Journal of Elasticity

, Volume 135, Issue 1–2, pp 91–115 | Cite as

Interactions in a Multi-scale Representation of Sparse Media: From Mechanics to Thermodynamics

  • Gianfranco Capriz
  • Paolo Maria MarianoEmail author


We develop further a discrete-to-continuum approach to sparse media for which we do not grant the common axiom of permanent identification of the material elements. After refining our previous work on this topic, we focus our attention on the identification of stresses and self-actions at continuum scale in terms of the molecular interactions. Moreover, we introduce and discuss a notion of tensorial temperature by considering a grand canonical statistical ensemble constituted by molecules freely flowing in and out a control volume.


Continuum thermodynamics Multi-scale models Invariance Kinetic theory Granular matter Discrete-to-continuum schemes 

Mathematics Subject Classification

05C38 15A15 05A15 15A18 



This work has been developed within the programs of the research group in ‘Theoretical Mechanics’ of the “Centro di Ricerca Matematica Ennio De Giorgi” of the Scuola Normale Superiore in Pisa. The support of GNFM-INDAM is acknowledged.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica, Università di PisaAccademia dei LinceiRomeItaly
  2. 2.DICeAUniversità di FirenzeFirenzeItaly

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