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https://www.nist.gov/itl/math/acmd-seminar-entropy-inequality-and-ordered-rate-constitutive-theories-homogeneous

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# ACMD Seminar: On Entropy Inequality and Ordered Rate Constitutive Theories for Homogeneous, Isotropic, and Compressible matter under finite deformation with thermal effects

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Daniel Nunez*LPI, Inc.*

Tuesday, Dec 3, 2019, 3:00–4:00 PM	Building 101, West Square	Gaithersburg

Tuesday, Dec 3, 2019, 1:00–2:00 PM	Building 1, Room 4072	Boulder

This talk will be broadcast on-line using BlueJeans.  Contact acmdseminar [at] nist.gov (acmdseminar[at]nist[dot]gov) for details.

**Host:** Jeffrey Fong

**Abstract:**  The purpose of this talk is to demonstrate that commonly used constitutive equations are subsets of newly-developed rate constitutive theories, thus showing limitations in the range of applications of many well-known equations such as those of elasticity, viscoelasticity in solids and fluids, and viscous fluids.

It is well-known that continuity equation, momentum equations and energy equation hold regardless of the constitution of the matter, and provide, of course, no mechanism to derive constitutive equations. However, entropy inequality does provide a set of conditions that can be used on the onset of their derivations.  Historically, the development of constitutive equations began with empirical relations based on experimental evidence without considering entropy inequality. Even though there seems to be a lack of a systematic approach, there are physical principles and axioms that can be used to obtain a methodical framework. In this talk, we address such framework and present the development of "Ordered Rate Constitutive Theories" for homogeneous, isotropic, compressible matter under finite deformation with thermal effects.

The choices of dependent variables (stress [σ] , heat vector {*q*} , entropy density η  etc) are made using entropy inequality. The material presented here will focus on the constitutive theories for [σ]  and {*q*} . The choice of their arguments is dictated strictly by the physics we wish to consider: temperature *T*  is obvious for thermal expansion; temperature gradients {*g*}  is needed for heat transfer etc. Based on the *principle of equipresence*, all dependent variables must contain the same arguments, but conditions resulting from entropy inequality also provide restrictions on the chosen arguments.  The consideration of the complete set of basis is referred to as the *principle of integrity*. It is shown that commonly used constitutive equations are subsets of these constitutive theories with complete set of basis, i.e. simplifications of these more complete constitutive equations are made by neglecting terms to obtain commonly used constitutive equations.

We will illustrate with examples some simple ordered rate constitutive theories that include viscous (fluids and solids), thermoelastic (solids), relaxation (solids), and viscoelastic (fluids) effects.  If time permits, we will also consider [ε] as arguments of {*q*} , leading to a more complex theory than the classical Fourier heat conduction law**.**

**Bio:**Dr. Nunez was born in Asuncion, Paraguay, and educated at the University of Kansas, Lawrence, KS, with B.S. (Aerospace Eng., 2003), M.S. (Aerospace Eng., 2008), and Ph.D. (Mech. Eng., 2012).  Dr. Nunez worked as a Post-doctoral Researcher in Mechanical Engineering at the University of Kansas for two years (2013 and 2014), and has been a Lead Engineer in LPI, Inc. Consulting Engineering, Richland, WA, since April 2015.  He has published numerous papers in Computational Mechanics (on subtopics such as thermal shock, finite element analysis of flaws, fatigue damage modeling, simulation error measures, etc.), and continuum mechanics (new rate constitutive theories for thermofluids, thermoelastic and thermoviscoelastic matter in Lagrangian and Eulerian descriptions, etc.).

**Note:** Visitors from outside NIST must contact Cathy Graham; (301) 975-3800; at least 24 hours in advance.

Mathematics and statistics

## Contacts

                -  Jeffrey T. Fong  jeffrey.fong@nist.gov      (301) 219-9333   
                -  Stephen Langer  stephen.langer@nist.gov      (301) 975-5423   

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