Volume)

A methodology is devised to utilize the statistical mechanical entropy of an isolated, constrained atomistic system to define the dissipative driving-force and energetic fields in continuum thermomechanics. A thermodynamic model of dislocation mechanics is discussed. One outcome is a definition for the mesoscale back-stress tensor and the symmetric, polar dislocation density-dependent, Cauchy stress tensor from atomistic ingredients.

Hanqing Jiang's picture

A Thermodynamic Model of Physical Gels

Physical gels are characterized by dynamic cross-linksthat are constantly created and broken, changing its state between solid andliquid under influence of environmental factors.

How is the entropy of polarization in dielectric material

In the study of thermoelastic actuation of dielectric elastomer, we can write the Helmholtz free-energy as a function of stretch ratio, nominal electric displacement and temperature (T).

The entropy (S) is the negative partial differential coefficient of W with respect of temperature (T). And we can see the change of S is due to three components: deformation, heat conduction and polarization. In an isothermal state, the deformation part has been fully investigated by Arruda and Boyce in 1993, but the polarization-induced entropy (Sp) has not been clearly stated.

Eran Bouchbinder's picture

Nonequilibrium Thermodynamics in Solid Mechanics

Solids that are driven beyond their elastic limit exhibit strongly disspative and irreversible dynamical behaviors. Such behaviors call for the development of nonequilibrium approaches that go beyond standard equilibrium thermodynamics. In a recent work we have developed an internal-variable, effective-temperature non-equilibrium thermodynamics for glass-forming and polycrystalline materials driven away from thermodynamic equilibrium by external forces [1, 2]. The basic idea is that the slow configurational (structural) degrees of freedom of such materials are weakly coupled to the fast kinetic-vibrational degrees of freedom and therefore these two subsystems can be described by different temperatures during deformation. The configurational subsystem is defined by the mechanically stable positions of the constituent atoms, i.e. the "inherent structures", and is characterized by an effective temperature. The kinetic-vibrational subsystem is defined by the momenta and the displacements of the atoms at small distances away from their stable positions, and is characterized by the bath temperature.

Ajit R. Jadhav's picture

Food for Thought: A Few Recent arXiv Papers

Since my research touches on the basics of QM, I have developed this habit of visiting every now and then. Last week or so, at, I found a couple of interesting articles on physics in general. I would like to share these with you.

Adrien Haxaire's picture

Looking for a Post-Doc position in Geomechanics, in Europe

Dear all,

My name is Adrien Haxaire. I am currently Associate Professor at LGCIE, INSA Lyon, France, until end of August. I am looking for a
Post-Doc position in geomechanics in Europe.

During my PhD, I developped a thermodynamical model capable of describing coupled THMC phenomena in unsaturated porous media. It was implemented in Cast3M. 

I am very interested in chemical reactions in porous media, their modelling and implementation. I am also interested in the field of CO2 sequestration.

You will find more informations on my CV, and please do not hesitate to contact me, I will be glad to answer you.



Srinivasan Sivakumar's picture


Series on Advances in Mathematics for Applied Sciences - Vol. 80

INELASTICITY OF MATERIALS- An Engineering Approach and a Practical Guide


Arun R Srinivasa (Texas A&M University, USA) &

Sivakumar M Srinivasan (Indian Institute of Technology, Madras, India)

With the advent of a host of new materials ranging from shape memory alloys to biomaterials to multiphase alloys, acquiring the capacity to model inelastic behavior and to choose the right model in a commercial analysis software has become a pressing need for practicing engineers. Even with the traditional materials, there is a continued emphasis on optimizing and extending their full range of capability in the applications. This textbook builds upon the existing knowledge of elasticity and thermodynamics, and allows the reader to gain confidence in extending one's skills in understanding and analyzing problems in inelasticity. By reading this textbook and working through the assigned exercises, the reader will gain a level of comfort and competence in developing and using inelasticity models. Thus, the book serves as a valuable book for practicing engineers and senior-level undergraduate/graduate-level students in the mechanical, civil, aeronautical, metallurgical and other disciplines.

Robert C. Cammarata's picture

New papers on thermodynamics and mechanics of surfaces

Please allow me to note that I have recently published in Philosophical Magazine a paper that presents a general approach to Gibbsian surface thermodynamics that includes a treatment of solid surfaces.  It can be accessed through the following link:

If you send me your e-mail address I can send you a pdf of the "author's copy" (I cannot post it owing to copyright issues).  If interested, I can also send a pdf of an "author's copy" of a more comprehensive article that is to appear in Solid State Physics.


WaiChing Sun's picture

potential functional for material exhibts non-associative elastoplastic response

Does anyone knows where I can find any paper discuss the existence of potential functinoal for materials that violate the maximum plastic dissipation principle (due to non-convex yield function and/or non-associately fluw rule)?

Zhigang Suo's picture

Learning temperature, pressure, and chemical potential

I have updated sections of my notes on thermodynamics.  A few thoughts on learning are collected here.  Of our world the following facts are known:

  • An isolated system has a set of quantum states, or microstates, for want of a single word.
  • The isolated system flips rapidly and ceaselessly from one microstate to another.
  • After a system is isolated for a long time, all microstates of the system are equally probable (the fundamental postulate).

For an account of these facts, see notes on Isolated Systems (

Robert G. Parker's picture

Lecturer Positions in Mechanics/Materials at Univ of Mich-Shanghai Jiao Tong Univ Joint Institute

Lecturers - University of Michigan-Shanghai Jiao Tong University Joint Institute

The University of Michigan (UM) and Shanghai Jiao Tong University (SJTU) have established a Joint Institute (JI) in Shanghai with a commitment to build a world-class academic institution with educational and research missions. The UM-SJTU Joint Institute invites applications for lecturers in several disciplines. With its unique academic mission in China, the JI offers an extraordinary academic environment. The JI has been given a high degree of autonomy to model itself on world-class US universities. The students are among China’s best.

Zhigang Suo's picture

Free Energy

For a system in thermal contact with the rest of the world, we have described three quantities: entropy, energy, and temperature. We have also described the idea of a constraint internal to the system, and associated this constraint to an internal variable.

The system can be isolated at a particular value of energy. For such an isolated system, of all values of the internal variable, the most probable value maximizes entropy. We will paraphrase this statement under two different conditions, either when the entropy is fixed, or when the temperature is fixed. Under these conditions, the system is no longer isolated. Consequently, we need to maximize or minimize quantities other than entropy.

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