Type of Publication:  Journal article 
Publication status:  Published 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:3522uppco4q63oyg6 
Author:  Haussmann, Rudolf 
Year of publication:  2022 
Published in:  Journal of Statistical Mechanics: Theory and Experiment ; 5 (2022).  053210.  Institute of Physics Publishing (IOP).  eISSN 17425468 
DOI (citable link):  https://dx.doi.org/10.1088/17425468/ac6d61 
Summary: 
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuummechanics equations of nonlinear elasticity theory with fluctuations which describe the macroscopic phenomena of a solid crystal. As the relevant variables we specify the coarsegrained densities of the conserved quantities and a properly defined displacement field which describes the local translations, rotations, and deformations. In order to stay within the framework of the conventional densityfunctional theory we first and mainly consider the isothermal case and omit the effects of heat transport and warming by friction where later we extend our theory to the general case and include these effects. We proceed in two steps. First, we apply the concept of local thermodynamic equilibrium and minimize the free energy functional under the constraints that the macroscopic relevant variables are fixed. As results we obtain the local free energy density and we derive explicit formulas for the elastic constants which are exact within the framework of densityfunctional theory. Second, we apply the methods of nonequilibrium statistical mechanics with projectionoperator techniques. We extend the projection operators in order to include the effects of coarsegraining and the displacement field. As a result we obtain the timeevolution equations for the relevant variables with three kinds of terms on the righthand sides: reversible, dissipative, and fluctuating terms. We find explicit formulas for the transport coefficients which are exact in the limit of continuum mechanics if the projection operators are properly defined. By construction the theory allows the diffusion of particles in terms of point defects where, however, in a normal crystal this diffusion is suppressed.

Subject (DDC):  530 Physics 
Keywords:  elasticity, fluctuating hydrodynamics, dynamical processes, transport properties 
Link to License:  In Copyright 
Bibliography of Konstanz:  Yes 
Refereed:  Yes 
HAUSSMANN, Rudolf, 2022. Microscopic densityfunctional approach to nonlinear elasticity theory. In: Journal of Statistical Mechanics: Theory and Experiment. Institute of Physics Publishing (IOP). 5, 053210. eISSN 17425468. Available under: doi: 10.1088/17425468/ac6d61
@article{Haussmann2022Micro57763, title={Microscopic densityfunctional approach to nonlinear elasticity theory}, year={2022}, doi={10.1088/17425468/ac6d61}, volume={5}, journal={Journal of Statistical Mechanics: Theory and Experiment}, author={Haussmann, Rudolf}, note={Article Number: 053210} }
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